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BOOK 5 FIXED INCOME , DERIVATIVES, AND ALTERNATIVE INVESTMENTS -

Reading Assignments and Learning Outcome Statements Study Session 15 - Fixed Income: Basic Concepts

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Study Session 16- Fixed Income: Analysis and Valuation

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Study Session 18- Alternative Investments

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278

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314

Self-Test - Derivatives and Alternative Investments Formulas Index

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Self-Test - Fixed Income Investments Study Session 17- Derivatives

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SCHWESERNOTES™ 2013 CPA LEVEL I BOOK 5: FIXED INCOME, DERIVATIVES, AND ALTERNATIVE INVESTMENTS ©20 12 Kaplan, Inc. All rights reserved. Published in 2012 by Kaplan Schweser. Printed in the United States of America. ISBN: 978-1-4277-4265-0 1-4277-4265-0 PPN: 3200-2848 I

If this book does not have the hologram with the Kaplan Schweser logo on the back cover, it was distributed without permission of Kaplan Schweser, a Division of Kaplan, Inc., and is in direct violation of global copyright laws. Your assistance in pursuing potential violators of this law is greatly appreciated.

Required CFA Institute disclaimer: "CFA® and Chartered Financial Analyst® are trademarks owned by CFA Institute. CFA Institute (formerly the Association for Investment Management and Research) does not endorse, promote, review, or warrant the accuracy of the products or services offered by Kaplan Schweser." Certain materials contained within this text are the copyrighted property of CFA Institute. The following is the copyright disclosure for these materials: "Copyright, 2012, CFA Institute. Reproduced and republished from 2013 Learning Outcome Statements, Level I, II, and III questions from CFA® Program Materials, CFA Institute Standards of Professional Conduct, and CFA Institute's Global Investment Performance Standards with permission from CFA Institute. All Rights Reserved." These materials may not be copied without written permission from the author. The unauthorized duplication of these notes is a violation of global copyright laws and the CFA Institute Code of Ethics. Your assistance in pursuing potential violators of this law is greatly appreciated. Disclaimer: The SchweserNotes should be used in conjunction with the original readings as set forth by CFA Institute in their 2013 CFA Level I Study Guide. The information contained in these Notes covers

topics contained in the readings referenced by CFA Institute and is believed to be accurate. However, their accuracy cannot be guaranteed nor is any warranty conveyed as to your ultimate exam success. The authors of the referenced readings have not endorsed or sponsored these Notes.

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©2012 Kaplan, Inc.


READING ASSIGNMENTS AND L EARNING OUTCOME STATEMENTS

The following material is a review ofthe Fixed Income, Derivatives, andAlternative Investments principles designed to address the learning outcome statements setforth by CPA Institute. STUDY SESSION 15

Reading Assignments CFA Program 2013 Curriculum, Volume 5 (CFA Institute, 2012)52. Features of Debt Securities page 11 53.54. Risks Associated with Investi n g in Bonds page 25 page ew ofnBond page 4669 55. Overvi Understandi g YielSectors d Spreadsand Instruments Equity and Fixed Income,

STUDY SESSION 16

Reading Assignments CFA Program 2013 Curriculum, Volume 5 (CFA Institute, 2012)56. Introduction to the Valuation of Debt Securities page 87 page 101 57.58. Yield Measures,to theSpotMeasurement Rates, and Forward RatesRate Risk Introduction of Interest page 134 page 157 59. Fundamentals of Credit Analysis Equity and Fixed Income,

STUDY SESSION 17

Reading Assignments CFA Program 2013 Curriculum, Volume 6 (CFA60.Institute, 2012) page Deri v ati v e Markets and Instruments 191 page 213 61.62. Forward MarketsandandContracts Contracts 197 page Futures Markets page 226 63.64. Swap OptioMarkets n MarketsandandContracts Contracts page 254 page 268 65. Risk Management Applications of Option Strategies

Derivatives and Alternative Investments,

STUDY SESSION 18

Reading Assignments CFA Program 2013 Curriculum, Volume 6 (CFA66.Institute, 2012) Introductionin Commodities to Alternative Investments page 278 67. Investing page 303

Derivatives and Alternative Investments,

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Book 5 - Fixed Income, Derivatives, and Alternative Investments Reading Assignments and Learning Outcome Statements

LEARNING OUTCOME STATEMENTS (LOS )

The CPA Institute Learning Outcome Statements are listed below. These are repeated in each topic review; however, the order may have been changed in order to get a betterfit with the flow ofthe review. STUDY SESSION 15

The topical coverage corresponds with the following CPA Institute assigned reading:

ofdate should be able to: The candi a. expl a i n the purposes of a bond' s i n denture and describe affi r mati v e and negati v e covenants.the(page 11)features of a bond, the various coupon rate structures, and the b. describe basic structure of floating-rate securities. (pageclean12)price. (page 14) n e accrued i n terest, ful l price, and c.d. defi ain thecommon provisions for redemption anda bond retirement of bonds.the(page 14) e. expl identify options embedded in issue, explain importance ofbondholder. embedded(page options,16) and identify whether an option benefits the issuer or the describe methods used by (i.institutional investors in repurchase the bond market to finance the purchase of a security e . , margi n buyi n g and agreements). (page 17)

52. Features

Debt Securities

f.

The topical coverage corresponds with the following CPA Institute assigned reading:

53. Risks Associated with Investing in Bonds

The candidate should be able to:with investing in bonds. (page 25) a i n the ri s ks associated a.b. expl identify the rel a tions among a bond' s coupon rate, the yield required by the market, and the(pagebond'27)s price relative to par value (i.e., discount, premium, or equal to par). ain howratea bond maturity, coupon, embedded options and yield level affect c. iexpl t s interest risk. (page 27) d. bond identifyandthetherelprice ationofofthetheembedded price of a callable bond(page to the29)price of an option-free call option. a i n the interest rate risk of a fl o ati n g-rate security and why its price may e. expl dicalculate ffer fromandparinterpret value. (page 29) and dollar duration of a bond. (page 30) the duration describrisk. e yiel(page d-curve32)risk and explain why duration does not account for yield­ g. curve ain34)the disadvantages of a callable or prepayable security to an investor. h. expl (page identify the factors that affect the reinvestment risk of a security and explain why prepayable amortizingsecurities. securities(page expose34)investors to greater reinvestment risk than nonamortizing types of risk creditandriskwhyanditthemightmeaning and roletoofinvestors credit ratings. (page 35) k. describe expl a i n liquidity be important even if they expect to hold a security to the maturity date. (page 36) f.

1.

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Book 5 Fixed Income, Derivatives, and Alternative Investments Reading Assignments and Learning Outcome Statements -

describe thecurrency. exchange(pagerate37)risk an investor faces when a bond makes payments in a forei g n explaaiinn how inflatiyield on risk.volatil(pageity affects 37) the price of a bond with an embedded option m.n. expl and how(pagechanges in volatility affect the value of a callable bond and a purable bond. 37) o. describe sovereign risk and types of event risk. (page 38) Overview of Bond Sectors and Instruments The candidatefeatures, shouldcredit be ableriskto:characteristics, and distribution methods for describe a. government securities. (page 46) b. describe typesbonds, of securities issued byprotection the U.S. Department of thedistinguish Treasury (e.between g., bills,theon-the-run notes, and infl a tion securities), and andTreasury off-the-run Treasury securities.and(page 47) between describe strihowps stripped securities are created di s tinguish c. coupon and and principal strips. c(page 49) issued by U.S. federal agencies. d. describe the types characteristi s of securities (page 49) theowtypes and characteristi cfors ofeachmortgage-backed securities and explain e. describe the cash fl and prepayment risk type. (page 50) expl ain52)the motivation for creating a collateralized mortgage obligation. (page thebetween types oftax-backed securities issued by municipalities in(page the United States and g. describe distinguish debt and revenue bonds. 53) the characteristi c s and moti v ation for the various types of debt issued h. bydescribe corporations (inclpaper, udingnegotiable corporateCDs, bonds,andmedium-term notes, structured notes, commercial bankers acceptances). (page e55) defi n e an asset-backed security, describe the rol e of a special purpose vehicl in issue an asset-backed security'security, s transaction, state thethe types motivatiofoexternal n for a corporation toenhancements an asset-backed and describe credit for asset-backed securities. (page 59) describe col l aterali z ed debt obligations. (page 60) mechanithesmsprimary availableandforsecondary placing bonds market61)and k. describe distinguishthebetween marketsin theforprimary bonds. (page Understanding Yield Spreads The candi d ate should berateablepolicy to: tools available to a central bank. (page 69) identify thea yieldinterest a.b. describe curve andofthethevarious shapes ofoftheinyield curve. (pagedescribe 70) the a i n the basic theories term structure terest rates and c. expl implications of each theory for the shape of the yi e l d curve. (page 71) ne a spot rate. (pageyield 73) spread measures. (page 74) e.d. defi calculate and compare describe credi(page t spreads and relationships between credit spreads and economic conditions. 75) describe howliembedded options affectaffects yieldthespreads. (page 76)of a bond relative to h.g. expl a i n how q uidity and issue-size yield spread other similar securities. (page 76) I.

54.

The topical coverage corresponds with the following CFA Institute assigned reading:

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55.

The topical coverage corresponds with the following CFA Institute assigned reading:

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Book 5 Fixed Income, Derivatives, and Alternative Investments Reading Assignments and Learning Outcome Statements -

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calculate thesecurity. after-tax(page yield77)of a taxable security and the tax-equivalent yield of a tax-exempt defi n e and explain its importance to funded investors who borrow short term. (page 78) LIBOR

STUDY SESSION 16

The topical coverage corresponds with the following CFA Institute assigned reading:

56. The candidate should be able to: aibnesteps inofthebonds bondforvalwhiuation process. (page 87) cash flows is difficult. descri types c h estimating the expected b.a. expl (page 87) c.d. calculate the thevaluepriceof aofbond (coupon andifzero-coupon). (pagechanges 88) and as the expl a i n how a bond changes the discount rate bond its maturi tyofdate.a bond(pagegiven 91) a change in its discount rate. calculateapproaches the change i n value e. (page 92)and demonstrate the use of the arbitrage-free valuation approach and expl a i n descri b e how a dealer can generate an arbitrage profi t i f a bond i s mispriced. (page 94) 57. The candidate should be able to: describe theandsources of traditional return fromyield investimeasures ng in a forbond.fixed-rate (page 10bonds 1) and b.a. expl calculate interpret aiinn thei rreilimitations and assumptions. (pagein calculating 101) yield to maturity c. expl a the n vestment assumption implicit describeandtheinterpret factorsthethatbond affectequivalent reinvestment risk. (page 1 08) bond and the d. and calculate yield of an annual-pay annual-paytheyield of a semiannual-pay bond.Treasury (page 110) e. the describe cal c ulation of the theoretical spot rate curve and calculate val u e of a bond using spot rates. (page 111) f. expl ain these nominal, zero-vol aoption tility, and option-adjusted spreads and the relations among spreads and cost. (page 115) a i n a forward rate and cal c ul a te spot rates from forward rates, forward rates g. expl from spot rates, and the value of a bond using forward rates. (page 118) 58. The candidate should be able to: ntheguishduration/convexi between the fullty approach valuationforapproach (theinterest scenariorateanalysis approach) a. disti and measuring risk, and expl ibnethetheadvantage of usingcharacteri the fulslticsvaluation approach.callable, (page 134)prepayable, b. and descriaputable price volatility for option-free, bondsconvexi whentinterest ratesvchange. (page 136)their relation to bond describeandpositive y and negati e convexi t y, and c. price yield. (page 136) Introduction to the Valuation of Debt Securities

f.

The topical coverage corresponds with thefollowing CFA Institute assigned reading:

Yield Measures, Spot Rates, and Forward Rates

The topical coverage corresponds with the following CFA Institute assigned reading: Introduction to the Measurement of Interest Rate Risk

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Book 5 Fixed Income, Derivatives, and Alternative Investments Reading Assignments and Learning Outcome Statements -

d. e. f. g. h.

calculate and interpret thel increase effectiveandduration offora bond, gichanges ven information about how the bond' s price wil decrease gi v en i n interest rates. (page 139) calculate durati the approximate percentage priceinchange for a bond, given the bond's effective o n and a specifi e d change yield. (page 141) distinguish among the alternati v e defi n itions of duration and explain why effective durationoptions. is the most appropriate measure of interest rate risk for bonds with embedded (page 142) calculate the duration of atheportfolio, givenoftheportfolio durationduration. of the bonds comprising the portfolio, and explain limitations (page 144) describe the convexity measure of a bondandandconvexi estimatety and a bond' s percentage price change, given the bond' s duration a speci fied change in (page 145) idistinguish nterest rates.between modifi eadbasis convexi tyt and effective convexi titsy. relationship (page 147) to calculate the price val u e of poi n (PVBP), and explai n (pageimpact 147)of yield volatility on the interest rate risk of a bond. k. duration. describe the (page 148) 1.

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The topical coverage corresponds with the following CFA Institute assigned reading:

59. Fundamentals of Credit Analysis

The candidatecredishould beandablcredi e to:t-related risks affecting corporate bonds. (page 157) a.b. describe t ri s k descri b e seniority ranki n gs of corporate debt and expl a i n the potential violation of the prioritybetween of claimscorporate in a bankruptcy proceeding. (page 158) issuer credit rati n gs and issue credit ratings and c. distinguish descri b e the rati n g agency practice of "notching". (page 159) explaaiinn theriskscomponents in relying onofratitraditional ngs fromcredit creditanalysis. rating agencies. (page 160) d.e. expl (page 161) calculate and interpret fi n ancial ratios used in credi t analysis. (page 163) evaluatekeythefincredit quali tsyforofthea corporate bondthe issuer and(page a bond167)of that issuer, g. given anci a l rati o issuer and industry. factors thatimpact influenceof spread the levelchanges. and vol(page atility169) of yield spreads. (page 169) h. describe calculate the return explain special consideratidebt ons when credi172) t of high yield, sovereign, and municipal issuersevalanduating issues.the(page f.

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STUDY SESSION 17

The topical coverage corresponds with the following CFA Institute assigned reading:

60. The candidate should be able to: ne a derivatives. derivative and(pagedistinguish between exchange-traded and over-the颅 a. defi counter 191) contrast forwardcontracts, commitments andcontracts, contingentoptions claims.(calls(pageand191) c.b. defi n e forward futures puts), and swaps and compare their basi c characteristics. (page 192) purposes of and controversies related to deri v ati v e markets. (page 192) d.e. describe explain arbitrage and(pagethe 193) role it plays in determining prices and promoting market efficiency. Derivative Markets and Instruments

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Book 5 Fixed Income, Derivatives, and Alternative Investments Reading Assignments and Learning Outcome Statements -

The topical coverage corresponds with the following CPA Institute assigned reading:

61. The candidate should andbeContracts abl e to: ain delcontract. ivery/settl(page ement197)and default risk for both long and short positions in a. aexplforward bation e the procedures for settling aaffect forwardcredicontract at expiration, and how b. descri termi n prior to expiration can t ri s k. (page 198) nguish between a dealer andequityan end user contracts of a forwardandcontract. (page 199)on d.c. disti descri b e the characteristi c s of forward forward contracts zero-coupon and coupon bonds. (page 200) beandthe Euribor. characteristics of202)the Eurodollar time deposit market, and define e. descri LIBOR (page forward rate agreements (FRAs) and cal c ul a te the gain/loss on a FRA. f. describe (page 203)and interpret the payoff of a FRA and explain each of the component g. terms calculate payoff formula. 203)forward contracts. (page 205) cs of(page currency h. describeof thethe characteristi 62. The candidate should and Contracts be ablecsto:of futures contracts. (page 213) the characteristi a.b. describe compare contracts andin forward contracts. (pageand213)margin in the futures c. markets, disti nguishfutures between margin the securities markets andsettlement explain theinrolefutures of initrading. tial margin, maintenance margin, variation margin, and (page 214) d. descri b e price limits and the process of marki n g to market, and cal c ul a te and ithenterpret theprice. margi(page n balance, given the previous day's balance and the change in futures 216) how a futures contract can be terminated at or prior to expiration. e. describe (page 218) describe thebill,characteristi s of the folbond, lowinstock g typesindex, of futures contracts.(page 219) f. Treasury Eurodollar,cTreasury and currency. Forward Markets

The topical coverage corresponds with the following CPA Institute assigned reading:

Futures Markets

The topical coverage corresponds with thefollowing CPA Institute assigned reading:

63. The Optioncandidate should and Contracts be abloptions. e to: (page 226) call and put a.b. describe distinguitheshconcept betweenofEuropean andofAmerican options. (page 227) moneyness an option. (page 228) c.d. define compare exchange-traded options and over-the-counter options. (page 229) theinterest typesrateof options inwithtermsforward of therateunderlying instruments. (page230) 229) e. identify compare options agreements (FRAs). (page interest rate caps,option floors,payoffs and collars. (pageain231) calculate and interpret and expl how i n terest rate options h.g. define differnefrom othervalue typesandof time options.value,(pageand233) defi intrinsic explainof their relationship. (page 234) determine the minimum and maximum values European options and canandoptions. (pagethe237)lowest prices of European and American calls and k. Ameri calculate interpret puts based on the rules for minimum values and lower bounds. (page 238) Markets

f.

1.

j.

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Book 5 Fixed Income, Derivatives, and Alternative Investments Reading Assignments and Learning Outcome Statements -

expl ain how(page option242)prices are affected by the exercise price and the time to expiration. m. explain put-call parity for European options, and explain how put-cal l parity is atedain tohowarbicashtragefloandws onthetheconstruction ofassetsynthetic options.l pari (pagety 243) n. relexpl underlying affect put-cal and the lower bounds of option prices. (page 245) o. determine an option'stheprice.directional (page 246)effect ofan interest rate change or volatility change on

I.

The topical coverage corresponds with the following CFA Institute assigned reading:

64. The candidate should be able to: a. describe the characteristi c s of swap contracts and expl a i n how swaps are terminated.calculate, (page 255) nterpretswaps. the payments b. describe, interest rate swaps, and and iequity (page 256)of currency swaps, plain vanilla 65. The candidate should be able to: determine underl the valyuinge atprice expiration, the profit,andmaximum profioft,themaxistrategi mum eloss, a. breakeven at expiration, payoff graph sfor ofinvestors buyingusing and selthese ling strategi calls andes. puts and determine the potential outcomes (page 268) b. breakeven determine underl the valyuinge atprice expiratatiexpiration, on, profit, maximum profi t, maximum loss, and payoff graph of a covered calapplication l strategyofandeacha protective put strategy, and explain the ri s k management strategy. (page 272) Swap Markets and Contracts

The topical coverage corresponds with the following CFA Institute assigned reading:

Risk Management Applications of Option Strategies

STUDY SESSION 18

The topical coverage corresponds with the following CFA Institute assigned reading:

66. The candidate should be able to: compare categories alternativeofinalvestments wiinvestments. th traditional(pageinvestments. (page 278) b.c.a. describe t ernati v e 278) describe potential benefits of alternative investments in the context of portfolio management. (page 279) hedge funds, private equity,asrealapplicable, estate, commodities, and other d. describe alternati v e i n vestments, incl u ding, strategies, sub-categories, potential benefi t s and ri s ks, fee structures, and due diligence. (page 280) e. describe issuesestate,in valuing, and calculating returns on, hedge funds, private equity, real and commodities. (page 280) descri b e, calculate, and i n terpret management and i n centi v e fees and net-of-fees funds. (pageof alternati 292) ve investments. (page 294) describetoriskhedge management g. returns Introduction to Alternative Investments

f.

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Book 5 Fixed Income, Derivatives, and Alternative Investments Reading Assignments and Learning Outcome Statements -

The topical coverage corresponds with the following CPA Institute assigned reading:

67. The Investing inateCommodities candi d should be able to: ain the relationship between (page spot prices and expected future prices in terms a. ofexplcontango and backwardation. 303) bone thea portfolio sources ofof return andan allocation risk for a commodity investment and the b. descri effect adding to commodities. (page 304) ain why (page a commodity c. expl investment. 305) index strategy is generally considered an active

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The following is a review of the Analysis of Fixed Income Investments principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in:

FEATURES OF DEBT SECURITIES Study Session 15

EXAM FOCUS

xeda giincome securities,of years historical lythen , wererepay promises tooanpayamount a streamat ofthesemiannual payments forFicontract vbetween en number and the l maturi t y date. The the borrower andthatthethelender (the indenture) canofrealcontracts ly be desithat gnedareto have any payment stream or pattern parti e s agree to. Types frequently have specific names, and there is no shortage of those (for you to learn) here.used You specialof these) attention to how/when how the periodic payments ared (calls, determined (fixed,ng flfunds, oatishould ng,amortization, andpayvariants and to the principal is repai puts, sinki andwhen prepayments). These features all affectsecurities the valueandofcompare the securities and will come up again you learn how to value these their risks, both at Level I and Level II. LOS 52.a: Explain the purposes of a bond's indenture and describe affirmative and negative covenants. CFAÂŽ Program Curriculum, Volume 5, page 294

The contract that specifiis called es all thethe rights and obligations of the issuerdefiandnes thetheowners of a fixed income security The indenture obligations of and restrictions on theandborrower and These forms thecontract basis provisions for all futurearetransactions between the bondholder the issuer. known as and include(actions both that the borrower (prohibitions on the borrower) and promises to perform) sections. include restrictionsnegative on assetplesales (thecollateral company(thecan'company t sell assetscan't that have been pledged as collateral), dge of claimadditional that theborrowings same assets (the backcompany several debtcan'issues simultaneously), and unless restrictions onfinancial t borrow additional money certain conditions are met). include the For maintenance ofthecertain financial ratios andtothemaintain timely payment of principal and interest. example, borrower mi g ht promise theis notcompany' s current ratio at a value of two or higher. If thi s val u e of the current ratio maintained, then the bonds could be considered to be in (technical) default. bond indenture.

covenants affirmative

negative covenants

covenants

Negative covenants

Affirmative covenants

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Page 1 1


Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #52

-

Features of Debt Securities

LOS 52.b: Describe the basic features of a bond, the various coupon rate structures, and the structure of floating-rate securities. CPA® Program Curriculum, Volume 5, page 295

A6% (option-free) bond iyears s the from simplesttodaycase.in Consider a Treasury bondThisthatbondhas ias a and fi v e the amount of $1,000. promise . Treasury) of thefrom$1,0today. 00 (i.e., $60) each yearbyforthefive years(theandU.toSrepay the $1,to0pay 00 fi6%ve years Wi t h Treasury bonds and almost all U. S . corporate bonds, the annual interest is paid in(onetwoevery semiannual installments. Therefore, this bondof wi$1,ll0make nineparcoupon payments si x months) of $30 and a fi n al payment 30 (the value pl us thethe final coupon payment) at the end of five years. This stream of payments is fixed when bonds are issued and does not change over the life of the bond. Note that aseachan semiannual coupon is one-half thewhicoupon rate (whichcalled is alwtheays expressed annual rate) ti m es the par value, c h i s sometimes or payment of $4,An0008%every Treasury note wiandth aafacefinalvalpayment ue of $100, 000 wi000ll make amaturity. coupon six months of $104, at AotherU.Scurrenci . Treasuryes bond is The denominated (of course) in U.S.of adollars. BondsbycanthebeMexican issued in as well. bond issued government kely be Mexican pesos. Bonds can be issued that promise to make payments in wianyll licurrency. straight

coupon

matures issuer

par value

foce

value

maturity value.

currency denomination

Coupon Rate Structures: Zero-Coupon Bonds, Step-Up Notes, Deferred­ Coupon Bonds

arenterestbondsresults thatfrom do notthepayfactperiodic interest. They payaretheinitially par value atsoldmaturi t y and the i that zero-coupon bonds at a pricewe below (i.e., theywitharenosoldexpliat caitsignifi Sometimes will calparl debtvaluesecurities interestcantpayments at a specified rate. The increase may take placehave one orcoupon more rates timesthatduringincrease the lifover e oftithemeissue. carry coupons,accrue, but atthea initial couponrate,payments aredeferral deferredperiodfor some period. The coupon payments compound over the andpassed, are paidthese as a lump sum atregulthearendcoupon of thatinterest period.forAfter the initial deferment period has bonds pay the rest of the l i f e of the issue (to maturity). Zero-coupon bonds

discount to par value) . pure discount

securities.

Step-up notes

Deferred-coupon bonds

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #52 - Features of Debt Securities

Floating-Rate Securities

svary c r based i s areonbonds forewhich the rate coupon interest payments over the life ofinterest the security a specifi d i n terest or i n dex. For example, if market rateshave are movi ng up,thatthearecoupons on straight(normally floaters willeveryrise3,as6,wellor. 12In months) essence, these bonds coupons reset periodically based on prevailing market interest rates. The mostchcommon procedure for setting the, thecoupon rates on U.floSating-rate securities is one whi starts wi t h a (e. g . rate on certain . Treasury securities or the London Interbank Offeredrate.RateThe[LIBOR]) and thenn mayaddsalsoor vary subtracts atimstated to or from that reference quoted margi over e according to a scheduleThus, that istostated ascoupon the formula: find thein thenewindenture. coupon rate,Theyouschedul woulde isuseoftenthe referred followintog new coupon rate reference rate quoted margin Just th a fixed-coupon bond, a semiannual coupon payment will be one-half the (annualas wi) coupon is aratefloating-rate securityinterest with a coupon formulaandthatviactuall yA icoupon ncreasesformul the coupon when a reference rate decreases, c e versa. a such as coupon rate = 12% - reference rate accomplishes this. Some fl o ating-rate securities have coupon formulas based on infl a tion and are referred bond with a coupon of 3%security. annual change in theto asConsumer Price Index is anAexampl e of such an inflformula ation-linked The parties toratethebybondplacing contract canandlimloitwertheilimits r exposure tocoupon extremerate.fluctuations in thelimit,reference upper on the The upper whi c h is called a puts a maximum on the interest rate paid by the borrower/ issuer. Thepayments lower limit, callbyed thea lender/security puts a minimum onWhen the periodic coupon interest received owner. both limits are present simultaneously, the combination is called a Consider a fl o ati n g-rate security (fl o ater) with a coupon rate at issuance of 5%, a 7% cap, theandborrower a 3% floor.wilIfl paythe (lender coupon will ratereceive) (referenceonlyrate7%plusfortheas long margin) risescoupon aboverate, 7%, as the accordingwilto lthepayformula, remains attheor above 7%.rate,If according the coupontoratethe falls belowremains 3%, the borrower 3% for as long as coupon formula, at or below 3%. Floating-rate e

u

it e

reference rate

margin

coupon formula.

Âą

=

rate.

An inverse floater

+

inflation-indexed bonds.

cap,

floor,

collar.

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #52

-

Features of Debt Securities

LOS 52.c: Define accrued interest, full price, and clean price. CFA® Program Curriculum, Volume 5, page 301

When bondthetrades between coupon dates, thetheselldate er is ofentitltheedsale.to recei vies any interest earned afrom previous coupon date through This known as and isofantheamount that is payable byof thethe next buyercoupon (new owner) of and the will bond. The new owner bond wi l l recei v e all payment then recover any accrued i n terest pai d on the date of purchase. The accrued i n terest i s calculated as the fraction of the coupon period that has passed times the coupon. InthethebondUnited States, the convention i s for the bond buyer to pay any accrued interest to sel(theler. The amountplusthatanytheaccrued buyer pays to theIn selthelerUnited is the agreed-upon price of the bond interest. States, bonds trade withethright the next coupon attached,is said whictoh beis termed A bond traded without to the next coupon trading The total amount paid, including known as the of the bond. The full price = cleanaccrued price interest, accruedis interest. If the issuertheof thebondbondwillistrade in default ., has notinterest, made periodic coupon payments), without(i.eaccrued and it is obligatory said to be tradingflat. accrued interest

clean price)

cum coupon. ex-coupon.

+

full (or dirty) price

LOS 52.d: Explain the provisions for redemption and retirement of bonds. CFA® Program Curriculum, Volume 5, page 301

The redemptiontheprovisions circumstances principal forwillabebondrepaid.refer to how, when, and under what Coupon Treasury bonds andatmostwhichcorporate bonds arepar or face value isthat is, they pay onl y interest until maturity, ti m e the enti r e repaid. This repayment structure is referred toprincipal as a be repaidor through a series Alternati vely,over the bond terms may specify that the of payments time or al l at once prior to maturity, at the option of ei t her the bondholder or the issuer (putable and callable bonds). make periodic payments over the life of the bond. A conventional mortgageconsists is anofexampl e of an interest amortizingpayment loan; theandpayments are allof aequal, and each payment the periodic the repayment portion of the original principal. For a fully amortizing loan, the fi n al (l e vel) payment automobileat maturity loan). retires the last remaining principal on the loan (e.g., a typical options giThese ve theoptions issuer/borrower theinrimortgages ght to accelerate the principal repayment on a loan. are present and other amortizing loans. Amorti z i n g loans require a series of equal payments that cover the periodic i n terest and reduce the outstanding principal each ti m e a payment is made. When a person gets a home or anIfautomobile any thetime, in wholemortgage or in part. the borrowerloan,sellsshetheoften homehasor theauto,rightshetois prepay requiredittoat pay nonamortizing;

bullet bond

Amortizing securities

interest and principal

Prepayment

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bullet maturity.

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #52 - Features of Debt Securities

loan off in full. Thesecurity signifiicsance oftherea prepayment option to an investor in acashmortgage or mortgage-backed that i s additional uncertainty about the fl o ws to be received compared to a security that does not permit prepayment. Call provisions give the issuer the ri g ht (but not the obligation) to retire all or a part of an issue prior tobonds maturity. If thecallbonds are called,thethebonds bondholders have no choice buttheyto surrender their for the pri c e because qui t payi n g interest when arecoupon called.bonds Callwifeatures give the issuer th lower-coupon issues.the opportunity to replace higher-than-market Typical l y, there is a period of years after issuance during whi c h the bonds cannot be called.a This is termed the period ofthe period (if any)because thel protection bondholderhas ispassed, protected from call over this period. After of cal the bonds are referred to as There mayly,bewhen severala bond call dates specionfiedtheinfitherst indenture, each with athelowercall calpricel price. Customari is called permissible call date, is above theoverpartime value.accordi If thenbonds areschedule. not calForled example, entirely ora notcall called at all,maythespecifY call price decl i nes g to a schedule that acall20-year bond can be call e d after fi v e years at a pri c e of 110 (110% of par), wi t h the price declining to 105 after ten years and 100 in the 15th year. Nonrefundable bondsThus,prohibit themaycallbeofcallan aisblsuee butusinnotg therefundable. proceeds from a lothat wer is coupon bondhasissue. a bond A bond absolute priorother to maturi y. In contrast, a callable but bond protection can be calledagaifornstanya callreason than trefunding. When bondsbondsarearecalledsaidthrough a call optionIf a orlowerthrough theissue provisions oftoaprovide sinkingthe fund, the to be redeemed. coupon i s sol d funds to call the bonds, the bonds are said to be refunded. Sinking fund provisions provi d e for the repayment of principal through a series of payments overmaythe requi life ofrethethatissue. For example, a 20-miyllion ear issue wiprincipal th a face amount of $300 million the issuer reti r e $20 of the every year beginning in the sixth year. This can be accomplished in one of two or The issuer may deposit the required cash amount annually with the issue's trustee whong wia selection ll then retimethod re the such applicable proportion of bondssele(1/15 inthethis example) by usi as a l o ttery. The bonds cted by trustee are typically retired at par. The issuerred may purchase bonds with aandtotaldeliparvervalue equal to thetrusteeamount that i s to be reti i n that year i n the market them to the who will retire them. Ifis thethe less bondsexpensive are tradialntgernative. below parIf thevalue,bondsdelivery of bonds purchased i n the open market ares thetrading above thewaypartovalue, deliveri ng cash to the trustee to reti r e the bonds at par i less expensive satisfY the sinking fund requirement. call protection

currently callable.

noncallable nonrefundable

ways-cash

delivery: •

Cash payment.

Delivery ofsecurities.

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Page 1 5


Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #52

-

Features of Debt Securities

Anthanaccelerated sinking fundspecifi provision allosinki ws theng issuer the choice ofAsretianringexample, more the amount of bonds e d in the fund requirement. thechooseissuerto retire may beuprequired to redeem $5 million par val u e of bonds each year but may to $10 million par value of the issue. Regular and Special Redemption Prices

When bonds are asredeemed under the callandprovisions specifi eared inreferred the bondto asindenture, these are known regular redemptions, the call prices regular redemption prices. However,of awhen bondssalearemandated redeemedbytogovernment comply withauthority, a sinkingthe fund provisi o n or because property redemption prices (typically par value) are referred to as special redemption prices. Asset sales maybybeantitrust forced byauthori a regultieastoryor through authoritya governmental (e.g., the forcedunit'divesti thtureofofeminent an operating divi s ion s ri g domain). Exampl essalofe sales forced through theforgovernment' selright ofutilieminent domain woul d be a forced of privately held land erection of e ctric t y lines or for construction of a freeway. LOS 52.e: Identify common options embedded in a bond issue, explain the importance of embedded options, and identify whether an option benefits the issuer or the bondholder. CPAÂŽ Program Curriculum, Volume 5, page 302

The fol l o wing are exampl e s of embedded i n the sense that they are anoptions integralare part of the bond contract andtheareissuer not aofseparate securiandty.some Someareembedded exercisable at the option of the bond, exercisable at the option of the purchaser of the bond. Security ownerty options. In thegranted following cases, the option embedded ingithevesfiadditional xed­ income securi is an option to the security holder (lender) and value to the security, compared to an otherwise-identical straight (option-free) security. embedded options,

grants shares the holder of a bond the right to convert the bond i n to a 1. Afixed number of common ofis thesimilar issuer.butThisallowschoice/option hasthevaluebondforintothe a bondhol d er. An exchange option conversion of security other than the common stock of the issuer. 2. specified pricegipriveobondholders the ri g ht to sell (put) the bond to the issuer at a rortoclose maturito tpar.y. TheIf interest put priceratesis generally parand/or ifthethebonds were original l y issued at have ri s en creditworthiness of thetheissuer has deteriorated so that the market priceoption of suchandbonds has fall e n below par, bondholder may choose to exerci s e the put require the issuer to redeem the bonds at the put price. 3. couponsetratea minimum on theeachcoupon ratebasedforona floating-rate bond,usually a bonda short-term with a that changes period a reference rate, rate such as LIBOR or the T-bill rate. conversion option

Put provisions

Floors

Page 16

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #52 - Features of Debt Securities

Security issuerof the options. Inincome these security. cases, theSecurities embeddedwhere optiontheisissuer exercisabl e atwhether the option ofto theexercise issuer fi x ed chooses the embedded option wi l l be priced less (or wi t h a hi g her coupon) than otherwise identical securities that do not contain such an option. 1. maturity. The detai give lthes ofbond ht to redeem a callissuer featurethearerigcovered later in(paythisoff)topithec reviissueew.prior to 2. by mortgages or carareloans.included in many amortizing securities, such as thosethebacked A prepayment option gi v es the borrower/issuer riLoans ght to prepay the loan bal a nce pri o r to maturi t y, i n whole or i n part, wi t hout penal t y. may bein prepaid of a mortgage drop interest forratesa vari or theetysalofereasons, of a homesuchprioras theto itsrefinancing loan maturity date. due to a are proportion embedded options heldthan by theis required issuer thatbyalthelow thesinkiissuer to (annually) reti r e a l a rger of the issue ng fund provision, up to a specified limit. setrate a maximum on theeachcoupon ratebasedfor ona floaating-rate bond,usually a bonda wishort-term th a coupon that changes period reference rate, rate such as LIBOR or the T-hill rate. Callprovisions

Prepayment options

3. Accelerated sinkingfundprovisions

4.

Caps

Professor's Note: Caps andfloors do not need to be "exercised" by the issuer or bondholder. They are considered embedded options because a cap is equivalent to a series of interest rate call options and a floor is equivalent to a series of interest rate put options. This will be explained further in our topic review of Option Markets and Contracts in the Study Session covering derivatives.

Toto calsummarize, the(2)follanoaccel wingerated embedded options favor the issuer/borrower: (1)option, the rightand l the issue, si n king fund provision, a prepayment (4)borrower/issuer. a cap on the floating coupon rate that limi t s the amount of interest payable by the theseumoptions higher option-free market yieldbonds. s since bondholders willBonds requirewitha premi relativewitoll tend otherwito have se identical The ng embedded options favorinterest the payment to theconversion provisions, (2) aafolflputolorowioption. that guarantees a minimum bondholder, andbe lower The market yields on bonds with these options will tend to than attractiotherwise ve. identical option-free bonds since bondholders will find these options (3)

bondholders: (1)

(3)

LOS 52.f: Describe methods used by institutional investors in the bond market to finance the purchase of a security (i.e., margin buying and repurchase agreements). CFAÂŽ Program Curriculum, Volume 5, page 308

Marginthebuying involves borrowing fundscollateral from aforbroker or a bankloan.to purchase securities where securities themsel v es are the the margin The margi n amount (percentage of the bonds' val u e) i s regulated by the Federal Reserve i n the United States, under the Securities and Exchange Act of 1934.

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #52

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Features of Debt Securities

(repo) toagreement is anat arrangement bya whi cheand (higher) institutionprice.sellsThea security wiA repurchase th a commitment buy it back a l a ter date at specifi is greater than the sell i ng price and accounts for the interest charged by the buyer, who is, intheeffect, lendingwhifunds to theannuali sellezr.edThepercentage interest ratedifference impliedbetween by the two prices i s called c h i s the theagreement two prices. A repurchase agreement for one day is called an and an a wouldThe customarilycovering less thana thelongerrateperiod a bankisorcalled brokerage chargeinterest on a cost margiofn aloan. is Most bond-dealer financing is achieagreements ved througharerepurchase agreements rather than through margin loans. Repurchase not regulated by the Federal Reserve, and the collateral position of the lender/buyer in a repo is better i n the event of bankruptcy ofn totheselldealiteback r, sinceat thethe price securityspecifi is owned by therepurchase lender. The lender hasratheronly the obligati o e d i n the agreement, than simply having a claim against the assets of the dealer for the margin loan amount. repurchase price

repo rate,

overnight repo,

term repo.

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repo


Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #52 - Features of Debt Securities

KEY CONCEPTS

ALOS bond'ors buyer indenture contains the obligations, rights, and any options available to the issuer of a bond. Covenants arevethecovenants specific specify conditionsactionsof thethatobligation: Affi r mati the borrower/issuer must perform. Negative covenants prohibit certain actions by the borrower/issuer. LOS have the following features: Bonds Maturity-the term of the loan agreement. Par value ( f ace value)-the principal amount of the fi x ed income security that the bond issuerrate-the promisesratetoused pay theto determine bondholdersthe over the liinterest fe of thetobond. Coupon periodic be paid on onthethe principal amount. Interest can be pai d annually or semiannual l y , depending terms. Coupon rates may be fixed or variable. TypesOption-free of coupon (straight) rate structures: bonds pay periodic interest and repay the par value at maturi t y. Zero-coupon bonds pay no expli c it periodic interest and are sold at a discount to par value. Step-up notes have a coupon rate that increases over time according to a specified schedule. Deferred-coupon bonds initialof thely make no coupon payments (they(compound) are deferredinterest for a period of time). At the end deferral period, the accrued s flpaid, makehasregul ar coupon payments unti l maturity. Ai(usually oatingandLIBOR) (varitheabonds ble)andrateathen bond a coupon formula that i s based on a reference rate quoted margin.coupon A caprateis athemaxibondholder mum coupon rate theve onissuerany must pay, and a fl o or i s a minimum will recei coupon date. LOS Accrued interestto aisbond the interest a bond buyer seller. earned since the last coupon payment date and is paid by Clean price is the quoted price of the bond without accrued interest. Full price refers to the quoted price plus any accrued interest. 52.a

52.b

52.c

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Page 1 9


Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #52

-

Features of Debt Securities

LOS 52.d BondAmortizing retirementsecurities (payoff) make provisions: periodic payments that include both interest and principal paymentsoccurs. so that the entire principal is paid off with the last payment unless prepayment Ato prepayment option is contained in some amortizing debt and allows the borrower pay offfundprincipal at anyrequire time prior topartmaturity, in whole or reti in part. Sinking provisions that a of a bond issue be red at specified dates, typical l y annuall y . Cal l provi s ions enable the borrower (issuer) to buy back the bonds from the iCalnvestors (redeem them) at abonds call price(s) specifi eprior d in theto maturity, bond indenture. l abl e but nonrefundable can be call e d their rate. redemption cannot be funded by the issuance of bonds with a lowerbutcoupon LOS 52.e options that benefit the issuer reduce the bond's value (increase the yield) to Embedded a bondCallpurchaser. Examples are: provisions. Accelerated sinking fund provisions. Caps (maximum interest rates) on floating-rate bonds. Embedded optionspurchaser. that benefit bondholders increase the bond's value (decrease the yield)Conversion to a bond Examples are: optisocommon ns (the option of bondholders to convert their bonds into shares of thePut bond i s suer' stock). options (theprice). option of bondholders to return their bonds to the issuer at a predetermined Floors (minimum interest rates) on floating-rate bonds. LOS 52. f Institutions can financeprice,secondary market bond purchases by) or,margi n buying (borrowi ng some of the purchase using the securi t i e s as coll a teral more commonl y , by repurchase (repo)to agreements, ananarrangement inhigher whichprice an institution sells date a security with a promise buy it back at agreed-upon at a specified i n the future. •

• •

• •

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #52 - Features of Debt Securities

CONCEPT CHECKERS

s indenture: 1. AA. bond' contains i t s covenants. the same C.B. isrelates onlyastoaitsdebenture. interest and principal payments. 2. Asemiannual bond haslya. parWhatvaluisetheof $5,dollar000amount and a coupon rate of 8. 5 %coupon payablepayment? of the semiannual A.B. $238. $212.353.0. $425.00. 3. would From theaddperspective of the bondholder, which of the following pairs of options value to a straight (option-free) bond? A.B. Put Calloption optionandandconversion conversionoption. option. C. Prepayment option and put option. 4. Aby10-year bond pays no interest for three years, then pays $229. 2 5, foll o wed payments ofs bond $35 semiannually for seven years and an additional $1,000 at maturi t y. Thi i s a: A.B. step-up bond. bond.bond. C. zero-coupon deferred-coupon a $11 andmilJuly lion semiannual-pay, floating-raterateissue where theLIBOR, rate isandreset 5. Consider ontheJanuary 1 each year. The reference is 6-month stated margin is + 1.25%. If 6-month LIBOR i s 6.5% on July 1, what wil l semiannual coupon be on this issue? A.theB. next $38, 7 50. $65, 0 00. $77,500. of thehavefollcapsowinandg statements is with regard to floating-rate 6. Which issues that fl o ors? A. AiSSUer. cap is an advantage to the bondholder, while a floor is an advantage to the B. AiSSUer. floor is an advantage to the bondholder, while a cap is an advantage to the C. Aa diflsoadvantage or is an advantage to both the issuer and the bondholder, whi l e a cap i s to both the issuer and the bondholder. investorcoupon paid adates, full priandceaccrued of $1,059.interest 04 eachwasfor$23.10054bonds. TheWhat purchase was 7. Anbetween per bond. is each bond' s clean price? A.B. $1,$1,035. 000.050.0. $1,082.58. c.

c.

most accurate

c.

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Page 2 1


Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #52

-

Features of Debt Securities

of the following statements is with regard to a call 8. Which provision? A.B. AA callable call provision will benefit the issuer i n times of declining interest rates. bond will trade at a higher price than an identical noncallable bond. C. Anoncallable nonrefundabl e bond provides more protection to the bondholder than a bond. ofy callable the follobond? wing describes the maximum price for a 9. Which currentl A.B. The Its parcallvalue. C. The presentprice.value of its par value. and Consider $1,are000,cal0lable 00 parandvalue, 10-year, 6.n5g%fundcoupon bondsTheissuedmarket on January 1,sim2005. The bonds there i s a sinki provision. rate for bonds is currently 5.7%. The main points of the prospectus are summarized as follows:ilar Call dates and prices: 2005 through 1,2009: After January 2010:103.102. Additional information: The bonds are non-refundable. The sinkingamount fund provision requires that theundercompany redeem $100, 000 fund of the principal each year. Bonds called the terms of the sinking provision will be redeemed at par. The credit rating of the bonds is currently the same as at issuance. 10. A.Usingtheonlybondsthedopreceding information, Gould should conclude that: not have call protection. issuedtheatbonds and currentl B.C. githevenbonds currentwererates, will likelyy trade be calatleda premium. and new bonds issued. 11. Which of the following statements about the sinking fund provisions for these bonds is A. Anof theinvestor would benefit from having his bonds called under the provision sinking fund. B. Anunderinvestor will recei vethea premium if the bond is redeemed prior to maturity the provisi o n of sinki n g fund. C. The bonds do not have an accelerated sinking fund provision. 12. AnA. investor buying bonds on margin: interestbyongovernment a loan. regulation of margin lending. B.C. actually imust s notpayrestricted lends the bonds to a bank or brokerage house. most accurate

most accurately

Use the following information to answer Questions 10

• •

• •

most accurate?

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©2012 Kaplan, Inc.

11.


Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #52 - Features of Debt Securities

13. byWhich of the following is a provision for the early retirement of debt the issuer? A.B. AA conversion option. C. A call sinkingoption. fund. is loan. 14. A.A mortgage a col l ateralized B.C. characterized subject to earlbyy retirement. highly predictable cash flows. least likely

least likely:

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #52 - Features of Debt Securities

ANSWERS - CONCEPT CHECKERS

1.

A

An indenture is the contract between the company and its bondholders and contains the bond's covenants.

2.

A

The annual interest is 8.5% of the $5,000 par value, or $425. Each semiannual payment is one-half of that, or $212.50.

3.

B

A put option and a conversion option have positive value to the bondholder. The other options favor the issuer and result in a lower value than a straight bond.

4.

C

This pattern describes a deferred-coupon bond. The first payment of $229.25 is the value of the accrued coupon payments for the first three years.

5.

A

The coupon rate is 6.5 + 1 .25 7.75. The semiannual coupon payment equals (0.5)(0.0775)($1 ,000,000) $38,750. =

=

6.

B

A cap is a maximum on the coupon rate and is advantageous to the issuer. A floor is a minimum on the coupon rate and is, therefore, advantageous to the bondholder.

7.

B

The full price includes accrued interest, while the clean price does not. Therefore, the clean price is 1 ,059.04 - 23.54 $ 1 ,035.50. =

Page 24

8.

A

A call provision gives the bond issuer the right to call the bond at a price specified in the bond indenture. A bond issuer may want to call a bond if interest rates have decreased so that borrowing costs can be decreased by replacing the bond with a lower coupon issue.

9.

B

Whenever the price of the bond increases above the strike price stipulated on the call option, it will be optimal for the issuer to call the bond. So theoretically, the price of a currently callable bond should never rise above its call price.

10. A

The bonds are callable in 2005, indicating that there is no period of call protection. We have no information about the pricing of the bonds at issuance. The company may not refond the bonds (i.e., they cannot call the bonds with the proceeds of a new debt offering at the currently lower market yield) .

11. C

The sinking fund provision does not provide for an acceleration of the sinking fund redemptions. With rates currently below the coupon rate, the bonds will be trading at a premium to par value. Thus, a sinking fund call at par would not benefit a bondholder.

12. A

Margin loans require the payment of interest, and the rate is typically higher than funding costs when repurchase agreements are used.

13. A

A conversion option allows bondholders to exchange their bonds for common stock. The option is held by the boldholder, not the issuer.

14. C

A mortgage can typically be retired early in whole or in part (a prepayment option), and this makes the cash flows difficult to predict with any accuracy.

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The following is a review of the Analysis of Fixed Income Investments principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in:

RISKS ASSOCIATED WITH INVESTING IN B ONDS Study Session 1 5

EXAM FOCUS

This topic review introduces variousThesources of here risk that investors "areTheexposed to when investi n g i n fi x ed income securities. key word i s "introduces. most important source interest rateafterrisk,thehasmaterial its ownonfullthetopic reviewofinfixedStudyincome Sessionsecurities. 16 and iPrepayment s moreoffulrisk, lyriskdeveloped valuation has i t s own topic review at Level II, and credit risk and reinvestment risk revisitedsome to a significant extent in other partsriskofmeasures the LevelandI curriculum. In factors this revithat ew, wearewillpresent worki n g definitions of the identify the affect theseassured risks.thatTo your avoidunderstanding unnecessary repetition, some ofwilthel bemateri aleteis abbreviated here, but be of this material compl by the time you work through this Study Session and the one that follows. LOS 53.a: Explain the risks associated with investing in bonds. CFAÂŽ Program Curriculum, Volume 5, page 320

refers interest to the effect ofrischanges in uthees prevaili ngismarket rate ofof interest interest onratebond values. When rates e, bond val fall. This the source risk which is approximated by a measure called Yield arirelati ses from the possibility of changes in the shape of duration the yield curve (whi c h shows the o n between bond yields and maturity). While is achanges useful measure of i n terest rate risk for equal changes in yi e ld at every maturi t y (paral l el indifferent the yieldamounts curve),forchanges in the shape of the yiel d curve mean that yields change by bonds with different maturities. arises fromreturned the factandthatmustwhenbe reinvested interest ratesat thefall,new a callable bond investor' s principal may be lower rates. Certainly bonds thatratesarearenotmorecallavolatile, ble havecallnoacall risk, andhavecalrell protecti omore n reduces calsk lbecause risk. When interest ble bonds a ti v ely cal l ri of an increased probability of yields falling to a level where the bonds will be called. ions similar to calllorisk. Prepayments areaprincipal repayments in excess ofprepayments those required amortizing ans, such as residenti l mortgages. If rates fall, causing to increase, an investor must rei n vest these prepayments at the new l rate. Just as with call risk, an increase in interest rate volatility increases prepaymentowerrisk. refers to the fact that when market rates fall, the cash fl o ws (both interest and principal) from fixed-income securities must be reinvested at lower rates, Interest rate risk

duration.

curve risk

Call risk

Prepayment risk

Reinvestment risk

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #53

-

Risks Associated With Investing in Bonds

reducing the returns anrisk.investor wiofll these earn. Note that reinvestment risk ofis related to cash call rifloskwsandat lprepayment In both cases, it is the reinvestment principal o wer rates than were expected that negati v ely i m pacts the investor. Coupon bonds that contain neitherthecallcoupon nor prepayment provisionsmustwillbealsoreibenvested subjectas tothey are reinvestment risk, because interest payments received. that investors can be faced wihasthnoa choice betweenrisreik novervestment riskbecause and price risk. ANote noncallable zero-coupon bond rei n vestment its life there are nointerest cash rate flowsriskto reithannvest,a coupon but a zero-coupon bondmaturity. (as we wilTherefore, l cover shortly) has morebond bond of the same the coupon will have more reinvestment risk and less price risk. risk that the creditworthiness of a fixed-income s issuer will deteriorate, iisnthecreasing the requi red return and decreasing the securisecurity' ty's value. has to do wi t h the ri s k that the sale of a fi x ed-income security must be made Treasury at a pricebonds less thanhavefaiexcellent r market livalue because of a lack ofmillion liquiditydollars for a worth particular issue. q uidity, so selling a few atof thethe prevailing market price can be easily and quickly accomplished. At the other end liquidity spectrum, a valuabl e painting, collectible anti q ue automobile, or unique and expensiprefer ve home may be quiteto less, difficult to selliquickly at fais rliquidity -market value. Since its investors more l i quidity a decrease n a security' will decrease price, as the required yield will be higher. arises fromofthehis uncertainty aboutcurrency. the valueWhileof foreign currency bicashll fl(T-bill) ows to may an investor in terms home-country a U.S. Treasury be considered quite linvestor ow risk orwileven risk-freebyto aa depreciation U.S.-based investor, the valU.Su.e dolof lthear'sT-bill to a European l be reduced of the value relative to the euro. mipurchasing-power ght be better described as a $10,000inflzero-coupon ation risk andTreasury even morebond descri p ti v ely as risk. While can provide a payment of $10,and000services in thethatfuture$10,wi0t00h near certaiatnty,thethere is date. uncertainty about the amount of goods wil l buy future This uncertai n ty about the amount of goods and services that a security' s cash fl o ws wi ll purchase is referred to here as inflation risk. i s present for fi x ed-income securities that have embedded options, such as calltheoptions, prepayment options, orthus,putaffect options.the Changes isecurities n interest wirateth volembedded atility affect val u e of these options and, val u es of options. encompasses outside takeovers. the risks of financial markets, such as the risks posed by natural disasterstheandriskscorporate the credit risk of a sovereign bond issued by a country other than the investor'is essentially s home country. Credit risk

Liquidity risk

Exchange-rate risk

Inflation risk

unexpected

Volatility risk

Event risk

Sovereign risk

Page 26

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing in Bonds

LOS 53.b: Identify the relations among a bond's coupon rate, the yield required by the market, and the bond's price relative to par value (i.e., discount, premium, or equal to par). CFA® Program Curriculum, Volume 5, page 320

When coupon on a thebondcoupon is equalratetoonitsbonds marketisyitypicall eld, they setbondat orwilnear l tradetheat iprevail ts itheng market Whenyirateeissued, ld on similar bonds so that the bonds trade initially at or near their par Ifwithell yifalelldandrequired intradethe atmarket for thetobond subsequently rises,Thetherequi pricered ofyieldthevalue. bond i t will a (below) its par value. cantoincrease becausefor theinterest rates havehasincreased, because the theextrarisyiel dtheinvestors require compensate bond' s risk increased, or because k of bond has increased was issued. the bond price will increase andsincetheit bond will tradeConversel at a y, if the required to (above)yieldits parfalls,value. The relation is illustrated in Figure 1. 1: 8% par value.

discount

premium

Figure

Market Yield vs. Bond Value for an

Coupon Bond

Bond Value

Premium to Par Par Value

I

- - - - - -------------------

-------------------

------------------

Discount to Par

'------''- Market Yield 7% 6% 8% 9% 10%

Professor's Note: This is a crucial concept and the reasons underlying this relation will be clear after you cover the material on bond valuation methods in the next Study Session.

LOS 53.c: Explain how a bond maturity, coupon, embedded options and yield level affect its interest rate risk. CFA® Program Curriculum, Volume 5, page 322

Interest rate risk, as we are using i t here, refers to the sensitivity of a bond' s value to changes n market interestprirates/yields. thereprices is an inverse between iyield and bond ces-when yiRemember elds increase,thatbond decrease.relationship The term we ©20 12 Kaplan, Inc.

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Risks Associated With Investing in Bonds

interestfor rate is in yield.which gives us a good approximation ofusea forbond'thes measure change inofprice a givenriskchange duration,

� Professor's Note: This is a very important concept. Notice that the terms "interest � rate risk, " "interest rate sensitivity, " and "duration" are used interchangeably.

We s concepttobyinterest simplyratelooking at how a bond's maturity and coupon affectintroduce its price thisensitivity changes. If twogreater bondsduration are identical except forl havematuria greater ty, thepercentage one with thechange longerinmaturity hasa the because i t wil val u e for giForventwochange in yield.identical bonds, the one with the higher coupon rate has the otherwise lower gher coupon coupon bond rate wiwill lchange for a giduration. ven changeTheinprice yieldofthanthethebondpricewitofh thethe hilower . less The presence of embedded options also affects the sensi t i v ity of a bond' s value to interest rate changes duration). Pricesofofstraiputable and callablebonds bondswill. will react differently to changes in yie(iltds than the prices ght (option-free) Adecline; call feature limits theng,upside priceprimovement ofriasebond when interest ratesThis leads loosely speaki the bond c e wi l l not above the call price. to thechanges conclusion that the valueidentical of a callable bond wibond. ll be less sensitive to interest rate than an otherwise option-free Arisput feature li m i t s the downside price movement of a bond when interest rates e;conclusion loosely speaking, thevaluebondofprice will notbondfallwibelow thesensi put tprice. This leadsrateto thechanges that the a putable l l be less i v e to i n terest than an otherwise identical option-free bond. The relations we have developed so far are summarized in Figure 2. •

Figure 2: Bond Characteristics and Interest Rate Risk Characteristic

Interest Rate Risk

Duration

Maturity up

Interest rate risk up

Duration up

Coupon up

Interest rate risk down

Duration down

Add a call

Interest rate risk down

Duration down

Add a put

Interest rate risk down

Duration down

Professor's Note: We have examined several factors that affect interest rate risk, but only maturity is positively related to interest rate risk (longer maturity, higher duration). To remember this, note that the words "maturity" and "duration" both have to do with time. The other factors, coupon rate, yield, and the presence ofputs and calls, are all negatively related to interest rate risk (duration). Higher coupons, higher yields, and embedded options all decrease interest rate sensitivity (duration).

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing in Bonds

LOS 53.d: Identify the relation of the price of a callable bond to the price of an option-free bond and the price of the embedded call option. CFA® Program Curriculum, Volume 5, page 322

Asbondwe relati notedveearlto ianer,otherwise a call optionidentical favorsoption-free the issuer andbond.decreases the value of a call a bl e The issuer anownsoption-free the call. bond Essentiall y , when you purchase a callable bond, you have purchased but en a call option ssuer. Theequalvalueto ofthethevalcaluelable less than the valuhave e of angivoption-free bondtobythean iamount of thebondcall isoption. This relation can be shown as: callable bond value = value of option-free bond - value of embedded call option Figure shows thisfalls,relationship. Theinvalue ofbetween the callaoption is bond greaterandat laocallable wer yieldsbondso that as the yield the di f ference price straight Increases. 3

Figure Price-Yield Curves for Callable and Noncallable Bonds Pr ice

call pnce

3:

call op rion value �

j t

- ��::- - - - - - - - ----

T

----

- - -

---

i ------- --�-----

,

callable bond value

o

roo-fc" bood "'""'

L------'--

y'

Yield

LOS 53.e: Explain the interest rate risk of a Boating-rate security and why its price may differ from par value. CFA® Program Curriculum, Volume 5, page 324

Recalbased l that flonoating-rate securities havereference a couponrate.rateThethatobjecti floats,ve iofn that it is periodically reset a market-determined the resetting mechanism i s to bring the coupon rate in l i ne wi t h the current market yield so the bond sells at ortonearchanges its parinvalue. Thisyiewill makea fixed-coupon the price of a bond floating-rate security muchThat'lesss sensitive market lds than of equal maturity. the point of a floating-rate security, less interest rate risk. Between dates, there is a timhappens e lag between in market yield andthe a change coupon in the coupon rate (which on theanynextchangedate). The longer reset

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Risks Associated With Investing in Bonds

tiflmuctuation. e period between thewetwocandates, the thegreater the (shorter) amount ofthepotential bondthepricegreater In general, say that longer reset period, (less) the interest rate risk of a floating-rate security at any reset date. long as the required margin above the reference rate exactly compensates for the bond' s risk, thethe price ofrate a floating-rate security wilsecurity return istovery par atsmalleachasreset date. date For this reason, interest ri s k of a fl o ating-rate the reset approaches. There are presence two primary reasons that a bond' s pricerate)maycandiffer fromtheparinterest at its coupon resetof date. The of a cap (maximum coupon i n crease rate risk a floating-rate securi ty. If theyields reference rate increases enough thatWhen the captheratemarket is reached, further increases i n market will decrease the fl o ater' s price. yield iextent s abovethatits thecapped coupon rate, a fl o ating-rate security will trade at a discount. To the cap fi x es the coupon rate on the fl o ater, i t s price sensitivity to changes i n market yield will be increased. This is sometimes referred to as cap risk. Aissuance. floater'sConsider price canaalsofirmdiffer fromissued par duefloating-rate to the factdebtthatwith the margi n is fiformula xed at of that has a coupon LIBORty.+If2%.the This 2%credimargin shouldimproves, reflect thethecredit riskisandlessliquidity riskwilloftrade the at securi fi r m' s t worthiness fl o ater ri s ky and amarket' premium to rpar.ed yield Evenpremium if the firm'fors credi trworthi nkesslevelremains constant, a change infltheoater s requi the fi m' s ri s wi l l cause the value of the to differ from par.

As

LOS 53.f: Calculate and interpret the duration and dollar duration of a bond. CPAÂŽ Program Curriculum, Volume 5, page 326

Bychanges now you knowSpecifical that duration is abemeasure of theasprice sensitivity of aofsecurity to i n yield. l y, it can interpreted an approximation the change in the security price for a change in yield. We can al s o interpret duration as the of the percentage change in price to the change in yield in percent. This relation is: change in bond price duration percentage yield change in percent When calcularelated. ting theIfdiyourection of theapriratece decrease, change, remember thatshould yieldsindicate and prices areincrease. inversely are given your resul t a pritoceits Also note that the durati o n of a zero-coupon bond i s approximately equal years to maturi t y, and the duration of a fl o ater i s equal to the fraction of a year until the next reset date. percentage

1%

ratio

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing in Bonds

Let's consider some numerical examples. Example: Approximate price change when yields increase Ifapproximate a bond haspercentage a duration change of 5 andinthetheyield bondincreases price. from 7% to 8%, calculate the Answer: -5decreased. 1 o/o = -5%, or a 5% decrease in price. Because the yield increased, the price x

Example: Approximate price change when yields decrease Aapproximate bond has apercentage duration ofchange 7 .2. Ifithen theyielbond d decreases from 8.3% to 7 . 9 %, calculate the price. Answer: -7.2 (-0.4%) = 2. 88%. Here the yield decreased and the price increased. x

The formula for what we just did (because duration is al w ays expressed as a positive number and because of the negative relation between yield and price) is: percentage price change = -duration (yield change in o/o) Sometimes the interest rate risk ofprice a bondchange or portfoli o isinexpressed astoitsa dollar duration, whi c h i s simply the approximate in dollars response change in yiel d basis points o/o). Withthea duration of 5.2 andas 5.a2bond value=of$62,400. $1.of 100 2 million, we can(1calculate dollar duration % $1.market 2 million Now let's dochange it in reverse and calculate in the bond' s price. the duration from the change in yield and the Example: Calculating duration given a yield increase If a bond's yield rises from 7% to 8% and its price falls 5%, calculate the duration. Answer: change in price -5.0% = 5 duration = percentage + l.Oo/o change in yield x

x

percentage

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #53

Example: Calculating duration given a yield decrease Ifduration. a bond's yield decreases by 0.1% and its price increases by 1.5%, calculate its Answer: change in price -- 1.5 % -1 5 duratton -- percentage change in yield -0.1% .

Risks Associated With Investing in Bonds

_

_

---

_

Professor's Note: Because bond price changes for yield increases andfor yield decreases are typically different, duration is typically calculated using an average ofthe price changes for an increase and for a decrease in yield. In a subsequent reading on interest rate risk we cover this calculation of "effective duration. " Here we simply illustrate the basic concept ofduration as the approximate percentage price change for a change in yield of I %.

Example: Calculating the new price of a bond A8. 5bond at $1,calculate 034.50,thehasnew a yieldpriceof7.of3the8%,bond. and has a duration of . If theis currently yield risestrading to 7.77%, Answer: The change in yield is 7.77% - 7.38% = 0.39%. The approximate price change is -8.5 0.39% = -3.315%. Since the yield the price will decrease by this The new price is (1 - 0.03315) $1,034.50 = $1,000.2 1. x

increased,

percentage.

x

LOS 53.g: Describe yield-curve risk and explain why duration does not account for yield-curve risk. CPAÂŽ Program Curriculum, Volume 5, page 327

The for a portfolio of bonds hasinthe same interpretation aschange for a single bond; itDuration is theduration approximate percentage change value for a 1% i n yields. the sensitivity of a portfolio's value to an equal change in yield forforallatheportfoli bondso measures in the portfolio. AThegraphyieldofcurve the relationship and yieldownward d is knownsloping, as a yieldflacurve. can have anybetween shape: maturity upward sloping, t, or some portfolio

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing in Bonds

combination slopes. oChanging shapes leadbytotheyield curvemeasure. risk, the interest rate riofskthese of a portfoli of bondsyielthatd icurve s not captured duration Inincrease, Figurea4,paral we lilellustrate that thelel shiyieldft. curve might shift when interest rates shift andtwoa ways non-paral Figure 4: Yield Curve Shifts Yield

ďż˝------

A non-parallel shift

Yield Curve

Maturity

The theduration of a bondof theportfol ioportfol can beiocalculated from intheeachindividual bond durations and proportions total value invested of the bonds. That is, thethe portfolio duration is a market-wei ghtedchange averagebyofthethesame individual bond'percent s durations. If yields on al l the bonds in the portfolio absolute amount, wesensiterm parallelioshift. Portfolioshifduration is an curve. approximation of the price tivitythatof aa portfol to parallel ts of the yield For a non-paral l el shi f t in the yield curve, the yields on di f ferent bonds in a portfoli o byondithefferent amounts, and duration alone cannot capture the effectvalueof afrom yican echanges ldchange change value of the portfolio. This ri s k of decreases in portfolio is termedinyitheeld shape curve ofrisk.the yield curve (i.e., from non-parallel shifts in the yield curve) Considering the non-parall e l yiel d curve shift i n Figure 4, the yield on short maturity bonds hasinincreased byconsequence. a small amount, andmaturity they wilbonds l havehaveexperiexperienced enced onlya asignifi smallcant decrease value as a Long increase in yieldofandthesisensitivity gnificant decreases in value as a result. Duration can beeal shifts poor in approximation of the value of a bond portfolio to non-parall the yield curve. To estimate the whi impact of non-parall el shitivity fts, ofbondtheportfolio managers calculate key rate durations, c h measure the sensi portfol i o ' s value to changes i n yielinds fordetailspecifi c maturiti e s (or portions of the yield curve). Key rate durati o n is described at Level II.

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Risks Associated With Investing in Bonds

LOS 53.h: Explain the disadvantages of a callable or prepayable security to an investor. CPA® Program Curriculum, Volume 5, page 331

Compared to an option-free bond, bonds wi t h call provisions and securities wi t h prepayment less certainofcashcallable flow and stream.prepayabl This uncertainty the timing ofoptions cash flooffer ws isaonemuchdisadvantage e securities.about Aprepayments second disadvantage stemssecurities from thearefactboththatmore the calprobable l of a bond andinterest increased of amortizing when rates have decreased. The di s advantage here i s that more principal (all of the principal, i n the case of a callare) islessreturned whenWhen the opportunities foryoureigetnvestment of theseback principal repayments attractive. rates are l o w, more principal that must bearereinvested at the new lower rates. When rates ri s e and opportunities for reinvestment better, less principal is likely to be returned early. Asecurities third disadvantage i s that the potential pri c e appreciation of callable and prepayable from decreases icalln market yieldstheis callessl price than that ofanoption-free securi tiebond' s of liske maturi t y. For a currently a ble bond, puts upper limit on the pritheceffect e appreciation. Whi l e there is no equival e nt price limit on a prepayable securi t y, prepayment similatorlyfallto iangcalmarket l featureyields. and reduces the appreciationof thepotential of the option securitiesoperates in response related uncertainty about the yields atOverall which, thefundsriskscanofbeearlreiynreturn vested ofareprincipal termed and the and respectively. call risk

prepayment risk,

LOS 53.i: Identify the factors that affect the reinvestment risk of a security and explain why prepayable amortizing securities expose investors to greater reinvestment risk than nonamortizing securities. CPA® Program Curriculum, Volume 5, page 331

Asmaturity noted from in ourcoupon earlier interest discussionpayments, of reinvestment risk,principal cash flowspayments prior toonstated bond calls, amortizing securities, and prepayments all subject securityrateholders todecreases reinvestment risk. Remember, acompared lower coupon increases duration (interest risk) but reinvestment risk to an otherwise identical higher coupon issue. A security has reinvestment risk under the following conditions: The coupon is higher. so that interest cash flows are higher. ItIt has a call feature an amortizing securityoption . . It iscontai ns a prepayment Asreturnnotedof earli er, when interest ratessecurities. decline, The thereearlis any return increased probabilityincreases of thetheearly principal for prepayable of principal amount that must be reinvested at lower prevailing rates. With prepayable securities, more

• • • •

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing in Bonds

the uncertainty about theratesbondholder' return ofriprincipal and the prevai ling reinvestment when it iss return returneddue(i.toe., early reinvestment sk) is greater. LOS 53.j: Describe types of credit risk and the meaning and role of credit ratings. CPAÂŽ Program Curriculum, Volume 5, page 332

Aprobability bond's of itsisissuer used tonotindicate itstimrelelyativeinterest probability of default,payments which isasthepromised maki n g and principal in the bondofindenture. A bond rating of AAbondis ians lessindication thatof thean Aexpected probability default over the l i f e of the than that rated bond, whi c h has a lower expected probability of default than a BBB (triple B) rated bond, and sori k,onthethrough the lower ratings. We can say that l o wer-rated bonds have more riskor principal that a bondpayments). will fail toBecause make promised/scheduled payments (eithera lower­ interest payments investors prefer less ri s k of default, rated i s sue must promise a higher yi e ld to compensate i n vestors for taki n g on a greater probability of default. The di f ference between the yi e ld on a Treasury security, which is assumed to be default ricredi sk-free, t and the yield on a similar maturity bond with a lower rating is termed the yield on a risky bond = yield on a default-free bond + credit spread to the even fact that thee thedefault riskTreasury premiumsecurities requiredofinsimilar the market formaturity a givenremains rating unchanged. canrefersincrease, whi l yi e l d on An i n crease i n thi s credit spread increases the required yield and decreases the price of a bond. is the ri s k that a credi t rati n g agency wi l l lower a bond' s rating. The resulthetinbond. g increase inngtheincrease yield required byaninvestors wiandll lead tohavea decrease in theeffect, price ofdecreasing A rati is termed will the opposite the required yield and increasing the price. Rating agenciof thees girivsekbonds ratingsWhilwhiectheh areratings meantaretoprimarily give bondbased purchasers anfinancial indication of default. on the strength ofratings the company, difonferentdifferences bonds ofinthecollateral same company can havein theslightlpriority y of different depending or di ff erences theseniorbondholders' cl a i m (e. g . , junior or subordinated bonds may get lower ratings than ratingsprobabi are notlityabsolute but ratherandgibonds. ve an indicatibonds). on of theBondrelative of defaultmeasures across theof default range ofrisk,companies For ratijudged ngs gitovenhaveby Standard andsk ofPoor'failing s Corporation, apromised bond ratedinterest AAA and (triplprincipal e-A) has been the l e ast ri to make i t s payments (defaul t i n g) over i t s life. Bonds with greater risk of defaulting on promised payments havesecurities lower ratings AA (double-A), A (single-A), BBB,anBB,AAAandrating. so on. U.S. Treasury and asuch smallasnumber of corporate bonds receive rating

default

s

spread.

Credit spread risk

Downgrade risk

upgrade

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Risks Associated With Investing in Bonds

Plusesa and minuses arethanusedAA,towhich indicateis better differences in default riskratedwithiAAAn categories, with AA+ better rating than AA-. Bonds through BBB areandconsidered and bonds rated BB and below are considered specul a ti v e sometimes termed or,ativemoreandpositi vely,rated D are currentlBonds rated CCC, CC, and C are highl y specul bonds y in default. Moody' s Investor Services, Inc. , another prominent issuer of bond ratings, classi f i e s bonds siwimthilarllower y butratings uses AalcarryashiS&P usespromised AA+, Aa2 as inAA,theAa3market as AA-,because and soinvestors on. Bonds g her yields exposed greater to moredefault defaultrisrik.sk require a higher promised return to compensate them for bearing investment grade junk bonds

high-yield bonds.

LOS 53.k: Explain liquidity risk and why it might be important to investors even if they expect to hold a security to the maturity date. CPAÂŽ Program Curriculum, Volume 5, page 336

We described liquidity earlier and noted that i n vestors prefer more liquidity to less. This means that diinfvestors willbetween requirethea prihigher yielddealforerslessareliquid securities, other things(the equal . The ference c e that wil l i n g to pay for a security bid) and the priceTheat bid-ask which dealers areis anwilinlidingcatitooselln ofa thesecurity (theity ofask)theismarket called thefor a spread l i qui d securi ty. Ifand traditheng activi in a particularto besecurity declines, the bid-ask spread will widen (increase), issue tisy considered less liquid. Ifincrease investorsthearebid-ask planning to sellleadatosecurity prior toprice,maturiandty,cana decrease intheliquidity wionllthe spread, a l o wer sal e decrease returns position. Even i f an i n vestor plans to hold the security until maturi t y rather than trade it, poor liquidityvaluescan tohaveportfolio adversesecurities. consequences stemming from theisneed to periodically assi gn current This periodic valuation referred to bidas When a security has little liquidity, the vari a ti o n i n dealers' prices or the absence ofordealpriecrinbidsg servialtogether makesto establi valuation difficultvalue. and Ifmaythisrequi ree that a valuation model c e be used s h current val u is low, institutional investors may be hurt in two situations. 1. portfoli Institutional investors may need to mark their holdings to market to determine their o's value for periodic reportiingnmarket g and performance measurement purposes. If thesecurity market is illiquid, the prevail price may misstate the true value of the and can reduce returns/performance. 2. Marki n g-to-market i s also necessary wi t h repurchase agreements to ensure that the colcanlateral is adequate the funds being lead tovalue a higher cost oftofundssupport and decreasing portfolborrowed. io returns.A lower valuation bid-ask spread.

marking-to-market.

Professor's Note: CPA Institute seems to use "Low Liquidity" and "high Liquidity risk" interchangeably. I believe you can treat these (liquidity and Liquidity risk) as the same concept on the exam, although you should remember that Low Liquidity means high Liquidity risk.

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing in Bonds

LOS 53.1: Describe the exchange rate risk an investor faces when a bond makes payments in a foreign currency. CFA® Program Curriculum, Volume 5, page 338

Ifreturns a U.Son. investor purchases a bond that makes payments in a forei g n currency, dollar the investment will depend on thein value) exchangeof therateforeibetween the dolwilarll andreducethe foreign currency. A depreciation (decrease g n currency theflowsreturns to a dollar-based investor. Exchange rate risk i s the risk that the actual cash the investment may be worth less in domestic currency than was expected when from the bond was purchased. LOS 53.m: Explain inflation risk. CFA® Program Curriculum, Volume 5, page 338

Inflation risk refers to the possibility that prices of goods and servi c es in general will moreincome, than anexpected. Because filexveled-coupon bonds pay a constant periodicandstream ofincrease i n terest increasing pri c e decreases the amount of real goods services that bond payments will purchase. For thi s reason, infl a ti o n risk is sometimes referred toin asnominal purchasing power risk.redWhen expected inflationthe valincreases, the resulting increase rates and requi yiel d s wi l decrease u es of previousl y issued fixed-income securities. LOS 53.n: Explain how yield volatility affects the price of a bond with an embedded option and how changes in volatility affect the value of a callable bond and a putable bond. CFA® Program Curriculum, Volume 5, page 339

Without any volatil i t y in interest rates, a cal l provi s ion and a put provision have littl e value, if any,inassumi ng no changes initycredit qualityincreases that affect market values. In general, anandincallcrease the yield/price vol a ti l of a bond the val u es of both put options options. We alreadyoption-free saw that the(straight) value ofbonda callbyablethebond isoflessthethan theoptionvaluebecause of an otherwise­ identical value call the cal l option is retained by the issuer, not owned by the bondholder. The relation is: value of a callable bond = value of an option-free bond -value of the call Anmarket increase in yi e ld volatil i ty i n creases the val u e of the call option and decreases the value of a callable bond. A put option is owned by the bondholder, and the price relation can be described by: value of a putable bond = value of an option-free bond + value of the put ©20 12 Kaplan, Inc.

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Risks Associated With Investing in Bonds

Anvaluincrease in yieldbond. volatility increases the value of the put option and increases the e of a putable Therefore, we conclude thatbonds increases in interestways.rateVolatility volatilityriskaffectforthecallable pricesbonds of is call a bl e bonds and putable in opposite thevolarisk lity will increase, and volatility risk for putable bonds is the risk that tilitythatwillvolati decrease. LOS 53.o: Describe sovereign risk and types of event risk. CFA® Program Curriculum, Volume 5, page 339

Event risk occurs when something signifi c ant happens to a company (or segment of the market) thatg valhasue aofsudden and substanti al riimpact onrespect its financial condition andmany on the underl y i n an i n vestment. Event s k, wi t h to bonds, can take forms: (e. g . , hurricanes, earthquakes, or industrial accidents) impair the ability ofexample, a corporation to meetcompany' its debtsobligations if thedebtdisaster reducesmaycashbeflaffected ow. For by an insurance ability to make payments property/casualty insurance payments in the event of a di s aster. [e.g., ofspin-offs, leveraged buyouts (LBOs), and mergers] mays have an impact on the value a company' s debt obli g ations by affecting the fi r m' cash flows and/or the underlying assets that serve asar colcompanies lateral. This maysameresulindustry. t in bond-rating downgrades and may also affect si m i l i n the suchexpenditures as changestoinmeet cleannewair requirements, maymaycausereduce companies tocashincuravailarge cash regulations. This then the l abl e to bondholders and result i n a rati n gs downgrade. A change i regulaoftiosecuri ns forty,somesuchfinasancial institutions prohibiting them fromcanholding certain types junk bonds (those rated bel o w BBB), l e ad to a volume of sales that decreases prices for the whole sector of the market. Investors buy bonds foreignreasons governments face sovereign with credit risk, we canwhoidentify threeofseparate that soverei gn bond pririsk.cesJustmayasdecline. The credit spread for a sovereign bond may increase although its rating has not 1. changed. 2. A sovereign bond's credit rating may decline. A sovereign bond can default. Pria foreign ce declines in sovereign bonds dueintoterest creditandevents usuallyin result from This deterioration in government' s abil i ty to pay principal the future. inability tohigpayh government typically is spending, the result orof both. poor economic conditions that result i n low tax revenues, cant decline in Greek government debt prices in 2009-2010 is an example ofThesuchsignifi a scenario. With foreign bonds we must also consider the fact that the forei g n government may refuse topoorpayfi(repudiate) the poor debt ateconomic some future date. Historical ly,theinability tocause pay of due to s cal policy and conditions has been primary sovereign defaults. •

Disasters

Corporate restructurings

Regulatory issues,

3.

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing in Bonds

KEY CONCEPTS

LOS There are many risk-uncertainty types of risk associated with fixprices ed income securities: about bond due to changes in market interest rates.risk-the risk that a bond will be called (redeemed) prior to maturity under the terms of the call provision and that the funds must then be rei n vested at the then-currentri(lower) yiuncertainty eld. about the amount of bond principal that will be s k-the repaid priorritosk-the matuririskty. that changes in the shape of the yield curve will reduce bond values. the risk of a decrease in bond value amcrease. ratingsrisk-includes downgrade, and the riofskdefault, that thethecrediriskt spread for a particular ratingduewiltol risk-the riskprice). that an immediate sale will result in a price below fair value (the prevailing market risk-the risk that the domestic currency val u e of bond payments i n a foreign currency wirisk ll decrease due toinexchange rateinterest changes.rate volatility will affect the ri s k-the that changes expected values ofrisk-the bonds witrihskembedded options. thatcashinflfloawstionfrom will abefixhigher than security. expected, eroding the purchasing power of the ed income risk-the risk of decreases i n a security' s value from disasters, corporate restructurings, or regulatory changes that negatively affect theorfirnot m. be able to make risk-the ri s k that governments may repudi a te debt debt payments in the future. LOS a bond's coupon rate is less than its market yield, the bond will trade at a discount When to its par value. When a bond' s coupon rate i s greater than its market yield, the bond will trade at a premium to its par value. LOS ThePositively level of a relbond'ateds interest rate risk (duration) is: to its maturity. Negativelyy relrelaatedted toto itsits market coupon YTM. rate. Negativel Less over some ranges for bonds with embedded options. LOSprice of a callable bond equals the price of an identical option-free bond minus the The value of the embedded call. 53.a

Interest rate

Call

Prepayment

Yield curve

Credit

Liquidity

Exchange rate

Volatility

Inflation

Event

Sovereign 53.b

53.c

• •

53.d

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #53

-

Risks Associated With Investing in Bonds

LOS 53.e bonds have interest rate risk between reset dates, and their prices can differ Floating-rate from their par values, even at reset dates, due t o changes i n liquidity or i n credit ri s k after they have been issued. LOS 53.f of a bond is the approximate percentage price change for a change in The duration yield. The yield.dollar duration of a bond is the approximate dollar price change for a change in LOS 53.g Yiportfolio' eld curves value risk ofmaya bond portfolio isathenon-paral risk (inleaddition totheinyield terestcurve rate risk) thatintheits decrease due to l shift in (change shape). When yielthed true curvepriceshiftseffects are notbecause parallel,yieldstheonduration of a bond portfol ioportfolio does notmay capture the various bonds in the change by different amounts. LOS 53.h to an investor of a callable or prepayable security: Disadvantages Timing of cash fl o ws is uncertain. Principal is most liokw.ely to be returned early when interest rates available for reinvestment are l Potential price appreciation is less than that of option-free bonds. 53.i has more reinvestment risk when it has a higher coupon, is callable, is an ALOS security amortizing security, or has a prepayment option. Aofprepayable security haswhengreater risk because of the probability acceleratedamortizing principal payments interestreinvestment rates, including reinvestment rates, fall. LOS 53.t riskj includes: CrediDefaul t ri s k-the probability of default. Downgrade risrik-the probabilityabout of a reduction inyield the bond rating. Credi t spread s k-uncertainty the bond' s spread to Treasuries based on its bond rating. Credi t ratings arewitdesigned to indicate to investors a bond' serelati ve probability of rated default. Bonds h the lowest probability of default recei v ratings of Bonds AA, BBBBBareoralslower. o considered investment grade bonds. Speculative or high yield bondsA,areandrated 1%

1%

• •

AAA .

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing in Bonds

LOS of liquidity can have adverse effects on calculated portfolio values and, therefore, Lack onevenperformance measures for a portfolio. Thi s makes liquidity a concern for a manager though sale of the bonds is not anticipated. LOSinvestor who buys a bond with cash flows denominated in a foreign currency will see thethe valforeiuegnofcurrency the bonddecli decrease if the forei g n currency depreciates (the exchange val u e of nes) relative to the investor's home currency. LOS If inflationandincreases decreased bond valunexpectedl ues fall. y, the purchasing power of a bond's future cash flows is LOS Increasesdecreasi in yielndgvoltheatility increase theablevalue of(because put andthecallbondholder options embedded in call) bonds, val u e of a cal l bond i s short the and increasing the value of putable bonds (because the bondholder is long the put). LOS Event riskdiencompasses non-fintheancialissuer'events thatngscanorhurt the value ofvalues; a bond,takeovers or including s asters that reduce s earni diminish asset restructuri nregul gs thatatiocann thathavecannegati ve effects on thes earnings priority ofor bondholders' claims;foranda changes in decrease the issuer' narrow the market particular class of bonds. Soverei gton repay risk isithe possibility that a economic foreign government willandrefuse to pay deficit or become unable t s debts due to poor conditions government spending. 53.k

An

53.1

53.m

53.n

53.o

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #53

-

Risks Associated With Investing in Bonds

CONCEPT CHECKERS

with a 7.3% yield has a duration of 5.4 and i s tradi n g at $985. If the 1. Ayiebond decreases to 7.1 o/o, the new bond price is to: A.B. ld$974. 4 0. $995. 6 0. $1 ,091.40. 2. price If interest rate volatility which of the following bonds will experience a A.B. AA putable callable bond. bond. C. A zero-coupon, option-free bond. 3. A noncallable, AA-rated, 5-year zero-coupon bond with a yield of 6% is to have: A.B. reinvestment interest rate risk.risk. C. default risk. The current price ofpricea bond is 102.50. IfWhat interestis rates change byof the0.5%,bond?the 4. value of the bond changes by 2.50. the duration A.B. 2.50. 2.44. 4.88. of the following bonds has the interest rate risk? 5. Which A.B. 5%5% 11 0-year 0-year callable bond. putable C. 5% 1 0-year option-freebond.bond. 6. AA.flotheating-rate security wi l have the greatest duration: theresetresetdate.date. the day day before after the B.C. never-fl oating-rate securities have a duration of zero. 7. The duration is 5.4of7, theandbond its current price isif$986. fol2%?lowing is theof a bondestimate price change interest30. Which rates of theby A.B. -$107. -$109.490.0. $109.40. 8. A$981. straight 5%calbond has twothatyearsis theremai ningin every to maturity andas theis priced at bond, 6 7. A l abl e bond same respect straight except for the call feature, is priced at $917. 6 0. Wi t h the yield curve fl a t at 6%, is the80.value of the embedded call option? A.what $45. B. $64. 07. $101.00. closest

c.

increases,

decrease?

least

likely

c.

greatest

best

increase

c.

c.

Page 42

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing in Bonds

straight 5%000coupon bond hasA putable two yearsbond,remaini nhgistothematurity andeveryis priced at 9. A$981. 6 7 ($1, par val u e). whi c same in respect asparthevalstraight bond except for the put provision, is priced at 101. 7 6 (percent of ue). With the yield curve flat at 6%, what is the value of the embedded put option? A.B. $17.60. $26. $35.797.3. 10. Which ofto thefixed-income following securities? is to fall under the heading of event risk with respect A.B. AOnechange inacquisition rate regulation. fi r m' s by another. C. A Federal Reserve decrease in money supply. 11. Which ofoating-rate the followibond. ng 5-year bonds has the interest rate risk? A.B. AA flzero-coupon bond.bond. C. A 5% fixed-coupon 12. Anbondsinvestor is concerned about interest ratety)risk.has Whi ch ofintheterestfollrate owingrisk?threeThe (similar except for yi e l d and maturi the A.B.bond5% 5%with:yiyieelldd and 10-year maturi ty.y. and 20-year maturi t C. 6% yield and 1 0-year maturity. 13. Which of the following statements about the risks of bond investing is A.B. AA bond rated callAAAprotection has no credit risk.atility risk. bond with has vol C. A U.S. Treasury bond has no reinvestment risk. 14. Which of theinvestor? following securities will have the reinvestment risk for a long-term A.B. AA 6-month 1 0-year, zero-coupon bond. T-bill. e amortizing bond. C. A 30-year, prepayabl 15. AA. 2-year, zero-coupon U.S. Treasury note is to have: i n fl a ti o n risk. currencyity risk. C.B. volatil risk. c.

least likely

highest

least

most

accurate?

least

least likely

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing in Bonds

ANSWERS - CONCEPT CHECKERS x

1.

B

The percentage price change, based on duration is equal to -5.4 The new price is 1 .0 1 08 x 985 = $995.64.

2.

A

An increase in volatility will increase the value of the call option and decrease the value of a callable bond. A putable bond will increase in value. The value of option-free bonds will be unaffected.

3.

B

A zero-coupon bond, as a security, has no reinvestment risk because there are no cash flows prior to maturity that must be reinvested. A double-A bond has some {small) default risk. Zero-coupon bonds have the most interest rate risk for a given maturity.

4.

C

The duration is computed as follows: . durauon

=

percentage change in price change in yield as a decimal

2.50

102.5 0.005

=

2. 44o/o 0.5%

=

(-0.2%) = 1 .08%.

4.88

5.

C

Embedded options reduce duration/interest rate risk.

6.

B

The duration of a floating-rate bond is higher the greater the time lag until the next coupon payment/reset date. The greatest duration/interest rate risk is, therefore, immediately after the coupon has been reset.

7.

B

The approximate dollar change in price is computed as follows: dollar price change = -5.47

8.

B

x

0.02

x

986.30 = -$107.90

The option value is the difference between the value of an option-free bond and the corresponding price of the callable bond. Its value is computed as: call option value = $981 .67 - $9 17.60 = $64.07

9.

C

The value of the embedded put option is the difference between the price of the putable bond and the price of the straight bond. So it is computed as: option value = $ 1 ,0 1 7.60 - $981 .67 = $35.93

Page 44

1 0. C

Event risk refers to events that can impact a firm's ability to pay its debt obligations that are separate from market risks. The Fed's actions can impact interest rates, but this is a market risk factor, not event risk.

11. B

The zero-coupon bond will have the greatest duration of any of the three bonds and, as such, will be subject to the greatest interest rate risk.

12. C

Interest rate risk is inversely related to the yield and directly related to maturity. All else equal, the lower the yield, the greater the interest rate risk. All else equal, the longer the maturity, the greater the interest rate risk. This bond has the higher yield and the shorter maturity, and, thus, has the lowest interest rate risk.

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing i n Bonds 13. B

A Treasury bond pays semiannual coupon interest and, therefore, has reinvestment risk. A triple-A rated bond can lose its AAA rating, so it has downgrade risk, a component of credit risk. A bond with a call feature has volatility risk even when the call cannot be exercised immediately. The call feature still has value (to the issuer), and its value will be affected by volatility changes.

14. A

A 10-year, zero-coupon bond has no cash Bows prior to maturity to reinvest while the entire amount invested in 6-month bills must be reinvested twice each year.

15. C

It will have inflation (purchasing power) risk. It will have currency risk to non-U.S. dollar investors. Volatility risk only applies to bonds with embedded options.

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The following is a review of the Analysis of Fixed Income Investments principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in:

OVERVIEW OF BOND SECTORS AND INSTRUMENTS Study Session 15

EXAM FOCUS

This reviology ew introduces thefixedvarious types of fixedPayincome securities andto thea fairmechanics amount ofof termi n rel a ti n g to income securities. special attention these securities; that is, how they pay, when they pay, and what they pay. The additional information s nice, butoutcome likely notstatements crucial. Tryso that to gaiyoun enough understanding ofwhen the terms liarestedusedin thein ailearning wil l understand them they question. Knowi n g the basics about Treasury securities, mortgage-backed securities, andtmunicipal securities is important asmore a foundation for muchonoffithexedmateri al onvaluation debt securi i e s that fol l ows, as well as for the detai l e d material income and risk that is contained in the Level II and Level III curriculum. LOS 54.a: Describe features, credit risk characteristics, and distribution methods for government securities. CFAÂŽ Program Curriculum, Volume 5, page 357

Bonds gissued byThea country' sgcentral government are referredconsists to as sovereign bonds or soverei n debt. soverei n debt of the U. S . government of U. S . Treasury securities, whi c h are considered to be essentially free of default risk. The sovereign debt ofbe other countries is considered to havemarket, varyinganother degreescountry' of credits forei risk.gSoverei gmarket, n debt canor issued in a country' s own domestic n bond in the Eurobond market. Sovereiingnother debt currencies is typicallyasissued inBond the currency of the issui ngascountry, butandcanPoor'be s, issued well . rati n g agencies, such Standard rate sovereign debt based on itsin theperceived credit risk,(localoftencurrency) giving different ratings to soverei g n debt denominated home currency and to the sovereign debt of the same country denominated in foreign currency. Professor's Note: Remember that it is often easier for a country to print currency (expand the money supply) in order to meet obligations denominated in the home currency than it is to exchange the local currency for a fixed amount offoreign currency. Thus, local currency sovereign debt often receives a higher rating than the foreign currency denominated debt ofthe same country.

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments

There are four primary methods used by central governments to issue sovereign debt. this price method,(lowest the debt isatauctioned 1. periodically according to a cycle and theUnderhighest yield) whi chsystem the enti r e issue to be auctioned can be sold i s awarded to all bidders. Thi s i s the used by the U.S. Treasury. 2. the bonds at the price(s) that they bid. Under this method, winning bidders receive refers tomarket a methodconditions where thearecentral government auctions 3. Annew securities when it determines advantageous. 4. Abonds. Underrefers to the issuance and auction of bonds identical to previousl y issued this system, bonds are sold periodically, not according to a regular cycle. Regular cycle auction-single price.

Regular cycle auction-multiple price. ad hoc auction system

tap system

LOS 54.b: Describe the types of securities issued by the U.S. Department of the Treasury (e.g., bills, notes, bonds, and inflation protection securities), and distinguish between on-the-run and off-the-run Treasury securities. CFA® Program Curriculum, Volume 5, page 358

(Treasuries) areU.S.issuedgovernment, by the U.S.theyTreasury. Because totheybe arefreebacked byfromthecredit full fairistkh and credit of the are considered (though they' re still subject to in(2)terestnotesrate/price risk).andThe(3)Treasury issues three distinct types of securities: (1) bills, and bonds, inflation­ protected securities. (T-bills) haveonlymaturiti es of(par)lessvalue than atonetheyearmaturi and tdoy date. not make explici t interest payments, paying the face T-bills are sold at(likea discount to parbonds). value and interest isonreceived when thempares calvalueled is paid at maturity zero-coupon The interest T-bills is someti siinnaceseparate, the interestexpl(difference between theon purchase pricenotes.andSecurities the par value) istype not made i cit payment, as it is bonds and of this are known as securities. There aredue to holidays. They are28,also91,known and 182as 4-week, days, adjustable byandone6-month day (up or down) 3-month, T-bills, respecti v ely. Periodical ly,daysthe Treasury also issues bills with maturities rangintog from a few to si x months to hel p overcome temporary cash shortages prior the quarterly receipt of tax payments. and pay semiannual coupon interest at a rate that is fi x ed atmaturities issuance.ofNotes original maturities of 2, 3, 5, and 10 years. Bonds have original 20 orhave 30 years. Prior to 1984, some Treasury issuedbonds that aresincecallable maturity. The Treasury has notbonds issuedwerecallable 1984. at par five years prior to Treasury securities

Treasury bills

implicit interest

pure discount

three maturity cycles:

Treasury notes

cash management

Treasury bonds

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments

Treasury bond and note prices in the secondary market are quoted in percent and 32nds of 1 o/o of face value. A quote of 102-5 (sometimes 102:5) is 102% plus 1._ % of par, which for a $100,000 face value T-bond, translates to a price of: [102 ;2 ] o/o $100,000 1.0215625 X $100,000 $102,1 56.25 32

+

X

=

=

Since 1997,infltheation-protected U.S. Treasury has issued1 0-year notes and 20-year bonds are offered(TIPS). Currently, 5and by the Treasury. TIPS work as follows: TIPS make semiannual coupon interest payments at a rate fi x ed at issuance, just li k e notesparandvalue bonds.of TIPS begins at $1,000 and is adjusted semiannually for changes The in theadjusted Consumer PriceisIndex (CPI).for If thereperiod. is deflTheationfixed(fallcoupon ing priceratelevels), the par value reduced i s paid semiannually asn thea percentage offromthethe inflation adjustment is taxed as income in the Any i n crease i par value year of the adjustment: . . .USted par value stated coupon rate TIPS coupon payment mflanon-adJ 2 For example, considerlater, a $100,the000 par rate valueofTIPS with(CPI) a 3o/o iscoupon rate,parsetvalue will be issuance. Six months infl a tion 4%. The increased by one-half of the 4% (i.e., 2%) and will be 1.02 100,000 = $102,000. The fi r st coupon wil l be one-half of the 3% coupon rate ti m es the inflation adjusted par value:period 1.5% wi102, 0used 00 = to$1,530. Any percentage change in0the00 toCPIa new over theinflation-adjusted next 6-month l l be adj u st the par value from $102, val u e, whi c h wi l l be multiplied by 1. 5 % to compute the next coupon payment. Ifreceithevesadjusted par value (per bond) i s greater than $1, 0 00 maturity, the holder adj000usted valuaetion), as theholders maturityreceipayment. adjustedty asparthisvalueis theis lminimum ess thanthe$1,repayment (dueparamount. to defl ve $1,000If thematuri Treasury Inflation-Protected Securities

that

inflation adjusted par value.

x

=

----''----

-

-

at

annual

semiannual

x

x

at

at

On-the-Run and Off-the-Run Treasury Securities

Treasury issues are divided into two categories based on their vintage: 1. are the most recently auctioned Treasury issues. 2. by a more recently auctioned are older issues thatIssueshavereplbeen replaced (asmore the most traded issue) issue. a ced by several recent issues are known as issues. On-the-run issues

Off-the-run issues

well off-the-run

Page 48

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments

The distinction isoff-the-run that the on-the-run issues prices are moreof on-the-run actively traded andprovide thereforebetter more liquid than issues. Market issues information about current market yields. LOS 54.c: Describe how stripped Treasury securities are created and distinguish between coupon strips and principal strips. CPA® Program Curriculum, Volume 5, page 360

Since the U.S. Treasury does not issue zero-coupon notes and bonds, investment bankers began stripping theinvestor couponsdemand. from Treasuries to createarezero-coupon securitTreasuries ies of variousor maturities to meet These securities termed stripped Treasury strips.Principal In 1985,Securities the Treasury introduced theUnder SeparatethisTrading of theRegiTreasury stered Interest and (STRIPS) program. program, issues coupon-bearing notes andto buy bondslargeas iamounts t normallofy does, butissues,thenstriitpalthelowscoupons certain government securities dealers these from the principal, repackage the cash fl o ws, and sell them separately as zero-coupon bonds, at discounts to par value. For example, a 10-year T-note has 20 coupons and one principal payment; these 21 cash flsecurities ows can be(Treasury repackaged as 21intodifferent zero-coupon securities. The stripped strips)andaresolddivided two groups: 1. stripped Coupon from stripsthe(denoted originalassecurirefers ty. to strips created from coupon payments 2. Principal strips refers to bond and note principal payments wi t h the coupons stripped stripped off. notesThose derived from stripped bonds are denoted and those from ci)

bp

np.

0

Proftssor's Note: While the payments on coupon strips and principal strips with the same maturity date are identical, certain countries treat them differently for tax purposes, and they often trade at slightly different prices.

STRIPS arefulltaxed by thee investors, IRS on theiresults r implicit interest (movement towardpriorpartovalue), which, for y taxabl in negati v e cash fl o ws i n years maturi t y. The TreasuryfromSTRIPS programpieces. also created a procedure for Treasury notes and bonds the individual reconstituting

LOS 54.d: Describe the types and characteristics of securities issued by U.S. federal agencies. CPA® Program Curriculum, Volume 5, page 363

Agency bonds are such debt assecurities issuedHome by various agencies(FHLB). and organizations the are U.S. government, the Federal Loan Bank Most agencyofissues ©20 12 Kaplan, Inc.

Page 49


Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments

obligations of the U.S. Treasury and technically should not be considered the same as Treasury securities. Even so, they are very high quality securities that have almost no risk of default. There are two types of federal agencies: 1. (Ginnie Mae) and the Tennessee suchVallas theey Authori Government National Mortgage Association t y (TVA), which are owned by the U.regiSs. trati government and arethese exemptsecurities from Securities andby Exchange Commission (SEC) o n. In general, are backed the full fai t h and credi t of theCorporation. U.S. government, except i n the case of the TVA and Pri v ate Export Funding Essentially, these securities are free from credit risk. 2. the Federal Home Loan Bank System, (GSEs)theinclude theNational Federal Mortgage Farm CreditAssociation System, Federal (Fannie Mae), the Federal Home Loan Bank Corporation (Freddi e Mac), and the Student Loan Marketi ng Association (Sallie Mae). These areU.Spri. Congress. vately owned, butissue publicly chartered organizations, and were created by the They their securities directly in the marketplace and expose i n vestors to some (albeit very little) credit risk. are securities that are notThesebacked bymany collateral (i.e., structures they are unsecured). GSEs commonly issue debentures. are of maturity coupon interest paying securities or discount securities (referred to as bills).and can be not

Federally related institutions,

Government sponsored enterprises

Debentures

LOS 54.e: Describe the types and characteristics of mortgage-backed securities and explain the cash flow and prepayment risk for each type. CFA® Program Curriculum, Volume 5, page 3 64

(MBSs)butarealsobacked (secured)tobyservice poolstheof mortgage loans, which not only provide the debt. A mortgage­ backed mortgages.security is any security where the collateral for the issued security is a pool of The cash flloans ows from a mortgageloans are diinfferent frommake the cash flowsof ofequala coupon bond. Mortgage are amortizing that they a series payments consisting of the periodic interest on the outstanding principal and a partial repayment of the principal amount. Residential real Inestatethe early mortgages arethetypigreater callyportion for 30 years and consist of 360 equal monthly payments. years, of the payment is interest, and the final payment, after 30 years, is almost all principal. Mortgage-backed securities

collateral

cash flows

� Professor's Note: Amortizing loans and amortization schedules are covered in the � Study Session on Quantitative Methods.

The Government National Mortgage Association (GNMA), the Federal National Mortgage Association (FNMA), and the Federal Home Loan Mortgage Corporation Page 50

©2012 Kaplan, Inc.


Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments

(FHLMC) allandissuetheymortgage-backed securities. All three areMae, sponsored byMae,the and U.S. government are known now by the names Ginnie Fannie Freddi e Mac. Each purchases mortgages from lenders to provide funds for mortgage loans. The agencies issuecollthree types ofmortgage mortgage-backed securities: mortgage passthrough securities, a teral i zed obligations, and stripped mortgage­ backed securities. Thi s process of combining many si m i l ar debt obligations as the collateral for issuing securitiestheisdebt'callsedattractiveness toTheinvestors primaryandreason for mortgage securitization i s to increase to decrease required rates of return, increasing the availability of funds for home mortgages.investor There are threeof principal, types of cash fl(3)owsprincipal from a mortgage: (1)inperiodic interest, (2)principal scheduled repayments and repayments excess of scheduled payments. Borrowerswithout (issuerspenalty, of mortgages) typical ly have the principal right to payamount additional principal amounts reducing the outstanding and thereby reducing future interest cash fl o ws. If the borrower sells the property backing thecan mortgage, the entire principal amount i s repaid at one time. Because the borrower accelerateriskprincipal repayment, theexcept ownerthatof prepayments a mortgage hasmay be part of or all Prepayment is similar to cal l risk ofcalledthe outstanding principal amount. (Partial prepayment of remaining principal is This,when in turn,yieldsubjects the mortgageareholder principal may be repaid s for reinvestment low. to reinvestment risk, as Ginnie Mae,interest Fanniand e Mae,principal and Freddi e Macfrom all guarantee the timely payment of They scheduled payments thei r mortgage-backed securities. arecertain ablestandards to do thisregarding because they only purchase or underwri t e loans that conform to to the value of the propertyborrower securing it.credit ratings, loan size, and the ratio of each loan Athrough proportionally to each security passesholder. the payments made onmortgage a pool ofpassthrough mortgages A holder of a security that owns a o/o portion of the issue wil l receive a 1 o/o share of al l the monthly cash flows Each from monthl all the mortgages, after a small percentage fee forprincipal administration is and deducted. y payment consists of interest, scheduled payments, prepayments ofalprincipal inws,excess of the scheduled amount. Since each holder recei ves aa sipercentage of l cash fl o a mortgage passthrough security has prepayment ri s k as ngle mortgage would,ofbutmortgages. there is some diversi ficationtend benefitto accelerate from the pooling of hundreds or thousands Since prepayments when interest rates fall, due to the refi n anci n g and early payoff of existing mortgage loans, security holders cansinceexpectthetomortgages receive greater decreased in the principal pool werepayments issued. when mortgage rates have (CMOs) are created securities, from mortgage passthrough certifi c ates and referred to as derivative mortgage-backed since they than are derived from a simpler MBS structure. CMOs have a more complex structure mortgage passthroughs. AtheCMOcashissue hasfromdifferent each of(i.whie., ctheir h hasclaims a are dinot fferent type of claim to fl o ws the pool of mortgages just a proportional claim on the total cash flows from the pool). securitization.

prepayment risk.

curtailment.)

mortgage passthrough security 1

Collateralized mortgage obligations

tranches,

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments

Professor's Note: Tranche is from the French wordfor "slice. " In finance, when a security issue consists ofdiffirent classes ofsecurities with diffiring claims and especially with diffiring risks, the diffirent classes ofsecurities are called tranches. You will likely run into this term only in reference to the diffirent classes of securities that make up a CMO.

Anillustrate exampla eCMO of a simple CMO structure with arethreecreated tranchesoutwiloflahelp to structure. Assume that three tranches passthrough security. Let'ng sparcallvalues. them The Tranches I, II, areandtheIII.detail Theys receive interest ontotheeachbasiofs theof their outstandi foll o wing of the payments three tranches. I (the segment of the issue) receives net interest on outstanding 1. Tranche principal andpaidall off.of the principal payments from the mortgage pool until it is completely 2. Tranche IIall(theof the principal payments receiafter ves itsTranche share ofI hasnet been interestcomplandetely startspaid off. receiving Prior to that, it only receives interest payments. IIIrepayments (the after Tranches receives monthly net interest and startspaid receivioff.ngPrior all to 3. Tranche principal I and II have been completely that, it only receives interest payments. Tranche I has the shortest expected maturity and may appeal to an investor wi t h a preference forinsecurities with a shortersecurities time horizon, whoOther previously couldwith not participate the mortgage-backed market. structures, prepayments primarily affecting only some of the tranches, are used to redistribute prepayment risk.Investors The tranches with lessto bear prepayment risk riwillsk will become more attractivewittoh some investors. better able prepayment fi n d the tranches higher prepayment risk attractive. are eitheraffect the principal orofinterest portions(IO)of astrips mortgage passthrough securi t y. Prepayments the val u es interest-only and prepayments principal-onlybecause (PO) strips differently. The holder ofis arecei principal-only strip will gain from the face val u e of the security v ed sooner rather than later. Theratesholarederhigher of an interest-only striis only p wilpaid l receive lessoutstanding total payments when prepayment since interest on the principal amount, which is decreased by prepayments. sequential

short-term

intermediate-term)

long-term)

Stripped mortgage-backed securities

LOS 54.f: Explain the motivation for creating a collateralized mortgage obligation. CFAÂŽ Program Curriculum, Volume 5, page 369

The passthrough securitiesCMOs is to inherent in mortgage and/or The CMOallstructure takesprincipal the cashpayments flows from(boththeschedul mortgageed payments pool and, andin aprepayments) simple structure, o cates any sequentially over time to holders of different CMO tranches, rather than equally to motivation for creating

Page 52

redistribute the prepayment risk create securities with various maturity ranges.

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments

all security Creatirinsgk.a CMO does not alter the risk of prepayment, it redi stributesholders. prepayment Aspreferences-maki a general rule, CMOs arencreated to satisfy a broader range of investor risk/return n g investi g i n mortgage-backed securi t ies more appeali n g to a wi d er audience and decreasing overall borrowing costs. overall

LOS 54.g: Describe the types of securities issued by municipalities in the United States and distinguish between tax-backed debt and revenue bonds. CFA® Program Curriculum, Volume 5, page 371

Debt securities issued(or by stateforandshort). local governments in theare Uni tedbyStates arecounties, known ascities, issued states, and other political subdivisions (e. g . , school, water, or sewer districts). These bonds ofteneachissuedwithas its own maturithatty date is, a and largercoupon issue israte.divided into a series of smallerareissues, Municipalis exempt bonds arefromoftenfederal referred to astaxes. Note that, or while interest bonds, since themay coupon interest income income beat taxthe free, real i zed capital gai n s are not. They are subject to normal capital gai n s taxes federal level. However, not all municipal bonds are tax exempt; some are taxable: Different states tax(i.municipal securities differently; theas taxvastexempt, majoritybut ofconsider states treat e . , those i s sued within the state) the interest income earned on out-of-state bonds as fullyoftaxabl estate . Thus,is freethe ifrom nterest income earned on most in-state bonds held by a resident that state and federal income tax.certain Such bonds arestandards referred into order as to qualify A municipal bond must meet federal for the tax-exempt status. If they don't, the bonds are considered taxable and the (they could stillthanbe the exempt from state taxes). rather rule, as most municipal issues are exempt from federal taxes. Anfirmopinion as to the tax-exempt status of the bonds, typically by a well-respected l a w issued.specializing in municipal bond issues, is provided to purchasers when the bonds are municipal bonds

munis

Municipal bonds

serial bonds,

tax-exempt

tax-free

Tax exempt.

their own bonds

both Taxable.

double tax free.

interest income on these bonds is subject to federal income tax Taxable municipal bonds are the exception

Tax-Backed Debt and Revenue Bonds

Tax-backed bonds, also called general obligation (GO) bonds, are backed by the ful l faith, of thespecial issuer.districts, Tax-backed debt is issued by school districts, towns,credit, cities, andcounties, states, and and include the followi ng types: to a statutory limit on taxes that may be raised to pay off the obligation. is subject the most common type of GO bond, is secured by the full faiincludes th andthecrediability t of theto impose borrowerindividual and backedincome by itstax,unlimited taxiproperty ng authority, which sal e s tax, tax, and corporate tax. This is the more secure form of GO. taxingpower

Limited tax GO debt

Unlimited tax GO debt,

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a special clabyss additional of GOs, areresources backed not only byinclude the issuing authority' s taxing power, but also that could fees, grants, and special charges that falarel outside the general fund. alsofundsknown as during times of shortfal Statesl. someti m es act as a back up source of for issuers However, the state' s obligation is not legall y binding, but is a "moral obligation. " Thesecurity state mayof appropriate funds from its general fund. This enhances the such bonds. Debt orsupported by programs possess a guarantee by the state federal government, whi c h i s a l e gal l y enforceable contract and i s used normally to assist the state's school system. Revenue bondsthearehelpsupported only through revenues generatedrevenue by projects thatcanarebe funded with of the original bond issue. For example, bonds issued to fund transportation systems, housing projects, higher education, health care, sports harbors, and ports. These bonds fall outside GO debt limits and do not requirearenas, voter approval. The distinctionbecause between a generalof aobligation and ais revenue bondto payis important for a bondholder, the issuer revenue bond obligated principal and ithere, nterestthe issuer does not make payments on the bond.by Inthecontrast, project. general If the funds aren' t obligation bonds are required to be servi c ed in a timel y fashion irrespective of the level ofvolve tax more income generated by the municipali t y. At issuance, revenue bonds typical l y i n risk than general obligation bonds and, therefore, provide higher yields. •

Double-barreled bonds,

Appropriation-backed obligations

moral obligation bonds. moral pledge

public credit enhancement

only ifa sufficient level ofrevenue is generated

Insured Bonds and Prerefunded Bonds

Insured bonds carrymadetheinguarantee of a thirdThepartythird-party that all principal and(insurance) interest payments wil l be a timely manner. guarantee typi c ally cannot be canceled; i t i s good for the life of the bond. There are several fi r ms that specialiresults ze in iprovi dingratings, insurancewhiforch municipal bond issues.yieldMunicipal bond insurance n higher reduces the required and improves the liquidi t y of the bonds. Insured bonds are especi a ll y common i n the revenue bond market, the general to broadenbuttheir appeal toobligation investors.bonds of smaller municipal issuers are often insured Prerefunded bondsescrow are bonds for which Treasurysuffi securities havemakebeenallpurchased and plrequi acedredinbond a special account in an amount c ient to the remai n ingmust payments. The Treasury securi t i e s' income and principal payments be suffi ccall ient date. to fundBonds the municipal bond's required payments until maturi ty orarethrough the fi r st that are prerefunded have l i t tle or no credit risk and likely to receive a rating of AAA .

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LOS 54.h: Describe the characteristics and motivation for the various types of debt issued by corporations (including corporate bonds, medium-term notes, structured notes, commercial paper, negotiable CDs, and bankers acceptances).

CFA® Program Curriculum, Volume 5, page 375 Rating Agencies and Credit Ratings

Rati n g agencies, such as Moody' s and S&P, rate specifi c debt issues of corporations. Some oftativethe factors factors can theybeconsider are quantitative, butratimany are issued qualitative. Even the quanti somewhat subjecti v e. The n gs are to indicate reltheatisecurity ve probability that all promised paymentslooking. on theRati debtngswionll belong-term made overbonds the liwifellof and, therefore, must be forward consider factors that may come into play over at least one full economic cycle. Some of the firm-specific factors considered are: Past repayment history. ability to adapt to changing conditions. Quali t y of management, The industry outlook andfirm.firm strategy. Overal l debt level of the Operating cashoffloliw,quidity ability(cash, to service debt.assets). Other sources sal a ble Competi position, regulatory environment, and union contracts/history. FiSusceptibility nancialtivemanagement and controls. to event risk and political risk. Some factors specific to a particular debt issue are: Priori t y of the claim being rated. Value/quality ofofanythecoldebtlateral pledged to secure the debt. The covenants issue. Any guarantees or obligations for parent company support. •

• • • •

• •

Professor's Note: It may help to remember the primary factors as all Cs: •�• Character ofthe issuer, Capacity to repay, the Collateral provided, and the Covenants of the debt issue. Secured Debt, Unsecured Debt, and Credit Enhancements for Corporate Bonds

Secured forms: debt is backed by the pledge of assets/collateral, which can take the following Personalproperty (e. g . , machinery, vehicles, patents) . Real property (e. g . , land and buildings) . Financial assets (e. g . , stocks, bonds, notes). These assets are marked to market from tiofmmore e to tiassets me toifmonitor theirinsuffiliquidati oBonds n values.backed Covenants may require a pledge values are c ient. by fi n ancial assets are called collateral trust bonds. • • •

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Inof default, all of thesethe cases, the bondholder holds a lienandon usethe thepledged property. In thethecase l i e n holder can sell the property proceeds to satisfy obligations of the borrower. In most cases of default, some mutual agreement wi l l be reached a new structure, but the ibondhol ders' claim on the pledged assets signifi cantlyforstrengthens their position n renegotiation. debt i s not backed by any pledge of specific col l ateral. Unsecured bonds are referred tobeen as debentures. They represent a general claim onassetsanygenerate assets offunds the issuer that have not pl e dged to secure other debt. If pl e dged upon liquidation i n excess of the obligation, then these excess funds are avai l abl e for satisfying thesatisfied claimsafterof unsecured debt holders. Subordinated debentures have claims that are (subordinate to) the claims of senior debt. Credi are theTypiguarantees be paidt enhancements in a timely manner. cally, theyof others take onethatofthethe corporate following debt forms:obligation wil Third-party guarantees that the debt obligations will be met. Often, parent companies guarantee the loans of their affiliates and subsidiaries. Letters ofcredit are issued by banks and guarantee that the bank will advance the funds to service the corporation's debt. Bond insurance can be obtained from firms that specialize in providing it. When analyzi n g credi t -enhanced debt, analysts should focus on the fi n anci a l strength of both theenhancement. corporationThe issuingprotection the debttoandthethebondfinancial strength of thethanpartytheprovidi ng credi t hol d er is no better promise ofguarantor the entity(enhancer) offering thecan credit enhancement. decrease in the creditworthiness of the A lead to a rating downgrade of the debt issue. Unsecured

Medium-Term Notes

Professor's Note: Be careful here. Medium-term notes are not necessarily medium-term or notes!

issues typicalanlyunderwriting (1) are sold alsyndi l at conce, (2) are soldtheonsalea fiofrm­the whole commitment basis whereby ate guarantees issue, and (3) consist of bonds with a single coupon rate and maturity. Medium-term (MTNs) differ from a regul a r corporate bond offering i n al l of these characteristics. MTNs are regi s tered under SEC Rule 415 (shelfregistration) which means that they need not bein sold all at once. Once registered, such securities can MTNs be "placedare sold on theovershelf" and sold the market over time at the discretion of the issuer. time, wi$1thmieach sal e satisfying some minimum dollar amount set by the i s suer, typical l y llion and up. MTNs are issued i n various maturities, rangi n g from nine months to periods as long as 100theyyears.wishIssuers provide maturity ranges (e.g., 18 months to two years) for MTNs that to sell and provide quotes forinterested those ranges, typicallytheas anotes spreadmaketo comparable maturity Treasury issues.yieldInvestors in purchasing Corporate bond

notes

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an offer to ranges the issuer'offered. s agent,Thespecifying theconfi facermsvaluetheandissuer'an sexact maturittoy wisellthinthose one of the agent then will i ngness MTNs and effects the transaction. The offering i s done by the issuer' s agent on a best-efforts basis. There is no firm commitment on the agent's part to sell a specific amount of bonds. MTNs can have fi x ed or fl o ating-rate coupons, can be denominated in any currency, and can have special features,cansuch as calls, caps, flderioors,vatiandve non-interest ratecreate indexed coupons. The notes issued be combined wi t h i n struments to the is special features that an investor requires. The combination of the deri v ati v e and notes called a structured security. Structured Notes

Aor note with a derivative. is a debtThissecurity created whena security the issuerthatcombines a typical bond is done to create has special appeal to the some institutional investors. The targeted institutional i n vestors face restrictions on types of securities they caninnovati purchase. Structured securities allow them to avoid these restrictions. As wi t h any v e debt securi t y, the motivation to i s sue them is to lower overall borrowing costs. Asor deri an example, consider anissuer institutional investora structured that is prohibited fromtheowning equity v ati v e securi t ies. An could create note where periodic coupon payments werenote basedwoulon dthestillperformance of an equity securityproduce or an equity index. This structured be a debt security, bur would returns closer to holdi n g the equity i n dex i t sel f . The mechani c s of creati n g this security would bederivative to issuethata debtrequires securitytheandpayment combineof aitfiwith an equity swap. An equity swap is a x ed rate of interest (theor equity couponindex rate oneachthe bond here), and pays i t s owner the rate of return on the equity period. By combining the bond wi t h the equity swap, a structured note is created that pays percentage rate of return on the equity semiannually instead of paying a fixed couponthepayment. Types of structured medium-term notes include: Step-up n tes Coupon rate increases over time on a preset schedule. Inversefl aters Coupon rate increases when the reference rate decreases and decreases when the reference rate increases. Deleveragedfl aters Coupon rate equals a fraction of the reference rate plus a constant margin. Dual-indexedfl aters Coupon rate is based on the difference between two reference rates. Range n es Coupon rate equals the reference rate if the reference rate falls within a speci f i e d range, or zero if the reference rate fall s outside that range. Index amortizing n tes Coupon rate is fixed but some principal is repaid before maturity, with the amount of principal prepaid based on the level of the reference rate. structured note

o o

-

-

o

• •

-

o

ot

-

-

o

-

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments

We wil cover equitynotes swaps,in interest rate swaps, andsession. otherForderiourvatipurposes ves commonly usedis tosufficient create structured a subsequent study here, it that you understand that structured notes are created by combining regular debt withtoderivati ve securiti es to maketheyaface"debtandsecuri ty" thatreduceallowsthecertain institutional investors get around restrictions thereby borrowing costs of the company creating the structured note. Commercial Paper: Directly-Placed and Dealer-Placed Paper

isrates a short-term, unsecured debtCommercial instrumentpaper used isbyissued corporations tomaturi borrow money at lower than bank rates. witorh less t i e s of 270 days or less, si n ce debt securities wi t h maturities of 270 days aremostexempt It is issued issues from beingSEC in theregistration. 2-day to 90-day range.with maturities as short as two days, with SimilaratosinglT-bills, commercial paperthe iface s typically issued as a pure discount security and makes e payment equal to val u e at maturity. There i s no active secondary market in commercial paper, and most buyers hold commercial paper until maturity. Commercial generall bycredicorporations hfirrelativel y strongorcredit and theinventories. proceedsFipaper arenance oftenissubsidiaries used toy fiissued nofancemanufacturi t givenng tofirmsthewitissue m'scommercial customers to fi n ance paper tobank fund customers' purchases of the parent company' s products. Issuers often keep unused lineeded nes oftocredipayt inoffplace to use in case new paper cannot be issued to generate the funds maturing paper. i s commercial paper that i s sol d to large investors without going through an agent broker-dealer. Large issuers willlarge deal wiamounts. th a select group of regular commercial paperorbuyers who customarily buy very iscommercial sold to purchasers throughto serve a commercial-paper dealer. Mostshort­ large investment firms have paper desks thei r customers' needs for term cash-management products. Commercial paper

Directly-placed paper

Dealer-placed paper

Negotiable CDs and Bankers' Acceptances

(CDs)bankaretoissued bya certain banks andamount sold plus to theirinterest customers. They represent a promi s e by the repay and, i n thatissuedway, arein speci similfaicr denominations to other bank deposits. In contrast to regul a r bank deposits, CDs are and for specifibyethed periods ofDeposit time thatInsurance can be ofCorporation any length. In(FDIC) the Uniuptedto States, CDs are insured Federal a maximum valuevalue in theareevent the issuing bank becomes only insolvent. Amounts above the maximum not insured and are, therefore, as secure as the bank that issues the CD. Typical bank CDsearliiner thethanUnited Statestycarry aofpenalty to the owner ifhowever, the funds arepermit withdrawn the maturi date the CD. sell thebyCDU.S.in banks the secondary at anyCDs, time.whereas Negotiable issued inthetheowner Unitedto States are termedmarket domestic U. S .CDs Certificates of deposit

CD Negotiable COs,

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dollaUnir denominated CDs issuedEurodollar by foreigCDs. n banksNegoti andabranches of U.S.maturities banks outside the t ed States are termed ble CDs have ranging from days up to fi v e years. The i n terest rate paid on them is call e d the London Interbank Offering Rate because they are primarily issued by banks' London branches. Bankers'are acceptances areofessential ly guarantees by a bank that ainternational loan will be trade. repaid.As They created as part commercial transactions, especially an example,45 consider antheimporter whoshipped. agrees The to payimporter for goodsgoesshipped tobankhimandbygets an exporter, days after goods are to his aletter lettermust of credi t statitontheg thatbanktheofbank will guarantee thethepayment, say $1actualmillion. Thisthe be sent the exporter before exporter will l y ship goods. When the exporter del i vers the shipping documents to her bank, she wil l recei v e forthe 45present days.value of the $1 million, discounted because the payment will not be made Theevidence final stepofinshipment the creationto theof aissuing bankers'bankacceptance is thats bank) the exporter' sthen bankaccepts presents the (the importer' which the evidence of shipment. It is this accepted promise to pay $1 million i n 45 days that is the bankers'andacceptance. Theborrower importerof wilthelfunds. sign documents evidencing hiss completed, obligationtheto hiimsporter bank becomes the When thi s final step i receives the documents necessary to receive the shipment of goods. The exporter' s bank canfundeitherinterested continueintoshort-term hold the acceptance oracceptance sell it to anis aindiscount vestor, often a money market paper. The instrument andthesellsshipping for thedate. present value of themarket single $1formillion payment to beismade 45limdays from The secondary bankers' acceptances itedtysodates. their liquidity is limited and most purchasers intend to hold them until their maturi The the riskfailthat the importer (the initial of thecredit funds)riskandof thea bankers' acceptiacceptance ng bank wilils both to make the promised payment.borrower LOS 54.i: Define an asset-backed security, describe the role of a special purpose vehicle in an asset-backed security's transaction, state the motivation for a corporation to issue an asset-backed security, and describe the types of external credit enhancements for asset-backed securities.

CFAÂŽ Program Curriculum, Volume 5, page 386

Credit card debt, automortgages loans, bank loans, and corporate recei vablfinancial es are often securitized iunderlying n the same way as are in the MBS structure. These assets areethethe collateral for bonds that are also asset-backed securities ( A BSs). Whil above types of underl y ing assets are the most common, innovati v e ABSs have al s o been created. David Bowie millionreleased dollar ABS where the underlyinIng one assetscase,weresinthegerroyalties from sold 25 ofa hi$55s albums priorissue to 1990. Š20 12 Kaplan, Inc.

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Role of a Special Purpose Vehicle

Awhich speciala corporation purpose vehicle, or special purpose corporation, is a separate legal entity to transfers the financial assets forto the an ABS issue.purpose The importance ofshithis i s that a legal transfer of the assets i s made special vehiclnge.itThis e lds the assets from the cl a i m s of the corporation' s general creditors, maki possibleBecause for the theABSassets issueareto receive athehigher credit ratingvehicle, than thetheycorporation asunlaikely whole. sold to special purpose are hi g hly tospecibeasubject to any cl a ims ari s i n g from the bankruptcy of the corporation, and the l purpose vehicle is termed a bankruptcy remote entity. Motivation for a Corporation to Issue an Asset-Backed Security

The motivation fornga thecorporation to aissue asset-backed securi tiescanis toissuereducethe borrowing costs. By transferri assets into separate entity, the entity bonds and receive her ratingyiethan reducesathehigrequired ld onthetheunsecured (ABS) debt.debt of the corporation. The higher rating External Credit Enhancements

Because asset-backed securities, on their own, may not receive the highest possible credit rating,or thesecurity. issuerCredit may choose tocanenhance the crediteitherratingexternal by providing additional guarantees quality be enhanced l y or i n ternall y. External credit enhancement commonly takes the following forms: Corporate guarantees, which may be provided by the corporation creating the ABS or itsLetters parent.ofcredit, which may be obtained from a bank for a fee. Bond insurance, which may be obtained from an insurance company or a provider speci a lizing in underwriting such structures. This is also referred to as an insurance wrap. None of thesetoenhancements comea tradeoff without between cost. Thethedecision ofenhancement how much and the enhancement provide involves cost of resulting decrease in the market yield required on the bonds. Noteguarantor, that the qual itytheofcredit a credit-enhanced security canis onlyrefleasctgood as the qualityinofthe the and rati n g of the security any deterioration guarantor's rating. •

LOS 54.j: Describe collateralized debt obligations.

CFA® Program Curriculum, Volume 5, page 388

Apromise collateralized debt obligation (CDO) is a debt instrument where the col l ateral for the to pay is andebtunderlying poolcanofbeother debt loans, obligations and evendebtother CDOs. These underlying obligations business mortgages, of devel oping countries, corporate bonds of various ratings, asset-backed securities, or even problem/ non-performing loans. Tranches of the CDO are created based on the seniority of the Page 60

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clainmgss todependi the cashng flonowstheofseniority the underlying assets, asandwelltheseas thearecreditworthiness given separate credit rati of the claim, of the underlying pool of debt securities. CDOs may be created by a sponsor that seeks to profi t on the spread between the rate to be earnedCDO), on theor underlying assets andor insurance the rate promised toseekithenCDO holderits(anloan arbitrage created by a bank company g to reduce exposure on its balance sheet (a balance sheet CDO). LOS 54.k: Describe the mechanisms available for placing bonds in the primary market and distinguish between the primary and secondary markets for bonds. CPAÂŽ Program Curriculum, Volume 5, page 389

The primary market for debt (newl y created debt securities) functions in a manner similar to thetheprimary marketandforin distributing equities. Typical liy,ng)antheinvestment bankertoisinvestors. involved iWhen n advising debt i s suer (sell debt securities thehaveinvestment banker actually purchases the entireis termed issue anda firm resellscommitment it, they are said to "underwri t ten" the issue. Thi s arrangement while the dealwiisll termed a put bought deal. In an underwritten offering of debt securities, the underwriter typi c al l y together a syndicancatereduce of othertheiinvestment bankers asto much aid in distributing the securities. The underwriters r risk by preselling ofexposure the offering asissuepossible to period their institutional clientsowniandnghedging the interest rate riskve of the for the they anticipate the securities. An al t ernati istermed for thedoiinvestment to sell all of the issue that they can and this is ng the offeribanker ng ontoa agree best efforts basis. Because the price paid for the issue and the anticipated sal e price are determined between the (lead) investment bank and the issuing company, the offering is termed asecurities negotiated offering. Another approach is an auction process where an issuer of debt determines theofsizmultiple e and termsinvestment of the issuebanks,andbidseveral investment banks, or underwri t i n g syndicates on what interest rate they require to sell it. The syndicate with the lowest interest rate bid will be awarded the deal. InthetheSEC.United States, securities to besecurities offered toispublic investorsformustsalebeto registered with When a new issue of debt not registered the public, stillRulemay144Abe offering sold to a(after smallthenumber of investors. Thistransactions). is called a private placement oritregistration rule that al l ows such Avoidance of the processnumber is valuable to the issuer and, because a pricanvatebe placement involneeds ves aandsalepreferences to a small of investors/institutions, the i s sue tailored to the ofregithestered, buyers.theBecause thewilissue cannota slightly be soldhigher to theinpublic unletoss itcompensate is subsequently buyers l require terest rate placement. them for the lack of liquidity of securities that are sold though a private The secondary market trading for debtnetworks. securitiesTraditionall includes exchanges, an over-the-counter dealer market, and electronic y , most secondary tradi n g in debt securitiesforwasandtransacted a dealer market, ers buyingMoreandrecently, selling bonds from theirininventories (i.e., actiwintgh asbroker/deal market makers). Š20 1 2 Kaplan, Inc.

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments

theoperations costs andhaverisksincreased of supplying the capital necessary toBecause adequatelofythis,fundelectroni bond trading and spreads have decreased. c trading haselectroni becomec networks a more important part of the secondary market for debt securities. These can be bidscustomer and offersbidsbyanda single dealposted er, bidons and offers byc multiple deal e rs, or simply anonymous offers an electroni trading system with a trade clearing system.

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KEY CONCEPTS

LOS 54.gna debt refers to the debt obligations of governments. U.S. Treasury securities are Soverei sovereign debt of the U.S. government and are considered free of credit ri s k. Soverei g n debt of other countries has varying degrees of credit risk. SovereiRegulgn adebt is typicyclcalleywith issuedtheusing one of four methods: r auction enti r e issue sold at a single price. Regul a r auction cycl e with bonds issued at multiple prices. AdTaphocsystem, auctionauctioning system with no regul a r cycle. new bonds identical to previously issued bonds. LOS 54.b issued by the U.S. Treasury include: Securities Bills-pure-discount securities maturing i n four weeks, three months, or six months. Notes-coupon securi ties maturi and ten years. Bonds-coupon securities maturingng inin two, 20 orfiv30e, years. Treasury InfliastionfixedProtected Securities (TIPS) areperiodical U.S. Treasury issues in which theon coupon rate but the par val u e is adjusted l y for infl a tion, based changes in the CPl. U.Treasuries S. Treasuries from the most recent auction are referred to as on-the-run issues, whi l e from previous auctions are referred to as off-the-run issues. LOS 54. c Strippedeach Treasury securities are created byandbondprincipal dealerspayments, who buy Treasury securities, separate of their scheduled coupon and resel l these as zero-coupon securities. Treasury strips are traded i n two forms-coupon strips and principal strips-and are taxed by the IRS on the basis of accrued interest, like other zero-coupon securities. LOS 54.dof the U.S. government, including federally related institutions and Agencies government-sponsored enterprises,to ibessuealmost bondsdefault that arerisknotfree.obligations of the U.S. Treasury bur are considered LOS 54. e A(themortgage passthrough securityy cash is backed bythata pool of amortizing mortgagescheduled loans col l ateral) and has monthl fl o ws include interest payments, principal payments, and prepayments of principal. Prepayment riskcontain is signifiacprepayment ant for investors in passthrough securities because mostto mortgage loans option, which al l ows the issuer (borrower) make additional principal payments at any time. •

• •

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Collateralinterest ized mortgage obliof mortgage gations (CMOs) are customized claimsredistribute to the principal payments passthrough securities and the and/or prepayment risk and/or maturity risk of the securities. LOS 54. f CMOsngarethecreated decrease borrowing by redistributing alteri maturittoy structure to better suicosts t investor preferences.prepayment risk or LOS 54.gpayments on state and local government securities (municipal securities, or Interest munis) are usual l y exempt from U. S . federal taxes, and from state taxes in the state of tssuance. Municipal bonds(general include:obligation) bonds backed by the taxing authority of the Tax-backed governmental unitbacked issuingonlythebysecurities. Revenue bonds, the revenues from the project specifi c ally financed by the bond issue. LOS 54.h debt securities include bonds, medium-term notes, and commercial paper. Corporate Bond rating agenci e s rate corporate bonds on capacity to repay (liquid assets and cash flcredi ow),t himanagement qualidebtty,leindustry prospects, corporate strategy, financial policies, s tory, overall vels, the collateral for the issue, and the nature of the covenants. Corporate may financial be securedassets, or unsecured debentures). Security can be in the form of realbonds property, or personal(called property/equipment. Medium-term notes (MTN) are issued periodically by corporations under a shelf regi stration,to sold on a best-efforts basis, and have maturities ranging from morebythanagents30 years. 9 months combine ainvestors. bond with a derivative to create a security that fills a need forStructured particulnotes ar institutional Commercial a short-term corporate finthan ancing270vehicle and does notin require regisDirectly-placed tration wipaper th theispaper SEC ifsoldits dimaturi t y is less days. CP comes two forms: rectly bythrough the issuer.agents/brokers. Dealer-placed paper sold to investors Negotiablaree CDs arebyissued inassets, a wideandrangeare termed of maturities by banks, trade indenominated a secondary market, backed bank Eurodollar CDs when in U.S. dollars and issued outside the United States. Bankers' acceptances are issued by banks to guarantee a future payment for goods lishipped, mited liqsolduidity.at a discount to the future payment they promise, short-term, and have •

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LOS 54.i securities (ABS) are debt that is supported by the cash flows from an Asset-backed underlying pool of mortgages, auto loans, credit card receivables, commercial loans, or other financial assets. Atransferred. special purpose vehi cle is an transferring entity to whithese ch theassets assetsgoesthatbankrupt, back an ABS are legall ynot If the corporation the assets are subject to cl a ims from its creditors. As a result, the ABS can recei v e a higher credit rating than the corporation and reduce the corporation's funding costs. External credit enhancement for an ABS can include corporate guarantees, letters of credit, or third-party bond insurance. LOS 54.j ized debt obligations (CDOs) are backed by an underlying pool of debt Coll a teral securities whichmortgage-backed may be any onesecurities, of a numberor other of types:CDOs. corporate bonds, loans, emerging markets debt, LOS 54. k The in bonds includes underwritten and best-efforts public offerings, as well primary as privatemarket placements. The secondary market indealer bondsmarket, includesandsome trading onnexchanges, awhimuchch arelargeran volume of tradi n g in a electroni c tradi g networks increasingly important part of the secondary market for bonds.

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments

CONCEPT CHECKERS

security i s quoted at 97-17 and has a par val u e of $100, 0 00. Whi c h 1. AofTreasury followi0n0.g is its quoted dollar price? A.B. the$97,170. $97,531. $100,000.205.0. investor(TIPS) holds that $100,carry 000 a(par2.5o/ovalue) worth of Treasury Infl a ti o n Protected 2. AnSecurities coupon.value If theofannual iafter nflatisixonmonths? rate is 3o/o, what is the inflasemiannual tion-adjustedpayprincipal the bond A.B. $102,500. $101,500. $103,000. holds $100, 0is00paid(parsemiannual value) worth ofTIPS currentlinflation y tradingrateat ipar. 3. AnTheinvestor coupon rate of 4o/o l y , and the annual s 2.months? 5o/o. What coupon payment will the investor receive at the end of the first six A.B. $2,$2,0000.25. $2,050. note li(T-note) principaltostriap6-month has six months remaining to maturity. 4. AHowTreasury i s i t s price k el y to compare Treasury bil l (T-bill) that has been issued? The T-note price should be: A.just lower. C.B. higher. the same. ch of theprincipal followingstrips statements aboutcreated Treasuryfromsecurities is bills. most accurate? 5. A.WhiTreasury are usually Treasury bonds maystripsbe make used tolower createcoupon Treasurypayments couponthanstrips.Treasury principal B.C. Treasury Treasury coupon strips. of thehigher followiyields? ng municipal bonds typically has the greater risk and is 6. Which issued with Revenue taxbonds. A.B. Limited C. Unlimited taxgeneral generalobligation obligationbonds. bonds. is serviced withis thecalledearnings from a pool ofTreasury securities 7. Athatbondhaveissuebeenthatplaced i n escrow a(n): A.B. prerefunded insured bond.bond. C. credit-enhanced obligation. c.

c.

c.

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments

8. 9. 10. 11. 12. 13. 14.

Ofthe therequirements following, oftheSECdebtRulsecurities that registration) are most oftenare:registered according to e 415 (shelf A.B. corporate bonds. medium-term notes.securities. C. mortgage-backed Aofcorporation issuing asset-backed securities can oftenbyimtransferring prove the credit rating the securities to above that of the issuing company the assets A.toB. a(n): asset trust. bond insurer. C. special purpose vehicle. Which ofon-the-run the followinissue: g is a between an on-the-run and an off-the-run issue? An A.B. hasis thea shorter most recentl y tissued security of that type. maturi y than an off-the-run issue. C. is publicly traded whereas an off-the-run issue is not. to a public offering, aeprild.vate placement of debt securities has: more liquidi t y and a l o wer yi A.Compared B.C. less liquidity and a l o wer yi e ld. less liquidity and a higher yield. to liquid. negotiable CDs, bankers acceptances: A.Compared are more B.C. have shorter maturities on average. are more likely to pay periodic interest. Adeveldebtopisecurity that isiscollateralizeda(n):by a pool of the sovereign debt of several n g countries A.B. CMO. CDO. C. ABS. vities inmaking. the primary market for debt securities would include: A.Acti market B.C. aa fibest-efforts offering. rm commitment. difference

Likely

most Likely

Least Likely

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments

ANSWERS - CONCEPT CHECKERS 1.

B

This value is computed as follows: dollar price = 97

17 32

o/o X $100,000 = 0.9753125 X $ 1 00,000 = $97,531.25.

2.

A

The annual inflation rate is 3%, which corresponds to 1 .5% semiannually. Therefore, the principal value has increased by 1 . 5%. So we have: new principal = $ 1 00,000 x 1 .015 = $ 1 0 1 ,500.

3.

B

This coupon payment is computed as follows: coupon payment = ($100,000 x l .0125)

Page 68

(�)

0 4 · = $2,025

4.

C

The T-note principal strip has exactly the same cash flows (the principal) as the T-bill. Therefore, the prices of the two securities should be (about) equal. However, market imperfections, such as illiquidity, may lead to differences.

5.

B

Treasury coupon and principal strips are created by separating (stripping) the principal and coupons from Treasury notes and bonds and selling packages of these single­ maturity cash flows as individual zero-coupon securities. Treasury bills cannot be used because they are already zero-coupon securities.

6.

A

Revenue bond issues are only obligated to pay principal and interest if revenue from the project that they helped fund is sufficient to service the issue. When issued, revenue bonds typically are riskier than general obligation bonds and, consequently, have higher yields.

7.

B

The cash flows generated by an escrow pool of Treasury securities are used to service prerefunded bonds. Insured bonds carry third-party guarantees. There are no securities formally known as absolute priority bonds or credit enhanced obligations (yet) .

8.

B

Shelf registration is used with medium-term notes. This permits the issue to be held in inventory (on the shelf) and sold in parcels at the discretion of the issuer. Corporate bonds and MBS are usually sold all at once.

9.

C

The assets are sold to a special purpose vehicle to protect them from general claims against the issuing corporation.

10. A

On-the-run issues are the most recently issued securities.

11. C

Investors require a higher yield to compensate for the fact that privately placed debt is not registered for public sale and is therefore less liquid than debt registered for public sale.

12. B

Bankers' acceptances are short-term and pay no periodic interest. Like negotiable COs, they are as good as the credit of the issuing bank but have a very limited secondary market.

13. B

A COO or collateralized debt obligation is backed by an underlying pool of debt securities which may be emerging markets debt. A CMO is backed by a pool of mortgages, and an ABS is backed by financial assets.

14. A

Market making refers to a dealer that trades in the secondary market for its own account from inventory. ©2012 Kaplan, Inc.


The following is a review of the Analysis of Fixed Income Investments principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in:

UNDERSTANDING YIELD SPREADS Study Session 1 5

EXAM FOCUS

Yiofedebt ld spreads are si m pl y di f ferences between the yiel d s of any two debt securiti e s or types securities.cs that Try drito vgete yiaeldgoodspreads. grip You on theshouldspreadknowtermiallnthree ologytheori in thiess ofrevitheewterm and thestructure, characteristi not only thei r impli c ati o ns for the shape of the yi e ld curve but also what the yiel d curve can tell yiel us under of thetax-free three andtheories. taxableshape and after-tax ds andeach between taxablLearn e equivthealentrelyiatieldsonships well. between LOS 55.a: Identify the interest rate policy tools available to a central bank. CPAÂŽ Program Curriculum, Volume 5, page 408

While theinterest are determined by a varito emanage ty of economic conditions, in theitsUnited States FederalratesReserve (Fed) attempts short-term rates through The four interest rate tools of the Fed are as follows: monetary policy tools.

1. The discount rate is the rate at whi c h banks can borrow reserves from the Fed. A l o wer rate tendsdiscount to increase lending, higher rate hasbankthereserves, oppositeencourage effect, raising rates.and decrease interest rates. A 2. Fed Openinmarket operations referstheto theFedbuying or sellingcash ofTreasury securities byinthe the open market. When buys securities, replaces securities iSales nvestorof securities accounts,bymorethe funds are avai l able for lending, and interest rates decrease. opposite effect, funds available for lendingFedashave welltheas increasing rates. reducing cash balances and reserveBy requirements arepercentage the percentage of deposits thatrequired banks must retainas(not 3. Bank loan out). increasi n g the of deposits banks are to retain thein amounts Fed effectively decreases the funds that toareinavail ablinterest e for lending. This decrease avail a ble for lending wil l tend crease rates. A decrease i n the percentage reserve requirement will increase the funds available for loans and tends to decrease interest rates. banks to tighten orattempts loosen their credittheirpolicies. By asking banksEncouraging to alter 4. Persuading thei r lending policies, the Fed to affect will i ngness to lend. lending wil tend to decrease rates and vice versa. The most commonly used policy tool is reserves,

open market operations.

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads

LOS 55.b: Describe a yield curve and the various shapes of the yield curve. CFAÂŽ Program Curriculum, Volume 5, page 410

WeFor have yieldTreasury curvesyielprevid curve ously asandjustrelated a plotinformation, of yields by years to maturity. a.bviloomberg. ewmentioned of a current you can l o ok at com/markets/rates/index. html.andThebonds) Treasurywithyieldmaturicurvetiesshows yimonths elds fortoU.30S.years. Treasury securities (bills, notes, from thethree We use four general shapes to describe yield curves: 1. Normal or upward sloping. 2. Inverted or downward sloping. 3. Flat. 4. Humped. These four shapes are illustrated in Figure 1. Figure Yield Curve Shapes

www

1:

Yield

Yield

Yield

Yield

Humped

Inverted

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads

Yionlyeldones curvesobserved. can takeThese on justfourabout any shape, vsoe don' t thinktypes, these and examples are theto be are representati of general you need fami l i ar wi t h what i s meant by an "upward sloping" or "normal" yi e ld curve and by an "inverted" ordescriptive "downwardnames sloping"andyield curve.t present Humpedanyandproblem. flat yieldJustcurves usuallthat y go a byflatjustyieldthosecurve shouldn' remember means that yields are all equal at every maturity. LOS 55.c: Explain the basic theories of the term structure of interest rates and describe the implications of each theory for the shape of the yield curve. CPA® Program Curriculum, Volume 5, page 413

The states that the yield for a particular maturity is an average (not arates simpleare average) oftotheriseshort-term ratesinterest that arerateexpected in thelongerfuture.maturities If short­will term expected in the future, yields on beIf short-term higher thanratesthoseareonexpected shorter tomaturities, and thelonger yieldmaturity curve wibonds ll be upward sloping. fal l over time, will be offered at lower yields. Proponents ofshort-term the rates, investors requirebelieve that, in addition to expectations about future a risk premium for holding longermaturity term bonds. This i s consistent wi t h the fact that interest rate risk i s greater for longer bonds. Under thiscompensation theory, the sizeinofvestors the liquidity premium withemll depend ononhow much additional requi r e to i n duce to take the greater risk of longer ofmaturi ty bonds or, alitsernati vlustration ely, how strong their preference for thepremium greateron a liquidity shorter term debt . i l of the effect of a liquidity yield curve, where expected future short-term rates are constant, is presented in Figure 2. pure expectations theory

liquidity preference theory

An

Figure 2: Liquidity Premium Yield Yield curve with liquidity preference

I

Liquidicy p«mium

Yield curve without liquidity preference (pure expectations)

u The i s based on the idea that i n vestors and borrowers have preferences for dithefferent Undertothilend)s theory, the supply of bondsyields(desire to borrow) and demand for bonds (desire determine equilibrium , _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ L_

Mat rity

market segmentation theory

maturity ranges.

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads

forfor thematurivarious maturithatty ranges. Institutional investors Limayfe ihave strong preferences t y ranges cl o sel y match thei r liabilities. n surers and pension funds may prefer long maturities due to the l o ng-term nature of the liabilities they must fund. bank thatsecurities. has liabilities of argument a relativelyforshortthe maturity may prefer to itheory nvestAiniscommercial shorter-term debt Another market segmentation that there are legal or institutional policy restrictions that prevent i n vestors from purchasingofsecuriti es wivarious th maturities outside aofparticul aldr maturity range. Thein determination yiel d s for maturi t y ranges the yi e curve is ill u strated Figure 3. 3: Figure

Market Segmentation Theory and the Yield Curve

Yield

Long-term Short-term

Intermediate-term 0

s

s

0 Maturiry

A somewhat weaker versionyields of thealsomarket segmentation theory is thefor various maturity Under thi s theory, depend on supply and demand move from theimaturi r preferred maturity ranges when yiranges, elds arebutsuffiinvestors ciently canhigherbe induced in other to(non-preferred) ty ranges. preferred habitat

theory.

Term Structure Theories and the Shape of the Yield Curve

The by itself has no implications for the shape of the yield curve. The various expectations and the shapes that are consistent with them are: Short-term rates expected to risefalliinn thethefuture upward sloping yieldyielcurve Short-term rates are expected future downward sloping d curve Short-term rates expected to rise then fal l humped yi e ld curve Short-term rates expected to remain constant flat yield curve The shape ofabout the yiienldvestor curve,expectati under theonspure theory,rates. provides us with information aboutexpectations future short-term theidenti liquidity theto falyieldl a great curvedealmayintaketheonfuture, any ofeventheaddi shapesng weaUnder have f i e d. If rates are expected liquidity premi u m to the resulting negati v el y sl o ped yield curve can resul t in a sloping yiadded eld curve. yieldnote curvethat,couldunder still thebe humped with a lidownward quidity premium to all Athehumped yields. Also liquidityeven preference pure expectations theory

-+

-+

-+

-+

preference theory,

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads

theory, yieldThicurve consistentin Figure with expectations of declining short-terman upward rates in sloping the future. s casecanis beillustrated 4. 4:

Figure

Liquidity Premium Added to Decreasing Expected Rates

Yield

Liquidity Preference Yield Curve

Pure Expectations Yield Curve (short-term rates expected to decline)

'------ Maturity

The of theandterm structure is consistent wiatteach h anymaturi yield tcurve shape. Under this theory, i t i s supply demand for debt securities y range thatthe determines theerentyieldmaturities, for that maturi ty range. There is no specific linkage among yields at diff although, under the higher at an adjtheiacent maturityrangerangeof can induce investors to purchase bonds with maturitiesratesoutside r preferred maturities. market segmentation theory

preferred habitat theory,

LOS 55.d: Define a spot rate. CPAÂŽ Program Curriculum, Volume 5, page 415

Yield to maturi t y is the singl e di s count rate that makes the present value of a bond' s promised flowscome equalattodifitsferent marketpointsprice.in Actually, the appropriate discount rates fordiscount cash flrate ocashwsforthat ti m e are typical l y not all the same. The a payment that comes one year from now i s not necessari l y the same discount rate that should be applied to a payment that comes fi v e or ten years from now. That is, the spot-rate yield curve is not (horizontal). The appropriate discount ratestimeforperiods individual future payments are calleda value equal to The spot rates for di f ferent that correctl y value (produce marketorprice) the cash flows from a Treasury bond arewillcalexami led ne the methodology Treasuryforspot rates, the We these rates and why theyratesare tocaldifferentiate led "arbitrage-free" spotcoupon rates a bitbondlater.yieHere weestimating j u st introduce the i d ea of spot them from lds (YTMs). Conceptuall y , spot rates are the discount rates for (yi e lds on) zero-coupon bonds, securities thatthanhavesemiannual only a singlepayments) cash flowwiatll aillustrate future date. A simpleasexampl e to (wi t h annual rather thi s concept applied coupon bonds. flat

spot rates.

arbitrage-free

theoretical Treasury spot-rate curve.

,

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads

Consider anmakeannual-pay bond wiFor th a a1 $1,Oo/o0coupon ratetheseandpayments three yearswiltol bematuri ty.inThis bond wi l l three payments. 00 bond, $100 one year, $1 00 at the end of two years, and $1,100 three years from now. Suppose we are given the following spot rates: 1 year = 8o/o 2 year = 9o/o 3 year = 1 Oo/o Discounting bond as: each promised payment by its corresponding spot rate, we can value the 100 + __!QQ_2 + 1,1003 1,003.21 1.08 1.09 1.10 =

LOS 55.e: Calculate and compare yield spread measures.

416 Abonds. yield Three spreaddiisffsierent mplyyitheeld difference betweenaretheas yields spread measures follows:on two bonds or two types of absolute yield spread is simplycaltheleddifference between yiAbsolute elds on twoyieldbonds. 1. The This simple measure i s sometimes the spreads are usually expressed in basis points (lOOths of 1 o/o). absolute yield spread = yield on the higher-yield bond-yield on the lower-yield bond 2. The relati v e yield spread is the absolute yield spread expressed as a percentage of the yield on the benchmark bond. yield spread re attve yt.eld spread = yieldabsolute on the benchmark bond 3. The yield ratio is the rati o of the yield on the subject bond to the yiel d on the benchmark bondsubj. ect bond yield -yt.eld ratt.o = --"- ---'benchmark bond-yi-eld Note that yieldmeasures ratio is simply one plusin thethe folrelalowing tive yieldexample. spread. The calculation of these yieldthespread is illustrated CPAÂŽ Program Curriculum, Volume 5, page

nominal spread.

1

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads

Example: yield spreads Consider two bonds, X andY. Thei r respective yields are 6.50% and 6. 7 5%. Using bond as thethebenchmark spread,Xand yield ratio bond, for thesecompute bonds.the absolute yield spread, the relative yield Answer: absolute yieldspread= spread =0.25% 6.75%-6.50% =0.0.25% or 25 basis points relyieldativratio= e yield 6.50% = 0 38 = 3.8% 6.75% 6.50% = 1.038 Computing

I

I

The mostsimplistic. commonlyAused yield spreadof theis theabsolute yieyildeldspread spread,is thatevenitthough it isn theconstant, most shortcoming may remai even though overall rates ri s e or fall. In thi s case, the effect of ri s i n g or fall i ng rates on spreads is captured by the relative yield spread or the yield ratio. For example, consider two yields that rise from 6. 5 % and 7.0% to 7. 0 % and 7. 5 %, respecti ely. Thefallabsolute at 50o decreases basis points,fromwhi1.l0e77theto rel1.0a71.tive vspread s from 7.yi6e9%ld spread to 7.14%remaiandns theconstant yield rati absolute

LOS 55.f: Describe credit spreads and relationships between credit spreads and economic conditions.

418 Ain credit (or except spread is therating.difference in yieldsof abetween two issues thatdifference are similar all respects for credit An example credit spread is the in yiGOeldsmunis between(an lintramarket ong AA ratedspread generalas weloblilgation (GO) municipal bondsshowandthelongeffectA rated ). Obviously, these spreads of credi t qual i t y on yi e l d s and reveal the ri s k-return tradeoff the i n vestor can expect (i.e., how mucht riadded percei ved credi sk). return an investor can earn by investing in issues with higher Credittspreads spreadsdecli are related to the state ofaretheexpected economy.to have Duringstronger an expanding economy, credi n e as corporations cash fl o ws. Onto a the other hand, during economic contractions, cash fl o ws are pressured, leading greater probability of default and hithey gheroften yieldssellonlow-quality lower-qualitissues y issues.andWhen investors antici p ate an economic downturn, buy high-quality issues, including Treasuries. This puts downward pressure on the prices of low-quality issues, raising their yields. CFAÂŽ Program Curriculum, Volume 5, page

quality)

flight to quality

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads

LOS 55.g: Describe how embedded options affect yield spreads. CFA® Program Curriculum, Volume 5, page 420

call option ontoa bond is antooption theFrombondtheissuer holds ands perspective, will only bea noncallable exercised if it isbondadvantageous the i s suer do so. bondholder' that iscompared otherwisetoidentical butbondcallable. Investors will feature. l require higheris preferred yieldyieldonspreads atocalla bond ableto abond, the same without the cal aTherefore, benchmark bond, such as a similar maturity Treasury issue, are higher forbondholders the callableforbond.the Byprepayment the same reasoning, yield spreads must bepassthrough greater to compensate option embedded in mortgage securities. The inclusioneffect; of a puttheprovision orwhether a conversion option withofathese bondoptions will haveis the thebondholder' opposite choice of to exerci s e ei t her s . Compared to an identical option-free bond, a putable bond wi l l have a lower bond. yield spread to Treasuries due to the value of the put feature included with the The fact thatforoption provisions affect yield spreads is important because forthiscredi tellstusrisk, that spreads bonds wi t h embedded options are not purely premiums liquidity differences, and maturity (duration) risk. A

LOS 55.h: Explain how liquidity and issue-size affects the yield spread of a bond relative to other similar securities. CFA® Program Curriculum, Volume 5, page 422

Bonds that have t o Treasuries. Investors prefer more liquidity to less and will payinaallpremium for greater liitquiisdmore ity. actihigher price for a bond that is identical to another aspects except that v el y traded-and therefore more liquid-translates into a lower yield compared to the less liquid bond. Liquidity is affected byactivel the sizey traded of an issue. because they are more i n the secondary market. Empirical evi d ence suggests that issueslerwiissues, th larger-size issues have lower yieldsWhen compared with identical but smal due to their greater liquidity. less liquidity have higher spreads

A

Larger issues normally have greater liquidity

greater size have lower yield spreads.

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads

LOS 55.i: Calculate the after-tax yield of a taxable security and the tax­ equivalent yield of a tax-exempt security. CFA® Program Curriculum, Volume 5, page 423

The

on a taxable security can be calculated as: after-tax yield = taxable yield (1-marginal tax rate) after-tax yield

X

Example: Computing after-tax yield

the after-tax yield on a corporate bond with a yield of 10% for an investor with aWhat 40%ismargi nal tax rate? Answer:

Investors arebe paid concerned wionth after-tax returns. Thelar ofmarginal taxinrate iscasetheinterest percentage that must in taxes one additi o nal dol income, thi s mcome. For an investor wi t h a marginal tax rate of 40%, 40 cents of every additional dollar of taxable inyiterest mustwibethpaida 40%in taxes. For ataxtaxable after-tax eld toincome an investor marginal rate wilbond l be:that yields 10%, the 10%(1 - 0.4) = 6.0% after tax Tax-exempt securities can offer lower yields compared to taxable securities because the yieldsthethey offer are after-tax Theissuehigcompared her an investor' s marginal taxTherate, the greater attractiveness ofis thea taxyieldyields. exempt to a taxable issue. a particular investor must earn on a taxable bond to have the sameis justafter-tax return theyofwould receive from particular calculation a rearrangement the after-tax yieldaformul a listedtax-exempt previouslissue. y. The tax-fre--'-e yield . yt.eld = (1-margi taxable-equivalent nal tax rate) taxable-equivalent yield

-

-

-

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads

Example: Taxable-equivalent yield

Consider a municipal bond that offers a yiel d of 4.5%. If an investor i s considering buying fully taxablor thee Treasury security a 6.7her5%marginal yield, should Treasurya security municipal bond,offering given that tax ratesheisbuy35%?the Answer:

We can approach this problem from two perspectives. First, the taxable equivalent yield 4·5 o/o 6.92%, which is higher than the taxable yield, so on the municipal bond is (1-0. 35) the municipal bond is preferred. Alternatively, the after-tax return on the taxable bond is 0.0675 X (1-0.35) 4.39%. bond (4.5%)bondis greater than the after-tax yiThus, eld onthetheafter-tax taxablereturn bond (4.on3the9%),municipal and the municipal is preferred. Either approach gives the same answer; she should buy the municipal bond. =

=

� �

Professor's Note: Because investors have different marginal tax rates, investors will have different tax-equivalent yields. Thus, the Treasury yield curve is not the appropriate benchmark to use for municipal bond yield spreads. The AAA rated municipal general obligation yield curve is the benchmark for municipal yield spreads.

LOS 55.j: Define LIBOR and explain its importance to funded investors who borrow short term. CPA® Program Curriculum, Volume 5, page 427

We mentioned theable CDs by banks and bank branches(LIBOR) in London. reference toLIBOR thepreviously rateshas paibecome d on negoti located in the most important benchmark or reference ratedayforandfloatipublished ng-rate debt securities and short-term lending. LIBOR is determi n ed each byandtheAustral BritishianBankers' Association for several currencies, including the U.francs, S., Canadian, dollars, the Euro, Japanese yen, Bri t ish pounds, and Swiss amongto others. Whil e the maturity of the CDs that banks invest i n can range from overnight five years, LIBOR is most important for short-term rates of one year or less. London Interbank Offered Rate

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads

funded investor is onein who borrowsistoasfianmeasure ance an iofnvestment position. The of LIBOR thi s context the funding costs becauseloansthe importance loans to fi n ance the i n vestment are most often fl o ati n g-rate loans or short-term where the reference rate is published LIBOR. Recalwilththata borrowing floating-raterateloans are based on a(60-day) reference rate plus a margin. funded investor of 2-month LIBOR 40 basis points would have a borrowing cost (annualized) of 2. 6 % when 2-month LIBOR is quoted at greater 2.2%. Thethanprofi t6s%ofannual such a rate fundedon theinvestor would depend on his or her ability to earn a 2. investments funded in such a manner.

A

+

A

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads

'

KEY CONCEPTS

55.a Reserve Board's tools for affecting short-term interest rates are the discount The Federal rate, operations, the reserve requirement, and persuasion to influence banks'open-market lending policies. 55.b Yield curves represent the plot of yield against maturity. The general yield curve shapes are upward or downward sloping, flat, or humped. 55.cof the yield curve and their implications for the shape of the yield curve are: Theories The arguesrates thatandratesisatconsistent longer maturities depend onlyshape. on expectati o ns of future short-term with any yiel d curve The of thefuture term structure statesratesthatandlonger-term rates refl e ct i n vestors' expectations about short-term an increasing liinqterest uidityratepremium to compensate i n vestors for exposure to greater amounts of risk atdownward longer maturities. The liquidity preference theoryin short-term can be rates consistent wi t h a sloping curve i f an expected decrease outweighs the liquidity premium.argues that lenders and borrowers have preferred The maturi ty rangesfor and that thewithin shapeeachof thematurity yield curve isindependent determined byof thethe supply and demand securities range, yield in other maturity ranges. It i s consistent wi t h any yi e ld curve shape and in a somewhat weaker form is known as the preferred habitat theory. 55.d Treasury spot rates arefromtheaappropriate discount ratesgivforen thesingletimecashuntilflowsthe(coupon oris to principal payments) U.S. Treasury security, payment be received. 55.e TypesTheof yield spreads: is the difference between the yield on a particular security oron-the-run sector andTreasury the yieldsecurities of a reference (benchmark) security or sector, which is often of l i k e maturi t y. The isarguably the absolute yield spread expressed as a percentage of the benchmark yield. This i s a superior measure to the absolute spread, since iremai t willnrefls constant. ect changes in the level of interest rates even when the absolute spread The is theorratiosector;of theit isyieldsimplyon aonesecurity benchmark security plus theor sector relativetoyitheeldyield spread.on a LOS

LOS

LOS •

pure expectations theory

liquidity preference theory

market segmentation theory

LOS

LOS •

absolute yield spread

relative yield spread

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yield ratio

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads

LOS 55.f

Acredicredit spread is the yield difference between two bond issues due to differences in their t ratings. Credi t spreads narrow when the economy is healthy and expanding, while they increase during contractions/recessions reflecting a flight to (higher) quality by investors. LOS 55.g

Call optionsbonds. and prepayment options increase yields and yield spreads compared to option-free Put options and conversion comparable option-free bonds.options decrease yields and yield spreads compared to Bonds h lessliquid liquidityand,areother less desirabl e and wilmustl haveofferlower a higyield her yield. issues arewitmore things equal, spreads.Larger bond

LOS 55.h

LOS 55.i

To compare ayield tax-exempt bond with(1a taxable issue, userate),eitherandofcompare the following: Mter-tax = taxabl e yield -margi n al tax it to tax-exempt yield. tax-free yield , and compare .tt to a taxable yteld. Taxable-equivalent yield (1-margi nal tax rate) LIBORmoney for various currencies isis determi nedimportant from ratesreference at whichratelargeglobally Londonforbanks loan to each other and the most floating-rate debt and short-term loans of various maturities. •

x

___:_ _ _ _

_ _ _ _

.

LOS 55.j

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads

CONCEPT CHECKERS

1. 2.

3.

4. 5.

Under theory, an inverted yield curve is interpreted as eviA. ddemand encethethat:purefor expectations long-term bonds tois falling. B.C. ishort-term rates are expected the future. nvestors have very little demandfallforinliquidity. According the liquidity preference theory, which of the following statements iA.s All elsetoequal, invvestors preferdifferenti short-term securitiesshort-term over long-term securities. B. Investors percei e littl e risk a l between and long-term securities. C. over Borrowers will paydebt.a premium for long-term funds to avoid having to roll short-term Witheory th respect to the term structure of interest rates, the market segmentation holds that: an increase in demand for long-term borrowings could lead to an inverted A. yield curve. expectations about theshapefutureof theof short-term interest rates are the major B. determi n ants of the yield curve. C. ithenvestors. yield curve reflects the maturity demands of financial institutions and mostdiscount commonly used tool of the Fed to control interest rates is: A.The the rate. the bank reserveoperations. requirement. B.C. open market For twoisbonds thatTheareyialeldikeratio in alils respectsto:except maturity, the relative yield spread 7.14%. A.B. 0.714. 1.0714. 107.14. Assume the fol l owi n g yields for di f ferent bonds issued by a corporation: 1-year bond: 5.50%. 2-year bond: 3-year bond: 6.00%. 7.00%. Ifthea 3-year 3-year corporate U.S. Treasury is yielding 5%, then what is the yield spread on issue? A.B. 0.10040.bp. 200 bp. least accurate?

closest

c.

6.

• • •

absolute

c.

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads

thebond: following corporate yield curve: 7. Assume 1-year 5.00%. 2-year bond: 6.00%. 3-year bond: 7.00%. If a 3-yearon theU.S.3-year Treasury yieldingis: 6% is the benchmark bond, the yield spread corporate A.B. 1.167. 16.67%. 14.28%. 8. bonds If a U.Sand. investor is forecasting thatis going the yield spreadwhibetween U.S.followi Treasuryng U. S . corporate bonds to widen, c h of the woul d he beisalsogoing to expand.to hold? A.beliefs The economy The economy C.B. There will be nois going changetoincontract. the economy. a Treasury bond and aiscorporate bond that areon altheikecorporate in all respects except 9. For credit risk, the yi e ld ratio 1.0833. If the yield bond is 6. 5 %, the Treasury (benchmark) bond yield is to: A.B. 6.5.50%. 0%. 8.033%. venntwo bonds that wiarel equi valanentinvestor in all respects exceptbetween tax status, the2% taxable 10. Gimargi al tax rate that make indi f ferent an 8. bond and39%.a 6.2% tax-exempt bond is to: A.B. 24. 43.37.404%. 7%. 11. Which ofthetheeconomic followinghealstatements describes the relationship between t h of a nation and credit spreads? A.B. Credit spreads and economic well-being are noteconomy correlated. Credit spreads decrease during an expanding because corporate cash Rowsspreads are expected to rise. an expanding economy because corporations C. invest Credit increase during in more speculative projects. 12. Which of the foll o wing describes the relationship between liquidity and yield spreads relative to Treasury issues? All else being equal, bonds with: A.B. less liquidity havehavelowerhigher yieldyispreads to Treasuries. greater liquidity e ld spreads to Treasuries. C. less liquidity have higher yield spreads to Treasuries. • • •

relative

c.

most likely

closest

c.

closest

c.

most accurately

most accurately

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads

13. Aofnarrowi ng ofngcredi t spreads would have the impact on the value of which the followi investments? A.B. AAA corporate bond. 30-yearratedTreasury C. BB+ corporatebond.bond. anofinvestor is7.in5 %thecorporate 31% margi nalthattax isbracket. She is considering the 14. Assume purchase either a bond sell i ng at par or a 5.25% municipal bond thatexcept is alstheir o selling at par.theGivinvestor en that theshould two buy bondsthe: areA.tax-exempt comparable i n all respects tax status, corporate bond, because i t has the higher yield of7. 5 0%. B.C. municipal bond, because becauseiitsts after-tax taxable-equi corporate bond, yieldvalent is higyield her. is 7.6 1 %. least

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads

ANSWERS - CONCEPT CHECKERS

1.

B

An inverted or downward-sloping yield curve, under the pure expectations theory, indicates that short-term rates are expected to decline in the future.

2.

B

Rational investors feel that long-term bonds have more risk exposure than short-term securities (i.e., long-term securities are less liquid and subject to more price volatility) . The other statements are correct.

3.

C

The market segmentation theory holds that certain types of financial institutions and investors prefer to confine (most of) their investment activity to certain maturity ranges of the fixed-income market and that supply and demand forces within each segment ultimately determine the shape of the yield curve.

4.

C

Open market operations are carried on frequently. The Fed's selling ofTreasuries in the open market takes money out of the economy, reducing the amount of loanable funds and increasing interest rates. The opposite occurs when the Fed buys Treasuries in the open market.

5.

B

The yield ratio is 1 + relative yield spread, or 1 + 0.0714 = 1 .0714.

6.

C

Absolute yield spread = yield on the 3-year corporate issue - yield on the on-the-run 3-year Treasury issue = 7.00o/o - 5.00% = 2.00o/o or 200 bp.

7.

A

8.

B . A contracting economy means lower corporate earnings which increases the probability of default on debt and increases yield spreads between corporate issues and Treasuries at a particular maturity.

9.

B

o · 7o 1. · yte · ld spread IS 7 0 , so the reIauve The y1e · ld on the corporate IS · 7o/ - 6o/o , wh1.ch 1·s 1/6 6 o/o or 16.67% of the 3-year Treasury yield.

. ld rano . = corporate bond yield = 1.0833. Given that the corporate bond yield is 6.5%, pe Treasury bond yield the Treasury bond yield can be calculated as:

10. A

6 5o/o · = 6.0 o/o . 1.0833

The tax rate that makes investors indifferent between two otherwise equivalent bonds is determined by solving for the tax rate in the equation: tax-exempt yield = (1 - tax rate) x taxable yield . Rearranging this relationship, we have: 6.2 tax-exempt rate . = 1 - - = 24.39%. margmal tax rate = 1 8.2 taxable rate

11. B

As an economy expands, credit spreads decline as expected corporate earnings rise. This is because, with stronger earnings, corporations are less likely to default on their debt.

12. C

The less liquidity a bond has, the higher its yield spread relative to Treasuries. This is because investors require a higher yield to compensate them for giving up liquidity, which results in a greater spread over Treasury issues, which are very liquid.

13. B

Because we usually speak of credit spreads as yield spreads to Treasuries, a change in the yield spread does not imply any change in the values ofTreasuries.

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Study Session 1 5 Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads

14. B

The taxable-equivalent yield on this municipal bond is

5 25 路 (1 - 0.31)

=

5 25 路 0.69

=

7.61 %.

Because this is higher than the yield on the (taxable) corporate bond, the municipal bond is preferred. Alternatively, the after-tax yield on the corporate is 7.5% ( 1 - 0.3 1) 5.175%, which is less than the tax-exempt yield, leading to the same decision.

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=


The following is a review of the Analysis of Fixed Income Investments principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in:

INTRODUCTION TO THE VALUATION OF DEBT SECURITIES Study Session 16 EXAM FOCUS

Bond valuation i s all about calculating the present val u e of the promised cash fl o ws. If your time-value-of-money (TVM) skilconcepts. ls are notThe up tomaterial speed, take thes topitimce revi nowewtoirevi sit theimportant. Study Session 2 review of TVM in thi s very Calculating the val u e of a bond by discounting expected cash fl o ws should become anrates easyand exercise. The fin"arbi al material, onbond discounting a bond' s expected cashasflwell. ows using spot the i d ea of t rage-free" valuation, is quite important A good understanding here will just make what follows easier to understand. LOS 56.a: Explain steps in the bond valuation process. CPA® Program Curriculum, Volume 5, page 447

The generalvalues procedure forthevaluing fixed-income securities (or anyup tosecurity) isvaltouetakeof the thesecuripresent of al l expected cash fl o ws and add them get the ty. There are three steps in the bond valuation process: over the l i f e of the security. For a bond, there are two types of cash flows: (1) the coupon paymentsbasedandon(2)thetheriskreturn of principal. of (uncertainty about) the receipt of the estimated cash flows. by multiplying the bond's expected cash flows by the appropriate discount factors. Step 1: Estimate the cash flows

Step 2: Determine the appropriate discount rate

Step 3: Calculate the present value of the estimated cash flows

LOS 56.b: Describe types of bonds for which estimating the expected cash Bows is difficult. CPA® Program Curriculum, Volume 5, page 448

Certainly, one problem inproblems estimatingthatfuture cash flows forofbonds icash s predicting defaults and any potential credit make the receipt future flows uncertain. Aside from credit risk, however, we can identify three situations where estimating future cash flows poses additional difficulties. 1. bonds with embedded options (puts, calls, prepayment options,This category includes and accelpayments erated is sinking fund provisions). For these bonds, the future stream of principal The principal repayment stream is not known with certainty.

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation of Debt Securities

uncertain andwerwirates l depend to a largeprepayments extent on theof mortgage future pathpassthrough of interest securities, rates. For example, l o will increase and principal will be repaid earlier. 2. future coupon payments depend on the path of interestWirates. th flWioating-rate securities, t h some floroating-rate securities, the coupon payments may depend on the price of a commodity the rate of inflation over some future period. information 3. about future stock prices and interest rates, we don't know when Without the cash flows will come or how large they will be. The coupon payments are not known with certainty.

The bond is convertible or exchangeable into another security.

LOS 56.c: Calculate the value of a bond (coupon and zero-coupon). CPAÂŽ Program Curriculum, Volume 5, page 449

For a Treasury bond,maythebeappropriate rateusedusedtotodiscount value theallpromised cashflows, flowsorisa the risk-free rate. This a single rate, of the cash series of discount rates that correspond to the times until each cash flow arrives. For non-Treasury securities, we must add a risk premium to the risk-free (Treasury) rate to measures determinecovered the appropriate discountrevirate. Thisisriskthe premium is one of the yield spread in the previous e w and added yield to compensate forusinggreater riskdiscount (credit risk, liquidity risk, calltherisk,riskprepayment risk, andtosotheon).risk-free When a single rate to value bonds, premium is added rate to get the appropriate discount rate for all of the expected cash flows. yield on a risky bond = yield on a default-free bond risk premium Other thi n gs being equal, the riskier the securi t y, the higher the yield di f ferential (or risk premium) we need to add to the on-the-run Treasury yields. +

Calculating the Value of a Coupon Bond

Recall that we valued an annuity using the tipayments me valuecanof money keys on the calculator. For an option-free coupon bond, the coupon be valued aswilanl enter annuithis ty. Infinorder to takeasintotheaccount the payment of the par value at maturi t y, we al payment future value. Thi s is the basic difference between valuing a coupon bond and valuing an annuity. For simplicity, considerata securi ty that(in wiltenl years). pay $100If theperappropriate year for tendiscount years andratemakeis 8%a single $1, 0 00 payment maturity for all the cash flows, the value is: 100 + 1002 + 1003 + 1004 + . . +--+-10010 1,00010 1.08 1.08 1.08 1.08 1.08 1.08 = $1,134.20 = present value of expected cash flows Valuation with a single yield (discount rate).

-

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Study Session 16 Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation o f Debt Securities

This is simandply$1,000 the sum(theof theprincipal presentrepayment) values of theto befuture cash atflothews, end $100ofpertheyeartenthfor ten years received year, at the same time as the final coupon payment. The calculator solution is: N = 10; PMT = 100; FV = 1,000; 1/Y = 8; CPT PV = -$1,134.20 where: NPMT == number of years the discount coupon payment 1/Y = the FV = the par value or sellingrateprice at the end of an assumed holding period -t

annual annual

� �

Professor's Note: Take note ofa couple ofpoints here. The discount rate is entered as a whole number in percent, 8, not 0.08. The ten coupon payments of$100 each are taken care ofin the N 10 entry, the principal repayment is in the FV 1,000 entry. Lastly, note that the PV is negative; it will be the opposite sign to the sign ofPMT and FV. The calculator is just "thinking" that ifyou receive the payments andfuture value (you own the bond), you must pay the present value of the bond today (you must buy the bond). That's why the PV amount is negative; it is a cash outflow to a bond buyer. just make sure that you give the payments and future value the same sign, and then you can ignore the sign on the answer (PV).

=

=

Valuation with a single yield and semiannual cash flows. Let' s cal c ulate the val u e of the same bond with semiannual payments. Rather than $100 per year, the security wi l l pay $50 every six months. Adjust the discount rate of 8% per year to 4% per six months. The par value remains $1,000. The calculator solution is: N = 20; PMT = 50; FV = 1,000; 1/Y = 4; CPT PV = -1,135.9 0 where: NPMT == thenumber of semiannual periods semiannual coupon payment 1/Y = the semiannual discount rate FV = the par value Calculating the Value of a Zero-Coupon Bond

Because a zero-coupon bond has only a si n gle payment at maturity, the val u e of a zero is simply theonpresent value ofbasis the paris: or face value. Given the yield to maturity, the calculation a semiannual t y val u e bond va ue (1 i)maturi number ofyears 2 1

=

+

x

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation of Debt Securities

Note that this valuation model requires just three pieces of information: The s maturidiscount ty value,rate,assumed to be $1,000. The lbond' semiannual 2.3.1. The ife of the bond, years. Alternatively, using the TVM keys, we can enter: PMT-=-+0;PVFV = par; N = years 2; 1/Y = YTM/2 = semiannual discount rate; CPT Although zero-coupon bonds do notrates.payNote coupons, it isis now customary to valtheuenumber zero-coupon bonds using semiannual discount that two times of years to maturi t y and that the semiannual di s count rate i s one-half the yield to maturity expressed as a BEY. Valuing zero-coupon bond Computeofthe8%.value of a 10-year, $1,000 face value zero-coupon bond with a yield to maturity Answer: findcalculate: the value of this bond given its yield to maturity of 8% (a 4% semiannual rate), weTo can 1,000 = $456.39 bond value= ( 0.1,00800) = (1.04 ) 1+ 2 Or, use the following inputs: N = 10 2 = 20; FV = 1,000; 1/Y = _% = 4; PMT = 0; CPT --+ PV = -$456.39 The di00)fference between thecompound current priceinterest of thethatbondwill($456. 39) andoveritsthepar1 0-year value life of ($1 , 0 i s the amount of be earned the issue. i.

N

#

x

N

Example:

a

l OxZ

20

x

� Professor's Note: Exam questions will likely specifY whether annual or semiannual � discounting should be used. just be prepared to value a zero-coupon bond either way.

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Study Session 16 Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation o f Debt Securities

LOS 56.d: Explain how the price of a bond changes if the discount rate changes and as the bond approaches its maturity date. CFA® Program Curriculum, Volume 5, page 450

Prior to maturity, a bond can be selling at a significant discount or premium to par value. However, regardless of itsarequired yield,$1,000 the price will converge to parlifevalue as maturity approaches. Consider bond with par value and a 3-year paying 6o/6%,o semiannual coupons. The bond values corresponding to required yields of 3%, and 12% as the bond approaches maturity are presented in Figure 1. Figure

1:

Bond Values and the Passage of Time

Time to Maturity

YTM = 3%

YTM = 6%

YTM = 12%

3.0 years

$ 1 ,085.46

$1,000.00

$852.48

2.5

1,071 .74

1,000.00

873.63

2.0

1,057.82

1,000.00

896.05

1 .5

1 ,043.68

1,000.00

919.81

1 .0

1,029.34

1,000.00

945.00

0.5

1,014.78

1,000.00

971 .69

0.0

1,000.00

1,000.00

1 ,000.00

Tobondcompute the change in bond value due to the passage of time, just revalue the withwith the number of periods (remaining until maturity) reduced. Theis FVval=ue1 of,000;a 6o/PMT o bond three years until maturity and a yield to maturity of 3o/o = 30; N = 6; 1/Y = 1.5; CPT � PV = $1,085. 4 6. To see the effect of the passage ofthetime (wi t h the yield to maturity held constant) just enter N = 5 CPT � PV to get one period x months) fromnownowofof$1,057.82. $1,071.74, or N = 4 CPT � PV to get the value value two periods(si(one year) from The change inin value with graphically the passage inofFigure time for2. the three bonds represented Figureassociated 1 is presented

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation of Debt Securities

Figure

2:

Premium, Par, and Discount Bonds

Bond Value ($) 1,0 8 5. 4 5 S

A premium bond (e.g. , a 6% bond trading at

IT M of3%) � r---� � .:_

A par value bond (e.g., a 6% bond trading at 1,000.00

ITM of6%) �

M

A discount bond (e.g., a 6% bond trading at ITM of l2%) � '-----

Time

LOS 56.e: Calculate the change in value of a bond given a change in its discount rate. CFA® Program Curriculum, Volume 5, page 450

Anflows; a decrease in theindiscount rate wilratel the present value of a bond' s expected cash the discount wiin lresponse l increasetothea change presentivalue of a bond'rates expected cash flows.asThethechange in bond value n the discount can be calculated di f ference between the present values of the cash flows at the two different discount rates. Bond values and bond yields are inversely related.

decrease

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increase


Study Session 16 Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation o f Debt Securities

Example: Changes in required yield

ACompute bond hasthea parbondvalvalues ue of $1,when000,thea 6o/oyieldsemiannual coupon, and three years to maturi t y. to maturity is 3o/o, 6o/o, and 12o/o. Answer:

60 CPT PV = -1,085.458 At II Y = -;32 N = 3x2; FV = 1,000; PMT =-; 2 At I I Y = .§_2 ; N = 3 x 2; FV = 1,000; PMT = 602 ; CPT PV = -1,000.000 12 N = 3 x 2; FV = 1,000; PMT = -; 60 CPT PV = -852.480 At I I Y = -; 2 2 We haverate, illustrated herevalaupoint covered earlier; ifyitheeldyielto dmaturity to maturiisthigher y equals{lothewer) than coupon the bond e is equal to par. If the the coupon rate, the bond is trading at a discount (premium) to par. We now calculate changeof thein price changesby:in yield. If the required yieldcandecreases from 6o/othetopercentage 3o/o, the value bondforincreases 1,085.46 = 8.546%. 1,000.00 Ifthe yield increases from 6o/o to 12o/o, the bond value decreases by: 852.48 -1 -14.752%. 1,000.00 ---t

---t

---t

-1

=

� �

Professor's Note: Notice that in these calculations, you only need to change the interest rate (flY) and then compute PV once the values ofN, PMT, and FV have been entered. The TVM keys remember the values for these inputs even after the calculator has been turned off!

If you iplot a bond'3. sHere yieldwetoseeits that corresponding value,are you' ll get awith graph li k e the one shown n Figure higher prices associated lbutoweris yields. ThisFor graph is callebonds, d the the price-yield curve Noteisthatconvex it is toward not a straitheghtorigin, line curved. option-free meaning it looks like half of a smile. Price-yield profile.

price-yield curve.

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation of Debt Securities

Figure

3:

The Price-Yield Profile

Bond Value (o/o of Par)

108.5 100.0 85.2

' ' ' ' ------- �-------� -------------'

'

'--' � .:... ._ _ _ _ _ _

3o/o

6%

12%

Marker Yield

LOS 56.f: Explain and demonstrate the use of the arbitrage-free valuation approach and describe how a dealer can generate an arbitrage profit if a bond is mispriced. CPA® Program Curriculum, Volume 5, page 462

Yield tono maturity is a summary measure and is essentially an internal rate of return based awebond'getsthecashyieldflowsto and its market price.withIn thematurity traditional valuation approach, maturity of bonds and risk characteristics similar to those of the bond we wish to value. Then we use this rate to discount the cash flows of the bond to be valued. With the we Again, these discount rates are called ratesatandvarious can betimthought as the required rates of return on zero-coupon bonds maturing es in theoffuture. The arbitrage-free valuati on approach simply saysthethatvaluetheofvalue of a Treasury bond based on (Treasury) spot rates must be equal to the parts (i. e . , the sum of thean arbipresent values of allty.ofIfthea bond expected cash flforows).less Ifthanthistheis notsumtheof case, there must be t rage opportuni is selling the present val u es ofbondits expected cash flows,thanan arbi tsum rageurof will buy theofbond and sell(indithevidpieces. If theflows), i s selling for more the the values the pieces ual cash tooneearncouldan buy arbittheragepieces, profit.package them to make a bond, and then sell the bond package Theappropriate first step inspot checkirates.ng forThearbisecond trage-free valuation is tothisvaluevaluea coupon bond using the step is to compare to the market price ofprofithet tobond. If the computed value i s not equal to the market price, there i s an arbi t rage becashearnedflows)by buying theng ltheower-priced alternati ve (eivte.herOfthecourse, bond thior stheassumes indi v idual and sell i higher-priced alternati that there are zero-coupon bonds available that correspond to the coupon bond' s cash flows. arbitrage-free valuation approach,

discount each cash flow using a discount rate that is specific to the maturity ofeach cash flow.

spot

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Study Session 16 Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation o f Debt Securities

Example: Arbitrage-free valuation ay)6o/oare:Treasury note= 5%, with1 1.5year=years6%,to maturi ty.years Spot=rates (expressed asis yields toforConsider maturi t 6 months and 1.5 7o/o. If the note selling $992, compute the arbitrage profit, and explain how a dealer would perform the arbitrage. Answer: To$1,value the note, note that the cash fl o ws (per $1, 0 00 par value) wi l l be $30, $30, and 030 and that the semiannual discount rates are half the stated yield to maturity. Using the semiannual spot rates, the present value of the expected cash flows is: 1,030 = $986.55 present value usmg. spot rates= 1.30025 + 1.3003 1.035 Thi s value is less thanbonds), the market pricthem e of theintonote, so we winotell buypackage, the indiandvidual cash flows (zero-coupon combine a 1.5-year sell the package for the market pri c e of the note. This wil l result in an immediate and riskl e ss profit of992.00 - 986.55 = $5.45 per bond. Determining whetherof thea bond isusing over- either or undervalued is a two-step process. First, compute the value bond the spot rates or yield to maturi ty,rate(s). rememberi n g that both are often gi v en as two ti m es the semiannual discount Second, compare this value to the market price gi v en in the problem to see whi c h is higher. --

2

--

+

3

---

How a Dealer Can Generate an Arbitrage Profit

Recal l that the Treasury STRIPS program all o ws dealers to divide Treasury bonds into their coupon payments (by date)alsoandaltheilowsr maturity payments in orderbonds/notes to create zero­by coupon securities. The program reconstitution ofTreasury putting theofindividual cashtheseflotransformations, ws back together theto create Treasury securities. Ignoring any costs performing ability to separate and reconstitute Treasury securities will insure that the arbitrage-free valuation condition is met. The program allowsitsforarbijusttrage-free the arbitrage wea dealoutlined previously. If the price ofcashtheSTRIPS bond i s greater than value, e r could buy the individual andits arbitrage-free sell the packagevalue,for thean arbitrageur market pricecanofmake the bond. If the priceandofrithesklessbond isprofilesstflows than an immediate by purchasing the bond and selling the parts for more than the cost of the bond. Such arbi t rage opportunities and the related buying of bonds priced too low and sal e s of bonds too highfurther will force prices toward equality with their arbitrage-free values,priced eliminating arbitragethe bond opportunities. Š20 12 Kaplan, Inc.

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation of Debt Securities

'

KEY CONCEPTS

LOS 56.a

To value a bond, one must:and timing of the bond's future payments of interest and Estimate the amount principal. Determi discountvaluesrate(s). Calculatenethethesumappropriate of the present of the bond's cash flows. •

LOS 56.b

Certain bond features, including embedded options, convertibil i ty, or fl o ating rates, can makeontheof bond estimation estimati values.of future cash flows uncertain, which adds complexity to the Toannuity compute the value of an option-free coupon bond, value the coupon payments as an and add the present value of the principal repayment at maturity. The val u e of a zero-coupon bond cal c ul a ted using a semiannual discount rate, (one-half its annual yield to maturity), is: tyofvalue ------=---'---=bond value = -(!--i)maturi number years X 2 LOS 56.c

i

+

LOS 56.d

When interest rates (yiel d s) do not change, a bond' s price wi l l move toward its par value as time passes and the maturity date approaches. Tobondcompute the change in value that i s attributabl e to the passage of time, revalue the with a smaller number of periods to maturity. LOS 56.e

The change inthevalchange ue thatinis theattributable to a change in the ondiscount ratediscount can be rate calcul a ted as bond' s present val u e based the new (yield). Asecuri Treasury spotayield curvethese is considered "arbitrage-free" if themarket presentprices. values of Treasury ties calcul ted using rates are equal to equilibrium If bondts byprices areg thenotlower-pri equal to ctheied alternative r arbitrage-free values, dealersor canthe generate arbicashtrage profi buyi n (ei t her the bond i n divi d ual flows) andof selltheingindividual the higher-priced ternative (either the individual cash flows or a package cash flowsalequivalent to the bond). LOS 56.f

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Study Session 16 Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation o f Debt Securities

CONCEPT CHECKERS

observes aHow 5-year,much1Oo/ois coupon bond payment? with semiannual payments. The 1. Anfaceanalyst val u e i s £1, 0 00. each coupon A.B. £50. £25. £100. 2. Abond20-year, 10o/o annual-pay bond has a par val u e of $1, 0 00. What would this be trading for if it were being priced to yield 15% as an annual rate? A.B. $685.14. $687. 0 3. $828.39. observes abelieves 5-year, that 1Oo/othesemiannual-pay bond. Thethisfacebondamount isbe 3. An£1,0analyst 00. The analyst yield to maturi t y for should 15%. Based on thi s yield estimate, the price of thi s bond would be: A.B. £1,189. £828.40.5 3. £1 ' 193.04. 4. priced Two bonds haved 8o/oparasvalues of $1,rate; 000.theBondotherA is(Bond a 5o/oB)annual -pay, 15-year bond to yiel an annual is a 7. 5 % annual-pay, 20-yearwould bond be:priced to yield 6o/o as an annual rate. The values of these two bonds Bond A Bond B A.B. $740. 611 $847. 0804 $740. 6 $1,172. $743.22 $1,172.04 Atyisofa 8o/o, 15-year, 10.Bond 5 % semiannual-pay bondsemiannual-pay priced with a bond yield topriced 5. Bond maturi whil e B i s a 15-year, 7% wi$1,th000,thethesameprices yieldoftothese maturitwoty.bonds Givenwould that both bonds have par values of be: Bond A Bond B A.B. $1,216.15 $913.54 $1,216.15 $944.5441 $746.61 $913. the 8. analystsemiannual-pay observes a 20-year, 8o/oto maturi option-free bonds bond withwassemiannual coupons. itThedrops to required yiel d t y on thi 8o/o, but suddenly 7.25%. of the drop, the price of this bond: 6. AsA. awiresult l l increase. decrease. C.B. will will stay the same. c.

c.

c.

c.

c.

Use

following data to answer Questions 6 through

An

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation of Debt Securities

7. A.Prio92.r to6the4. change in the required yield, what was the price of the bond? B. 107.85. 100.00. change in the price of this bond when the rate decreased is 8. The to:A. 7.percentage 8 6%. B. 8.7.070%. 9%. spotmonths rates=(expressed as=semiannual-pay yields to maturity) are as 9. Treasury follows: 6 4o/o , 1 year 5o/o, 1.5 years = 6o/o. A 1.5-year, 4o/o Treasury is trading at $965. Thepieces, arbitrage trade andperarbitrage profit are: A.B.notebuy the bond, sell the earn $7. 0 9 bond. bond. C. sell sell thethe bond, bond, buy buy thethe pieces, pieces, earn earn $7.$7.9109 per per bond. 10. Aremains $1,000,unchanged, 5o/o, 20-yearhowannual-pay bond has avalyieulde iofncrease 6.5%.overIf thetheyield much wi l l the bond next three years? A.B. $13.62. $13. $13.976.8. valsemiannual-pay ue of a 17-year,yield zero-coupon bond withto:a maturity value of $100,000 11. The and a of 8. 2 2% is A.B. $24,618. $25, 425. $26,108. c.

closest

c.

c.

closest

c.

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation o f Debt Securities

ANSWERS - CONCEPT CHECKERS 1. 2.

B

CPN = 1,000x

B

bond value

=

0.10

-

2

20

L t=l

= £50

100

(1+ 0.15)'

+

1,000

20

(1 + 0.15)

=

$687.03

N = 20; IIY = 15 ; FV = 1 ,000; PMT = 100; CPT --+ PV = -$687.03 3.

A

N = 10; IIY = 7.5; FV = 1 ,000; PMT = 50; CPT --+ PV = -$828.40

4.

C

Bond A: N = 1 5 ; I/Y = 8; FV = 1 ,000; PMT = 50; CPT --+ PV = -$743.22 Bond B: N = 20; I/Y = 6; FV = 1 ,000; PMT = 75; CPT --+ PV = -$ 1 , 1 72.04 Because the coupon on Bond A is less than its required yield, the bond will sell at a discount; conversely, because the coupon on Bond B is greater than its required yield, the bond will sell at a premium.

5.

A

8 105 Bond A: N = 15 x 2 = 30; I/Y = - = 4; FV = 1,000; PMT = - = 52.50; 2 2 CPT --+ PV = - $ 1 ,216. 1 5

Bond B: N = 15

x

8 2 = 30; I/Y = - = 4; 2

FV =

70 1,000; PMT = - = 35; 2

CPT --+ PV = - $9 1 3.54 6.

A

The price-yield relationship is inverse. If the required yield falls, the bond's price will rise, and vice versa.

7.

B

IfYTM = stated coupon rate =? bond price = 100 or par value.

8.

A

The new value is 40

=

N,

7 25 · 2

=

I I Y, 40

=

PMT, 1,000 = FV

CPT � PV = -1,078.55, an increase of7.855% 9.

A

. 20 20 arbitrage-free value = + 2 1.02 1 .025 -

--

+ -3

1020

1.03

=

$972.09

Since the bond price ($965) is less, buy the bond and sell the pieces for an arbitrage profit of $7.09 per bond. 10. A

With 20 years to maturity, the value of the bond with an annual-pay yield of 6.5% is 20 = N, 50 = PMT, 1 ,000 = FV, 6.5 = I/Y, CPT - PV = -834.72. With 17 = N, CPT --+ PV = -848.34, so the value will increase $ 1 3 .62.

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation of Debt Securities

11.

B

22 PMT = O, N = 2 x 17 = 34, I I Y = 8 · = 4. 1 1 , FV = 100,000 2 CPT � PV = -25,424.75,

or

100,000 = $25 ,424.76 (l .o4ur

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100

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The following is a review of the Analysis of Fixed Income Investments principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in:

YIELD MEASURES , SPOT RATES, AND FORWARD RATES Study Session 1 6

EXAM FOCUS

This topic revi ew gets aandlittlyield e moreto specific aboutpayyield measuresattention and introduces currentof yield, yield to maturity, cal l . Please particular to the concept aother bondimportant equivalentthiyinegldabout and how to convert vari o us yi e l d s to a bond equival e nt basis. The the yiellimitations. d measures here is to understand what they are telling you so that you understand their The final sectionratesofisthians revi ew introduces forward rates.youTheshould relationshi p betweento solve forwardfor rates and spot important one. At a minimum, be prepared spot rates givalenso forward ratesgripandontothesolveconcept for anofunknown forward ratespread, givenwhen two spotit isrates. You should get a firm an opti o n-adj u sted and how to interpret it, as well as how and when it differs from a zero-volatility spread.used LOS 57.a: Describe the sources of return from investing in a bond. CFA® Program Curriculum, Volume 5, page 492

Debt securities that make explicit interest payments have three sources of return: 1. The periodic made by the issuer. 2. The that occurs when the bond matures, is called, or is sold. 3. payments (i.e., the compound or the income earned from reinvesti n g the periodic coupon interest on reinvested coupon payments). The interestTheearned on reinabout vestedhow income important income source ofa bondholder return to bondwill investors. uncertainty muchis anreinvestment realize is what we have previously addressed as coupon interest payments

recovery ofprincipal, along with any capital gain or loss

Reinvestment income,

reinvestment risk.

LOS 57.b: Calculate and interpret traditional yield measures for fixed-rate bonds and explain their limitations and assumptions. CFA® Program Curriculum, Volume 5, page 493

Current yield is the simplest of al l return measures, but it offers limited information. This measure looks at just one source of return: does a bond's annual interest income-it

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

yinoteldconsider is: capital gains/losses or reinvestment income. The formula for the current payment current yield = annual cashbondcoupon price --'._ ---" .o...

_ _ _ _ _ _

Example: Computing current yield

Consider par value, at $802.07.a 20-year, Calculate$1,the000current yield.6%

semiannual-pay

bond that is currently trading

Answer:

The cash coupon payments total: annual cash coupon payment = par value stated coupon rate = $1,000 X 0.06 = $60 Because the bond is trading at $802.07, the current yield is: current yield = 802.6007 = 0.0748, or 7.48%. Note that current is based onbond withcoupon thatandit isprice. the same for a semiannual -pay andyieldannual-pay the sameinterest couponsorate annual

x

annual

(YTM)cashisflanows.annualized internal rate of return,coupon basedpayments, on a bond'thes priyieclde toandmaturity its promised For a bond wi t h semiannual i s stated as two ti m es the semiannual internal rate of return implied by the bond' The formula YTM for sa price. semiannual couponthatbondrelis:ates the bond price (including accrued interest) to 1 + CPN2 + . . . + CPN2N + Par bond price = (1 +CPN�) �t ( 1 + ( �t 1 + where: bond price == fulthel (semiannual) price includingcoupon accruedpayment interestreceived after semiannual periods CPN NYTM == yinumber of years to maturity eld to maturity YTM the sameyou information. is, given the YTM, you can calculate the priceandandpricegivencontain the price, can calculateThat the YTM. We cannotpayment easily solve for weYTMcouldfromsoltheve ibond price.andGiven a tryibondng price and valtheues of coupon amount, t by trial error, di f ferent YTM until the present value of the expected cash flows is equal to price. Fortunately, Yield to maturity

...,. ....- ....!. --:-;...

YT

--=.,...

-

YT

r

Page 102

N

YT

t

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Study Session 16 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

your calculator wid thell dodiscount exactly theratesame thing, only faster.sidesIt ofusesthea pritrialcinandg formula error algorithm to fi n that makes the two equal. YTM Consider a 20-year, $1, 0 00 par value bond, with a 6o/o coupon rate (semiannual payments) with a full price of $802.07. Calculate the YTM. Example: Computing

Answer:

Using a financial calculator, you'd find the YTM on this bond as follows: PV = -802.07; N = 20 x 2 = 40; FV = 1,000; PMT = 60/2 = 30; CPT ---+ 1/Y = 4.00 4o/o is the semiannual discount rate, YTM 2 in the formula, so the YTM = 2 x 4o/o = 8o/o. Note dothatthisthetosignsavoidofPMT and FV"Error are positive, andonthethesignTIofPV is negative; youget the must the dreaded 5" message calculator. If you "Error can assume negativedve from valuetheto thebond.price (PV) of5"themessage, bond andyoua positi ve signyouto thehavecashnotflassigned ows to bea recei There area certain relationships thatat exia discount, st betweenordiatfferent yield measures, dependingareon whether bond is trading at par, a premium. These relationships shown in Figure 1. Figure 1 : Par, Discount, and Premium Bond Bond Selling at:

Relationship

Par

coupon rate

=

current yield

Discount

coupon rate

<

current yield < yield to maturity

Premium

coupon rate

>

current yield

=

>

yield to maturity

yield to maturity

These conditions wiislllessholthan d in allits cases; every discount bond wiyielll dhavethataisnominal yielitsd (coupon rate) that current yi e l d and a current less than YTM. The yield to maturi tyacalculated in the previous(BEY), examplande (2wexwillthealsosemireferannualto itdiscount rate) i s referred to as as a semiannual YTM or that semiannual -paydivide YTM.byIftwoyoutoaregetgiven yields that arediscount identifirate.ed as BEY, you wi l l know you must the semiannual With bonds that make annual coupon payments, we can calculate an flows. which is simply the internal rate of return for the expected annual cash bond equivalent yield

annual-pay yield

to maturity,

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

Example: Calculating for annual coupon bonds Consider an annual-pay price of $802. 07. Calculate20-year, the $1,000 par value, with a 6o/o coupon rate and a full Answer: The relation between the price and the annual-pay YTM on this bond is: 60 r 1,000 YTM = 8.0 19%. 802.07 = I: (1 + YTM) YTM) Here we have separated the coupon cash flows and the principal repayment. The calculator solution is: PV8.0 19% = -802. 0 7; N = 20; FV = 1,000; PMT = 60; CPT ---7 IIY = 8.019; is the annual-pay YTM. Use a discount rate of 8. 0 19o/o, and you' l l fi n d the present value of the bond' s future cash flowspric(annual market e of thecoupon bond. payments and the recovery of principal) will equal the current For zero-coupon Treasury (semiannual-pay YTMs). bonds, the convention is to quote the yields as BEYs Example: Calculating for zero-coupon bonds Aannual-pay 5-year Treasury YTM.STRIP is priced at $768. Calculate the semiannual-pay YTM and Answer: The directis:calculation method, based on the geometric mean covered in Quantitative Methods, 1,000 ) 10 - 1 2 = 5.35o/o. the sem1annu . -pay YTM or BEY= (-768 1,000 )5 -1 = 5.42%. the annual-pay YTM = (-768 YTM

annual-pay YTM.

20

+

t=1

(I+

20

=>

The discount rate is the bond's YTM.

YTM

1

al

1

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X


Study Session 16 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

Using the TVM calculator functions: --+ 1/Y 2.675% 2 5.35% for PV -768; FV 1,000; PMT 0; N 10; CPT the semiannual-pay PV -768;YTM. FV 1,000; PMT 0; N 5; CPT ---+ 1/Y 5.42%YTM, for theandannual-pay The YTM ofgrow5.4to2%$1,means 5.42%annual-pay per year would 000 inthatfive$768 years.earning compound interest of =

=

=

=

=

x

=

=

=

= =

=

The yield topar. call Foris usedbondsto calculate thea premium yield on callable bonds that are may sellingbeatlessa premi u m to tradi n g at to par, the than the yi e ld to maturi t y. This can be the case when the call pri c e i s below the current market price. The culation the calculation oftheyield to maturity, exceptcalthat the of the yield to call is thefor same the paras value i n FV and for periods tofirmaturi tover y, theWhen a bond has a peri o d of cal l protection, we cal c ul a te the yield to st call period until may fiwerst canbe called, andtheuseyielthed first callsubsequent price in thecallcalculation astheFV. Inappropriate a simithelbond ar manner, calculate to any date using call price. If the abond contains a provision forusinga calltheatnumberat some timeuntiinl thethe future, wedatecanand calcul te the of years par call parmeasure, for thethematurity payment. If youcalculation; have a goodjustunderstanding ofabout the yieldthe tonumber maturityof YTC i s not a difficult be very careful years to the call and the call price for that date. An example wi l l il l ustrate the calculation of these yield measures. yield to call

callprice is substituted semiannual periods until the call date is substituted

number of N.

par

yield to first par call

Example: Computing the YTM, YTC, and yield to first par call Consider av20-year, 10% semiannual-pay bond withyears. a fullCalculate price of 112the that canYTC, be and call e d in fi e years at 102 and call e d at par in seven YTM, yield to first par call. Professor's Note: Bondprices are often expressed as a percent ofpar (e.g., 100 = par).

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

Answer: The YTM1/Ycan= 4.be361% calculated PV = -112; PMT = 5; FV = 100; CPT---+ 2 = as:8.7N2%= =40;YTM. Toperiods compute thetheyield to firstdatecall(10)(YTFC), we substi tstutecalthel pricenumber offorsemiannual until fi r st call for N, and the fi r (102) FV, as follows: N = PV = -112; PMT = 5; FV = CPT ---+ 1/Y = 3.71% and 2 3.71 = 7.42% = YTFC To calculateperiods the yielduntilto first par call (YTFPC), we forwillNsubstitute the number ofas semiannual the fi r st par call date (14) and par (100) for FV follows: N = PV = -112; PMT = 5; FV = CPT ---+ 1/Y = 3.873% 2 = 7.746% = YTFPC thatIf thethe yield towerecall,tradi7.4n2%,g atias significantly lowervalue,thanthere the yiel d tobematuri ty, to 8.Note 72%. bond discount to par would no reason calcul a te the yi e l d to cal l . For a discount bond, the YTC wi l l be hi g her than the YTM since the bondcalwill price. l appreciate morearerapidly witonh thea yicaleldl toto atcallleastbasisparwhen and,theperhaps, an even greater Bond yields quoted YTC i s less than the YTM, whi c h can only be the case for bonds trading at a premium to the call price. The yield toofworst is theInworst yield example, outcome oftheanyyielthat arefirstpossible gissventhanthethecallYTM provisions the bond. the above d to cal l is l e and less than the yield to first par cal l . So, the worst possible outcome i s a yi e ld of 7.42%; the yield to first call is the The yield to refunding refers to a specific situation where a bond i s currently callable and currentcontain rates make callinggithevingissueprotection attractivefromto therefunding issuer, but where thefuturebonddate. covenants provisions until some The calculation of the yiel d to refunding i s just l i k e that ofYTM or YTC. The di ff erence here is that theof periods yield toused refunding would use theis calthel price, but therefundi daten(and therefore theends.number in the calculation) date when g protection Recal l that bonds that are callable, but not currently refundable, can be called using funds from sources other than the issuance of a lower coupon bond. The yield to put (YTP) is used if a bond has a put feature and is selling at a discount. The yield toisputjustwilikllelithekelyyield be higher than thewityihetheld tonumber maturity.of semiannual The yield toperiods put until calculation to maturity the put date as N, and the put price as FV X

10;

102;

x

14;

100;

X

yield to worst.

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Study Session 16 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

YTM YTP Consider 000 is at par ibond. is sellingtheforYTMa fullandpricethe ofYTP.$925.40.a 3-year, The fir6%, st put$1,opportunity n two The years.bond Calculate Example: Computing

and

semiannual-pay

Answer:

Yield to maturity is calculated as: = 6; FV = 1,000; PMT = 30; PV = -925.40; CPT � 1/Y = 4.44 2 = 8.88% =NYTM x

Yield to put is calculated as: = 4; FV = 1,000; PMT = 30; PV = -925.40; CPT � 1/Y = 5.11 2 = 10.22% = YTP x

N

In this example, gher than the YTM and, therefore, would be the appropri ate yieldtheto lyielookdattoforputthisis hibond. The cash (CFY) is used for mortgage-backed securities and other amortizing asset-backedrepayment securitiescanthatbe have monthl ythecashamount flows. requi In many cases,amortithezeamount ofover the principal greater than r ed to the loan its original life. Cash flow yielodns(CFY) incorporates an assumed schedule of Once monthlywe cash flows based on assumpti as to how prepayments are likely to occur. have projected can calcul of return basedtheon monthly the marketcashpriflceows,of thewe securi ty. ate CFY as a internal rate flow yield

monthly

Professor's Note: I believe you are more likely to be required to interpret a CFY

� than to calculate one. Ifyou need to calculate a CFY, just use the cash flow keys, � put the price ofthe security as a negative value as CF0 , enter the monthly cash flows sequentially as CFn's, and solve for IRR, which will be a monthly rate.

The following formula is used to convert a (monthly) CFY into bond equivalent form: bond equivalent yield [(1 +monthly CFY)6 -1] 2 Here, we have converted the monthly yi e ld into a semiannual yield and then doubled it to make it equivalent to a semiannual-pay YTM or bond equivalent yield. Aassumed limitation of the CFY measure is that actual prepayment rates may di f fer from those in the calculation of CFY. =

X

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

The Assumptions and Limitations of Traditional Yield Measures

The primaryrate of return that we will realize on a fixed-income is that it idoes not telover l us theits life. compound n vestment This is because we do not know the rate of interest we wi l l real i z e on the rei n vested payments (theonreia bond. nvestment rate).earlReiiner,vestment income can be thea signifi cantonpart ofcoupon the overal l return As noted the uncertainty about return reinvestedrates,cashother flowsthiisnreferred gher forbonds bondsaswiwellth .higher coupon gs equalto, andas potentially higherItforis hicallable The yield onIt ias bond is computed the actual atcompound return that was earned on For the a ibond nitiarealized ltoinvestment. usually the end of the investment horizon. have aat the YTM, andequalthe tobondits YTM, allhelcashd until flowsmaturity. prior to maturity must bereinvestment reinvested must be If the average rate is below the YTM, the realized yield wi l l be below the YTM. For this reason, it is often stated that: limitation of the yield to maturity measure

reinvestment risk.

realized yield

The yield to maturity assumes cash flows will be reinvested at the YTM and assumes that the bond will be held until maturity.

The other internal ratetheyofarereturn measures, YTC andandYTP, sufferaccount from forthe reinvestment same shortcomings since calcul a ted li k e YTMs do not income. The CFY measure i s also an i n ternal rate of return measure and can differ greatl y fromandtheprepayments realized yieldmustif reinvestment scheduled principal payments be reinvestedrates alongarewithlow,thesinceinterest payments. LOS 57.c: Explain the reinvestment assumption implicit in calculating yield to maturity and describe the factors that affect reinvestment risk. CPAÂŽ Program Curriculum, Volume 5, page 495

is onimportant because iflethess thanreinvestment rateTheisreallessizedthanyieldthe will YTM, the realized yi e l d the bond wi l l be the YTM. always be between the YTM and the assumed reinvestment rate. bondholder a bondbyuntil maturity interest payments, theIf a total amountholds generated the bond overandits lifereinvests has threeall coupon components: 1. Bond principal. 2. Coupon interest. 3. Interest on reinvested coupons. Once we calculate the total amount needed for a particular level of compound return over a bond' s life, we canincome subtractnecessary the principal andevecoupon payments to example determinewithell amount of reinvestment to achi the target yi e ld. An illustrate this calculation. Reinvestment income

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Study Session 16 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

Example: Required reinvestment income for

a

bond

Ifmustyoubepurchase a 6%,over1 0-year Treasury bond at par, howwithmuch reinvestment income generated i t s l i fe to provide the investor a compound return of 6o/o on a semiannual basis? Answer:

Assumi ng thetenbondyearshas(20a parsemiannual value of $100, first calculate be generated periods)we from now as: the total value that must 100(1.03) 20 = $180.61 There bond tcoupons principalare at20maturi y. of$3 each, totaling $60, and a payment of$100 of Therefore, the required reinvestment income over the life of the bond is: 180.61 - 100-60 = $20.61 Professor's Note: Ifwe hadpurchased the bond at a premium or discount, we would still use the purchase price (which would not equal I 00) and the required compound return to calculate the totalfuture dollars required, and then subtract the maturity value and the total coupon payments to get the required reinvestment income.

Factors That Affect Reinvestment Risk

Other things being equal, a coupon bond's will with: because there' s more cash fl o w to reinvest. moreonofcoupon the totalcashvalueflows). of the investment is in the coupon cash flows (and interest In both cases, thereturn amountand,oftherefore, reinvestedintroduce income wimore ll playreinvestment a bigger rolrisk. e in Adetermining the bond' s total noncallable zero-coupon bond has no reinvestment risk over its l i f e because there are no cash fl o ws to reinvest prior to maturity. reinvestment risk

increase

Higher coupons Longer maturities-because -

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Page 109


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

LOS 57.d: Calculate and interpret the bond equivalent yield of an annual-pay bond and the annual-pay yield of a semiannual-pay bond. CFA® Program Curriculum, Volume 5, page 494

Thi s LOS requires that you be able t o turn a semiannual return into an annual return, and an annual return into a semiannual return. bonds with thatofa corporati on hasan annual a semiannual coupon bond trading in thewithUnia YTM ted States wi6.Suppose t3h0%.a YTM 6. 2 5%, and coupon bond trading i n Europe of Which bond has the greater yield? Answer: To(semiannual determine-pay) the answer, the yield to a bond equiwevcanalentconvert yield. That is: on BEY of an annual-pay bond = [(1 +annual YTM - 1] 2 Thus, the BEY of the 6.30% annual-pay bond is: [(1 0.0630)0·5 -1] 2 [1.031-1] 2 0.031 2 0.062 6.2% The 6.25% semiannual-pay bond provides the better (bond equivalent) yield. Alternati velyield) y, we tocouldan equi convert theannual-pay YTM of thebasis.semiannual-pay bondannual (whiyield ch is a bond equival e nt v alent The equi v alent (EAY is: to the 6.25% semiannual-pay YTM equivalent annual yield (1 0'0�25 r -1 0.0635 � 6.35% Example: Comparing

different coupon frequencies

the annual-pay bond 1

X

)2

+

X

X

=

X

=

=

=

-sometimes known as the effective annualyield)

=

+

=

The EAY ofbond. the semiannual-pay bond is 6.35%, which is greater thanyietheld as6.3%longforas thewe annual-pay Therefore, the semiannual-pay bond has a greater put theas bond yields equi on anvalent equivalent basis, calculating both yields (semiannual yieldsboth2).as annual yields or calculating x

Page 1 1 0

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Study Session 16 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

LOS 57 .e: Describe the calculation of the theoretical Treasury spot rate curve and calculate the value of a bond using spot rates. CFA® Program Curriculum, Volume 5, page 508

The par yi e ld curve gi v es the YTMs of bonds currentl y trading near their par values (YTM calcoupon need to use these yields to get the theoreti Treasuryrate)spotforratevarious curvematurities. by a processHere,callewed bootstrapping. The method of bootstrapping canc andbe detailed a little confusing, so legeneral t's first getideatheis that mainweideawilland then go through a more realisti example. The solve for spot rates by knowi n g the prices of coupon bonds. We always know one spot rate totwobeginspotwithrates,andwethencancalculate therdspot rateonforthethemarket next longer period. When we know get the thi based pri c e of a bond wi t h three cash flows by using the spot rates to get the present values of the first two cash flows. Asannual an exampl e of thisas shown method,in Ficonsider we know -pay bonds gure 2. that All three bondstheareprices tradingandatyields par orof$1,three000. �

r s and

Figure 2: P ice

Yield for Three

An

a Bonds

nual P y

Maturity

Coupon

Yield

Price

1 year

3%

3%

$ 1 ,000

2 years

4%

4%

$ 1 ,000

3 years

5%

5%

$ 1 ,000

-

Because thethe1-year bond makes only oneyipayment (its'ssingle an annual-pay bond) of $1,030 at maturi t y, 1-year spot rate is 3%, the e ld on thi payment. The 2-year bond makes two payments, a $40 coupon in one year and a $1, 0 40 payment at maturity i n two years.weBecause thethespotsumrateoftothediscount theval2-year bond'bond' s firsstcash cashflfloowsw imust s 3%,equal and because know that present u es of the its (no-arbitrage) price of $1,000, we can write: 40 1,040 2 $1,000 1.03 (1 2-year spot rate) Based on this, we can solve for the 2-year spot rate as follows: 1,-0---40----=-2 = 1,000- 40 = 1,000-38.83 = 961.17 1. --' 1.03 (1 2-year spot) 1,040 = (1 2-year spot)2 = 1.082 2. 961.17 +

+

=

-

+

---

+

1

3. 2-year spot= (1.082)2 -1 = 0.04019 = 4.019% ©20 1 2 Kaplan, Inc.

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

Now have both price that of thewe3-year bondtheto wri1-year te: and 2-year spot rates, we can use the cash flows and _2Q_ + 50 2 1,050 3 = 1,000 1. 03 (1.04019) (1 3-year spot) And solve for the 3-year spot rate: 50 1,050 1,000- _2Q_ 2 1.03 (1.04019) (1 3-year spod 1' 050 3 1,000-48.54-46.21 = (1 3-year spot) 1' 050 3 905.25 = (1 + 3-year spot) ( 1,o5o )X - 1 = 3-year spot = 0.05069 = 5. 069% 905.25 +

+

+

+

So, we can state that: _2Q_ 50 2 1,050 3 = $1,000 1.03 (1.040 19) (1.05069) We have just solved for the 2-year and 3-year spot rates by the method of bootstrapping. In practice, Treasury bondsillustrates pay semiannuall y, andofthei r YTMs arewhen semiannual-pay YTMs. The next example the method bootstrapping coupons are paid semiannually. Consider the yi e l d s on coupon Treasury bonds tradi n g at par gi v en in Figure 3. YTM for the bonds is expressed as a bond equivalent yield (semiannual-pay YTM). +

Figure

Page 1 1 2

3:

+

Par Yields for Three Semiannual-Pay

Maturity

YTM

Coupon

Price

6 months

5%

5%

1 00

1 year

6%

6%

1 00

1 8 months

7%

7%

1 00

Bonds

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

The wi0.0th25si=x 2.5% monthsorle5o/oft toonmaturity hasBEYa semiannual discount rate ofwill only 0.make 05 bond 2one= payment an annual basis. Because this bond 5 in six months, the YTM is the spot rate for cash flows to be received six monthsoffrom102.now. The bootstrapping process proceedswifromth thethisprice/YTM point usinginformation the fact thatonthethe6-month annualized spot rate is 5o/ o together 1-year bond. We wil l use the formula for valui n g a bond using spot rates that we covered earlier. Noti n g that the 1-year bond wi l l make two payments, one in six months of 3. 0 and one i(whi n onechyear 0, and from that thenow),appropriate spot rate to discount the coupon payment comesof si1 03.x months we can write: -1.o3-25 103 100, where is the annualized 1-year spot rate, (1 � ) 3 927=97.073 and solve for 1 ·n�l2 as: ( 103 =100---=100-2. 1. o 25 1 �) 1 0_3_ (1 121)2 ' so 'J97.073 _ {103 1 12I 97.073 0.030076 and 2 0.030076 0.060152 6.0152% Now thatce ofwethehave18-month the 6-month andto set1-year spot rates, weequalcantousethethisvalueinformation ands thecashpriflows bond the bond price of the bond' as: 3.5 3.5 2 103.5 00 1.025 (1.030076) (1 ?{r where is the annualized 1.5-year spot rate, and solve for ?{ 103· 5 =100-_22_ - 3· 5 2 = 100-3.4 15-3.30=93.285 (1 ?{r 1.025 (1.030076) I

+

2

+ 51.

51 0

=

·

5

+ 51.

=

+ 5Lo

51 .0

=

--

-

=

+

+

2

X

=

5Lo

=

=1

+ 5l.

=

)

51.

51 .5

+ 5l .

103.5 (1 121) 3 , so ( 103.5 )3 _ 1 12I 93.285 93.285 =

51. 5

=

+ 51. 5

1

=

51. 5

0.0705 7.05% =

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Page 1 13


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

To summarize the method of bootstrapping spot rates from the par yield curve: 1. Begin with the 6-month spot rate. 2. Set1-yearthespot valuerateof thedivid1-year present value of the cash flows with the ed bybond two asequal the onlto ytheunknown. 3. Solve for the 1-year spot rate. the 6-month and 1-year spot rates and equate the present value of the cash 4. Use flunknown. ows of the 1.5-year bond equal to its price, with the 1.5-year spot rate as the only 5. Solve for the 1.5-year spot rate. Professor's Note: You are responsible for "describing" this calculation, not for computing theoretical spot rates.

Example: Valuing a bond using spot rates

Given the following spot rates (in BEY form): 0.1.05 years years == 4% 5% 1.5 years = 6% Calculate the value of a 1.5-year, 8% Treasury bond. Answer:

Simply ay outsincethethey cashareflowsquoted and discount by the spot rates, which are one-halfthe quoted lrates in BEY form. 4 4 104 102.9 (1 0.�4 ) (1 0.�5 ) (1 0.�6 ) or, with the TVM function: NN == 2;1; PMT = 0; 1/Y = 2; FV = 4; CPT PV = -3. 9 2 PMT == 0;0; 1/Y N = 3; PMT 1/Y == 2.5; 3; FVFV= =104;4; CPT CPT PVPV==-3.81 -95.17 Add these values together to get 1 02.9. -:1 +

-

+

+

2

+

+

3

=

--t

--t

--t

Page 1 14

©2012 Kaplan, Inc.


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

LOS 57.f: Explain nominal, zero-volatility, and option-adjusted spreads and the relations among these spreads and option cost. CFAÂŽ Program Curriculum, Volume 5, page 513

The nominal spread is the simplest of the spread measures to use and to understand. It is simplythean iusessue'ofs YTM minus spread the YTMsuffers of a from Treasury security of similarasmaturity. Therefore, the nominal the same limitations the YTM. YTM uses aInsinfact, gle discount rate to val u e the cash fl o ws, so it YTMis forflat.a coupon bond is theoretically correct only to the extent that the spot rate curve

ignores the shape ofthe spot

yield curve.

The Zero-Volatility Spread

One way to get a bond' s nominal spread to Treasuries i s to add different amounts to the yield oftoathecomparable Treasury bond, and value thevaluebondequal withtothose YTMs. price The amount added Treasury yield that produces a bond the market of the bond must be the nominal yield spread. This themayzero-volatility seem like an odd wayorto static get thespread, spread,is but it makesThesensezero-volatil when youityseespread how spread, calculated. iins theorderequalto make amountthethatpresent we must addof theto each ratebond'ons thecashTreasury spotto yiits(Z-spread) eldmarket curveprice. value ri s ky fl o ws equal Instead of measuri n g the spread to YTM, the zero-vol a ti l i t y spread measures prithecesspread Treasury(i.e.spot rates necessary produce a spot rate curve that correctly a riskyto bond , produces its markettoprice). For a riskyspotbond,ratesthewilvall beuetooobtained from discounting thespotexpected cashlower flowsthanat those Treasury hi g h because the Treasury rates are appropri a te for a ri s ky bond. In order to val u e i t correctl y , we have to i n crease each of thesTreasury spotdiscounted rates by some equal amountspotso that theequals presentthe market value ofvalue the riofskythe bond' cash fl o ws at the (increased) rates bond. The following example wil illustrate the process for calculating the Z-spread.

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

Example: Zero-volatility spread 1-,Consider 2-, anda 3-year spot rates on Treasuries are 4%, 8.167%, and 12. 3 77%, respecti v ely. 3-year, 9o/o annual coupon corporate bondCompute tradingtheat 89.nominal 464. Thespread YTMandis 13.50%, and the YTM of a 3-year Treasury is 12%. the zero-volatility spread of the corporate bond. Answer: The is: = 13.50- 12.00 = 1.50%. nominal spread = YTM BondTomarket compute the Z-spread, set the present value of the bond' s cash fl o ws equal to today' s price. Discount eachZS.cash floforw atZSthein appropriate zero-coupon bondyouspot ratethe a fi x ed spread equals Solve the fol l owing equation and have Z-spread: 89.464 = (Lo4 9 zsY ( 1. 0 81679 zs)2 (1.12377109 zs)3 ZS 1.67% or 167 basis points Noteitthatintothithes spread is foundsidebyoftrial-and-error. In other words, pickequals a number "ZS,If" plug right-hand the equation, and see if the result 89. 4 64. theanother right-hand "ZS" andsidestartequalover.s the left, then you have found the Z-spread. If not, pick nominal spread

YTMTreasury

plus

+

+

+

+

+

=>

=

Professor's Note: This is not a calculation you are expected to make; this example is to help you understand how a Z-spread differsfrom a nominal spread.

There two primary factors that influence the difference between the nominal spread and theareZ-spread for a security. The steepermeasures. the benchmark spot ratedifference curve, thebetween greaterthethenominal differenceandbetween thewhen two spread There i s no Z-spread thelargerspotthanyieldthecurve is flaspread. t. If theThespotZ-spread yield curveis leisss upward sloping, thespread Z-spread is nominal than the nominal when theThespot yi e ld curve i s negatively sloped. earlmeasures. ier the bondFor principal is paid, theslopedgreateryieldthecurve, difference between security, the two spread a gi v en positively an amortizing such an MBS, will have greater difference between its Z-spread and nominal spreadasthan a coupon bondawill. •

Page 1 1 6

©2012 Kaplan, Inc.


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

The Option-Adjusted Spread

Thecallable bond, for example, s r (OAS) measure is usedyieldwhenthana bond has embedded options. Abond, must have a greater an identical option-free and a greater nominalmeasures spreadwiorllZ-spread. Without accounting forwhen, the value of thethe additional options, these spread suggest the bond is a great value in fact, yield is compensation for caloutl risk. Loosely speaking, thethe option­ takes the option yield component of the Z-spread measure; adjusted spread is the spread to the Treasury spot rate curve that the bond would have if itliqwere The OASrateisrisk. the spread for non-option characteristics like credit risk, uidityoption-free. risk, and interest option-adjusted p ead

option-adjusted

spread

Proftssor's Note: The actual method ofcalculation is reservedfor Level II; for our purposes, however, an understanding ofwhat the OAS is will be sufficient.

Embedded Option Cost

If we scalculate anTheoption-adjusted spread foryiaeldcallrequired able bond,to compensate it will be lessforthanthe thecall bond' Z-spread. di f ference is the extra option. Calling that extra yield the option cost, we can write: Z-spread - OAS = option cost in percent Example: Cost of an embedded option

Supposebonds you learn that a bondofis call167ablebasiand has anCompute OAS of the135bp.costYouof thealsoembedded know that similar have a Z-spread s points. option. Answer:

The option cost= Z-spread-OAS = 167- 135 = 32 basis points. For embedded short cal l s (e. g . , cal l abl e bonds): option cost> 0 (you receive compensation for writing the option to thethanissuer)for an option-free OAS < Z-spread. you bond.In other words, For embedded puts (e. g . , putable bonds), option cost < 0 (i. e . , you must pay for the option) > Z-spread. than for anOAS option-free bond.In other words, you �

require more yield on the callable bond �

require lessyield on theputable bond

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Page 1 17


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

LOS 57.g: Explain a forward rate and calculate spot rates from forward rates, forward rates from spot rates, and the value of a bond using forward rates. CPA® Program Curriculum, Volume 5, page 520

is a borrowing/lending rate for a loan to be made at some future date. The notation used must identifywilboth the length of the lending/borrowi ng period and when in the future the money l be loaned/borrowed. Thus, /1 is the rate for a 1-year loan one year from now and f i s the rate for a 1-year loan to be made two years from 1 2 now, andratesoason./o·Rather than introducevaluesa separate notation, we cancashrepresent theneedcurrent 1-year To get the present of a bond' s expected fl o ws, we to discount each cash fl o w by the forward rates for each of the periods until it i s received. (The present value of $1 to be recei v ed in peri o d di s counted by the forward rates for periods 1 to is called the for period

A forward rate

n,

forward discount factor

n,

n.)

The Relationship Between Short-Term Forward Rates and Spot Rates

The idea here is that Thi s relation i s il l ustrated as (1 5 3)3 = (1 /0)(1 1f )(1 /2) and the reverse as 3 53 = [(1 /0)(1 /1)(1 /2)] 1 1 - 1, which is the geometric mean we covered in Quantitative Methods.

borrowingfor three years at the 3-year rate or borrowingfor 1-year periods, three years in succession, should have the same cost. +

+

+

+

+

+

1

+

Example: Computing spot rates from forward rates

Ifforward the current 1-year rate is 2o/o, the 1-year forward rate ( f1) i s 3o/o and the 2-year 1 rate (1f2) is 4o/o, what is the 3-year spot rate? Answer:

[(1.02)(1.03)(1.04)] 1 13 - 1 = 2.997% This canproduce be interpreted toending mean valthatueaasdolaldollar ar compounded atcompound 2.997% forinterest threeofyears2o/o would the same that earns the first year, 3o/o the next year, and 4o/o for the third year. 53 =

Proftssor's Note: You can get a very good approximation ofthe 3-year spot rate with the simple average oftheforward rates. In the previous example, we calculated 2.997% and the simple average of the three annual rates is

2 3 4 3o/o. 3 + +

Page 1 1 8

=

©2012 Kaplan, Inc.


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

Forward Rates Given Spot Rates

Wecalculcanateuseforward the sameratesrelationship we used to calculate spot rates from forward rates to from spot rates. Our basic relation between forward rates and spot rates (for two periods) is: Which, again, tells us that an investment has the same expected yi e ld (borrowi n g has therate,same expected cost) whether we invest (borrow) for two periods at the 2-period spot 52, or for one period at the current rate, 5 1 , and for the next period at the expected forward rate, 1f1 • Clearly, given two of these rates, we can solve for the other. Example: Computing a forward rate from spot rates

The 2-period spot rate, 52, is 8% and the current 1-period (spot) rate is 4% (this is both 5 1 and /0). Calculate the forward rate for one period, one period from now, /1 • Answer:

The following figure illustrates the problem. Finding a Forward Rate

2-year bond (52 8.0%) =

1-year bond (today) (SI 4.000%) =

1-year bond (one year from roday)(J1

=

?)

2

0

©20 12 Kapl

an ,

In c

.

Page 1 19


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

From our original equality, (1 + S2)2 = (1 S1)(1 1f1), we can get (1(1+SS2t))2 -1 = ft or, because we know that both choices have the same payoff in two years: (1.08) 2 = (1.04)(1 /)) (1 f ) = (1.(1.008)4)2 f = (l.(1.008)4)2 -1= 1.1664 1.04 -1=12.154% Intheyother words, investors are wi l l i ng to accept 4. 0 % on the 1-year bond today (when 2-yearThis bondfuture today)rateonlythatbecause 12.154% 1-yearcould bondgetone8.0% yearonfromthetoday. can bethey lockedcaningettoday is a on a +

+

+

l

+

+ 1 1

l 1

forward rate.

Similarly, we can back other forward rates out of the spot rates. We know that: And that: This last theequation says thatvaliunevesting for threeforyears at theat3-year spot spot rate should produce same ending as i n vesting two years the 2-year then for a third year at f2, the 1-year forward rate, two years from now. rate and Solving for the forward rate, 1 f2, we get: 1

Page 120

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

Example: Forward rates from spot rates

Let' s extend the previ o us example to three periods. The current 1-year spot rate i s 4.0%, the current 2-year spot rate is 8.0%, and the current 3-year spot rate is 12.0%. Calculate the 1-year forward rates one and two years from now. Answer:

We know the following relation must hold: We can use it to solve for the 1-year forward rate one year from now: We also know that the relations:

(1 + S 3) 3 = (1 + S I )(1 + /I ) (1 + /z) + S 3) 3 = + S2)2 (1 + /2)

and, equivalently (1 (1 must hold. Substituting values for S3 and 52, we have: so that the 1-year forward rate two years from now is: f2 (1 .12)2 -1 20.45% 1

=

(1.08)

3

=

To verify these results, we can check our relations by calculating: s3 = [1(I.04)(1.121 54)(1 .2045)l 1 13 - 1= 12.ooo/o

Thi s may alperil seem a bi1-period t complirates cated,should but thehavebasictherelation, thatas borrowi ng forat successive o ds at same cost borrowing multiperiod spot rates, can be summed up as: 2 = (1 + S 1 )(1 + f1) for two periods, and (1 + S ) 3 = (1 + 52) 2 (1 + /2) for (1three+ 52)periods. 3 1

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

Professor's Note: Simple averages also give decent approximations for calculating forward rates from spot rates. In the above example, we had spot rates of4% for one year and 8% for two years. Two years at 8% is 16%, so if the first-year rate is 4%, the second-year rate is close to 16- 4 12% (actual is 12. 154). Given a 2-year spot rate of8% and a 3-year spot rate of 12%, we could approximate the 1-year forward rate from time two to time three as (3 x 12) - (2 x 8) 20. That may be close enough (actual is 20. 45) to answer a multiple-choice question and, in any case, serves as a good check to make sure the exact rate you calculate is reasonable.

=

=

We can al s o calculate implied forward rates for loans for more than one period. Gi v en spot rates of: 1-year = 5%, 2-year = 6%, 3-year = 7%, and 4-year = 8%, we can calculate l2 ' The implied forward rate on a 2-year loan two years from now is: Professor's Note: The approximation works for multi-periodforward rates as well.

��� Here, we have (4 8 -2 6 2) X

X

=

10 .

.

The difference between two years at 6% and

four years at 8% is approximately 20%. Since that is for two years, we divide by two to get an annual rate ofapproximately 10%.

Valuing a Bond Using Forward Rates Example: Computing a bond value using forward rates

The current 1-year rate (1 f0) is 4%, the 1-year forward rate for lending from time = 1 to time = 2 is /1 = 5%, and the 1-year forward rate for lending from time= 2 to time = 3 is 1 f2 = 6%. Value a 3-year annual-pay bond with a 5% coupon and a par value of $1,000. Answer:

_2Q_ +

50 + 1,050 $1 000. 98 1.04 (1.04)(1.05) (1.04)(1.05)(1 .06) ' =

Professor's Note: Ifyou think this looks a little like valuing a bond using spot rates, as we didfor arbitrage-free valuation, you are right. The discountfactors are equivalent to spot rate discountfactors. Page 122

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

KEY CONCEPTS LOS 57.a

ThreeCoupon sourcesinterest of returnpayments. to a coupon bond: Reinvestment couponvalue. cash flows. Capi tal gain orincome loss ononthetheprincipal Yield to amaturi tdiscount y (YTM)ratefor athatsemiannual-pay couponvaluebondof theis calculated as two times the semi nnual makes the present bond' s promised cash fltheowsYTM equalis tosimply its market price plus accrued interest. Forthean present annual-pay coupon bond, the annual discount rate that makes val u e of the bond's promised cash flows equal to its market price plus accrued interest. The current yield for a bond is its annual interest payment divided by its market price. Yi(put)eld and to callthe(put) is calculated as a YTMforbutthewithnumber the number of periods until theandcallthe call (put) pri c e substituted of periods to maturity maturity value. The cashtheflowcurrent yield ismarket a monthly rate of return based on a presumed rate and priceinofternal a mortgage-backed or asset-backed securiprepayment ty. Thesebeyidiscounted eld measuresat theare same limitedrate;by theirthecommon assumptions that: (1) all cash flows can bond wi l l be hel d to maturi tsy,YTM; with alandl coupons reinvested to maturi t y at a rate of return that equals the bond' (3) all coupon payments will be made as scheduled. YTM is not the realized yield on an investment unless the reinvestment rate is equal to the YTM. The amount of rei n vestment income requi r ed to generate the YTM over a bond' s l i f e i s thematuridifference price of and the bond, ty, and thebetween sum ofthethepurchase bond's interest principalcompounded cash flows.at the YTM until Reinvestment whentthey (coupon couponraterateheld is greater (maturity held constant) and when the bondriskhasislohigher nger maturi constant). The bond-equivalent yield of an annual-pay bond is: BEY= [�(1 + annual-pay YTM) - 1] •

LOS 57.b

(2 )

LOS 57.c

LOS 57.d

x

2

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

The annual-pay yield can be calculated from the YTM of a semiannual-pay bond as: YTM )2 -1 EAY = (1 semiannual-pay 2 +

LOS The theoretical Treasury spoton theratespot curverateis derived by Ncalculating themarket spot ratepricefor ofeacha successive period based for period 1 and the bond with coupon payments. Tousingcompute theratevalcorresponding ue of a bond using spotnumber rates, ofdiscount each separate cashflowfloiswto be the spot to the periods until the cash received. LOS commonly used yield spread measures: Three bond(Z-spread YTM -Treasury YTM. or static spread): the equal amount of additional yield addedforto aeachbondTreasury spotits market rate to getprice.spot rates that will producethata must presentbe value equal to (OAS): spread to the spot yield curve after adj u sting for the effects ofly.embedded options. OAS reflects the spread for credit risk and liquidity risk primari Theresteeper is no dithefference berween theandnominal andbond Z-spread whenisthepaidyield(amorti curvezinisgflat. The spot yiel d curve the earlier principal securities), the greater the difference in the rwo spread measures. The option cost for a bond with an embedded option is Z-spread OAS. For callable bonds, Z-spread > OAS and option cost > 0. For putable bonds, Z-spread < OAS and option cost < 0. LOS Forward rates are current lending/borrowi n g rates for short-term loans to be made in future periods. A spot rateThe for asame maturity ofon canperiods is theto solve geometric mean ofrateforward rates over thefor periods. relati be used for a forward gi v en spot rates rwo different periods. Toproduct valueofa bond one plususingeachforward forwardrates,ratediscount for periodsthe 1cashto flowsandatsumtimesthem.1 through by the 57.e

N

N

57.f

Nominal spread: Zero-volatility spread

Option-adjusted spread

-

57.g

N

N

N

N,

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

CONCEPT CHECKERS

4. An102.analyst observes a Widget &$1Co.,000).7.125%, 4-year,is callable semiannual-pay bond tradingandat 3 47% of par (where par = The bond at 101 i n two years putable at 100 in two years. 1. What i s the bond' s current yield? A.B. 6.7.9362%. 28%. 7.426%. i s the bond' s yi e ld to maturity? 2. What A.B. 3.5.8264%. 25%. 6.450%. i s the bond' s yield to call? 3. What A.B. 3.167%. 64%. 6.5.6334%. the bond's yield to put? 4. What A.B. 4.5.82is64%. 25%. 6.450%. Based on semiannual compounding, what would the tradi YTMngbeaton$331. a 15-year, 5. zero-coupon, $1, 0 00 par val u e bond that' s currently 4 0? A.B. 3.5.151%. 750%. 7.500%. analystWhat observes a bond wi t h an coupon that' s being priced to yield 6. An6.350%. is this issue's bond equivalent yield? A.B. 3.175%. 3.126%. 6.252%. determines that theequicashvalent flowyield? yield of GNMA Pool 3856 is 0.382% 7. An analyst What is the bond A.B. 4.9.3663%. 28%. 9.582%. Use the following data to answer Questions 1 through

c.

c.

c.

c.

c.

annual

c.

per month. c.

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

Ifnvestment the YTM iequals the actual an investor ithat: n a coupon bondcompound purchased atreturn a premium to par,realiit ziess on an A.B. cash flowswilwilllnotbe paid as promised. the bond be sold C. cash flows will be reinvestedat aatcapital the YTMloss.rate. 4-year spot rate is 9. 4 5%, and the 3-year spot rate is 9.85%. What i s the 9. The forward rate three years from today? A.B.1-year8.258%. 9.850%. 11.059%. 10. Anoptioninvestor purchases a bond that istheputable at theas option ofs thepoints.holder.TheThe has val u e. He has calculated Z-spread 223 basi spread will be: A.option-adjusted equal to 223 basis points. C.B. less greaterthanthan223223basisbasispoints. points. Use the following data to answer Questions 11 and 12. Given: Current 1-year rate = 5.5%. One-year forward rate one year from today ==7.12.18%. 63%. One-year forward rate two years from today One-year forward rate three years from today= 15.5 %. 11. The val u e of a 4-year, 10% annual-pay, $1, 0 00 par value bond would be A.to:B. $995. 89. $1,009.16. $1,085.62. 12. value Usingbond annualwould compounding, the value of a 3-year, zero-coupon, $1,000 par be: A.B. $785. $852. $948. s nominal spread,bond zero-volif: atility spread, and option-adjusted spread will 13. Aallbond' be equal for a coupon curve i s flat. A.B. thethe yield bond curve is optionis flatfree.and the bond has no embedded options. C. the yield 8.

least likely

c.

• •

closest

c.

c.

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

14. A.Theifzero-vol atilcurve ity spread will be zero: the yield i s fl a t. B.C. forfor ana zero-coupon bond. on-the-run Treasury bond. theyielTreasury spot-rate yield curvebond is upward sloping. Compared to the 15. Assume nominal d spread between a Treasury and an option-free corporate bond of similar maturity, the Z-spread will be: A.B. less greaterthanthanthethenominal nominspread. al spread. C. equal to the nominal spread. CHALLENGE PROBLEMS

1. Ansellsinvestor buys a 10-year, 7% coupon, semiannual-pay bond for 92. 8 0. He yearsisla6.ter,9%.justCoupon after receiving thehassixth coupon payment, whenthatits yiyieeldldsitto5%three maturity interest been placed i n an account bond and calculate the dollar return(BEY). fromState each thesourcesources basedofonreturn a $100,on 0thi00s bond. 2. What pricediats thepar?yield on a bond equivalent basis of an annual-pay 7% coupon bond 3. What bond? is the annual-pay yield to maturity of a 7% coupon semi-annual pay yield to maturi t y on a bond equival e nt basis on 6-month and 1-year T-bills 4. The andis the3.218-month %, respectivel y. A 1.5-year, 4% Treasury note is selling at par. A.B.are 2.8% What Treasury spot rate? Iffora 102. 1.5-year semiannual-pay corporate bond wisthbond? a 7%Iscoupon is sellingity 3 95, what is the nominal spread for thi the zero-volatil spread (in basis points) 127, 130, or 133? 5. Assume the following spot rates (as BEYs). Years to Maturity

Spot Rates

0.5

4.0o/o

1 .0

4.4o/o

1.5

5.0 o/o

2.0

5.4o/o

A.B. What iiss thethe 6-month forwardraterateoneoneyearyearfromfromnow?now? What 1-year forward C. What is the value of a 2-year, 4.5% coupon Treasury note? Š20 12 Kaplan, Inc.

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Study Session 16 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

6. Assume currentin the6-month is 3.5% and the 6-month forward rates (all as BEYs) arethethose followingratetable. Periods From Now

Forward Rates 3.8%

2

4.0%

3

4.4%

4

4.8%

A.B. What Calculisatethethevalue corresponding of a 1.5-year,spot4%rates.Treasury note? 7. Consider the follzero owingcoupon three bond bondspriced that allathave par0. values of $100,000. I.II. AA 5-year 1 0-year 48. 2 8% semiannual-pay semiannual-pay bond bond priced priced with with aa YTM YTM ofof 8%. III. A 5-year 9% 8%. Rank the three bonds in terms of how important reinvestment income is to an investorit towhomaturi wishesty. to realize the stated YTM of the bond at purchase by holding

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates

ANSWERS - CONCEPT CHECKERS 1.

A

2.

c

3.

4.

5.

c

B

c

71.25

current yield = 8

1 ,023.47

=

0.06962, or 6.962%

� YTM 6.450% 8 c=l (1 + YTM/2)' ( 1 + YTM/2) N = 8; FV = 1 ,000; PMT = 35.625; PV = - 1 ,023.47 ___. CPT IIY = 3.225

1 ,023.47 =

35.625

I:

1,000

+

=

1 ' 010 35 · 625 + � YTC 6.334% + + •= I (1 YTC I 2)' (1 YTC/2)4 N = 4; FV = 1 ,0 10; PMT = 35.625; PV = - 1 ,023.47; CPT ___. IIY = 3 . 1 67 6.334% 1 ,02 3.47 =

t

(

1 000 ' 331.40

t

)30

2 = 6.45%

=

1'000 35 625 + · � YTP 5.864% (1+ YTP/2)4 •=I (1+ YTP/2)' N = 4; FV = 1 ,000; PMT = 35.625; PV = - 1 ,023.47; CPT ___. 1/Y = 2.932 5.864% 1 ,023.47 =

x

x

2 =

x

2 =

=

I

X

-1

2

=

7.5%

or,

Solving with a financial calculator: N = 30; FV = 1 ,000; PMT = 0; PV = -331 .40; CPT ___. IIY = 3.750

2 = 7.500%

6.

C

bond equivalent yield = [ ( 1 + EAY) 112 - 1 ]

7.

A

bond equivalent yield = [(1 + CFY)6 - 1 ]

8.

B

For a bond purchased at a premium to par value, a decrease in the premium over time (a capital loss) is already factored into the calculation ofYTM.

9.

A

3 ( 1 . 0945)4 = (1 .0985) (1.0945)

4

-'----=-::-

(1 .0985)3

10. C

-1

=

1

f3

=

X

x

x

2 = [(1 .0635) 112

x

-

= [(1 .00382) 6 - 1 ]

1]

x

x

2 = 6.252%

2 = 4.628%

(1 + /3)

8.258%

For embedded puts (e.g., putable bonds): option cost < 0,

©20 1 2 Kaplan, Inc.

OAS

>

Z-spread.

Page 129


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates 11. B

Spot rates: 5 = 5.5%. 1 52 = [(1 .055)(1 .0763)]112 - 1 = 6.56% 53 = [(1 .055)(1 .0763) ( 1 . 1 2 1 8)] 113 - 1 = 8.39% 54 = [(1 .055)(1 .0763) ( 1 . 12 1 8 ) ( 1 . 155)] 114 - 1 = 1 0 . 1 3% Bond value: N = 1 ; FV = N = 2; FV = N = 3; FV = N = 4; FV =

12. A

100; I/Y = 5.5; CPT --+ PV= -94.79 100; I/Y = 6.56; CPT --+ PV= -88.07 100; I/Y = 8.39; CPT --+ PV= -78.53 1 , 100; 1/Y = 1 0 . 1 3 ; CPT --+ PV= -747.77 Total: $ 1 ,009 . 1 6

Find the spot rate for 3-year lending: 53 = [(1 .055)(1 .0763) ( 1 . 1 2 1 8)] 113 - 1 = 8.39% Value of the bond: N = 3 ; FV = 1 ,000; 1/Y = 8.39; CPT--+PV = -785.29 or

$ 1 000 ' = $785.05 (1.055)(1.0763)(1 . 1 2 1 8)

13. C

If the yield curve is flat, the nominal spread and the Z-spread are equal. If the bond is option-free, the Z-spread and OAS are equal.

14. C

A Treasury bond is the best answer. The Treasury spot yield curve will correctly price an on-the-run Treasury bond at its arbitrage-free price, so the Z-spread is zero.

15. A

The Z-spread will be greater than the nominal spread when the spot yield curve is upward sloping.

ANSWERS - CHALLENGE PROBLEMS 1.

The three sources of return are coupon interest payments, recovery of principal/capital gain or loss, and reinvestment income.

Coupon interest payments: 0.07 I 2

x

$ 100,000

x

6 = $ 2 1 ,000

Recovery ofprincipal/capital gain or loss: Calculate the sale price of the bond: N = (10 - 3) X 2 = 14; 1/Y = 6.9 I 2 = 3.45; PMT = 0.07 I 2 X 100,000 = 3,500; FV = 100,000; CPT --+ PV = - 1 00,548 Capital gain = 100,548 - 92,800 = $7,748

Reinvestment income: We can solve this by treating the coupon payments as a 6-period

annuity, calculating the future value based on the semiannual interest rate, and subtracting the coupon payments. The difference must be the interest earned by reinvesting the coupon payments. N=3

x

2 = 6; IIY = 5 I 2 = 2.5; PV = 0; PMT = -3,500; CPT --+ FV = $22,357

Reinvestment income = 22,357 - (6

Page 130

x

3,500) = $ 1 ,357

Š2012 Kaplan, Inc.


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates 2.

x

BEY = 2

semiannual discount rate

semiannual discount rate = ( 1 .07)112 - 1 = 0.344 = 3.44% X

BEY = 2

3.44% = 6.88%

(

3.

0.07 annual-pay YTM = 1 + -2

4.

A.

2 - 1 = 0.0712 = 7. 1 2%

Because the T-bills are zero-coupon instruments, their YTMs are the 6-month and 1-year spot rates. To solve for the 1 .5-year spot rate, we set the bond's market price equal to the present value of its (discounted) cash Rows: 100

=

100

(

1+

1+

2 + 0.028

--

2

(

2 1+

0.032

--

1 .9724 + 1.9375 +

=

sl

.5 2

1 +� 2

)3 =

=

2

(

) ( 2

+

102 1+

s

�5

)3

100 - 1.9724 - 1 .9375

x

=

)3

102 ---:s --.!.:2.. 1+ 2

-

102

1 . o6 1 s x

s � 5 = o.o2 o 1 . B.

)

=

1.0615

1 .0201

2 = o.o4o2 = 4.02%

Compute the YTM on the corporate bond:

N = 1.5 2.6588

x

X

2 = 3; PV = -102.395; PMT = 7 I 2 = 3.5; FV = 100; CPT -+ 1/Y = 2 = 5.32o/o

nominal spread = YTMBond - YTMTreasury = 5.32% - 4.0% = 1 .32%, or 132 bp Solve for the zero-volatility spread by setting the present value of the bond's cash Rows equal to the bond's price, discounting each cash Row by the Treasury spot rate plus a fixed Z-spread.

Substituting each of the choices into this equation gives the following bond values:

Z-spread

Bond value

127 bp

102.4821

130 bp

102.4387

133 bp

102.3953

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Page 1 3 1


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates Since the price of the bond is 102.395, a Z-spread of 133 bp is the correct one. Note that, assuming one of the three zero-volatility spreads given is correct, you could calculate the bond value using the middle spread ( 1 30) basis points, get a bond value ( 1 02.4387) that is too high, and know that the higher zero-volatility spread is the only one that could generate a present value equal to the bond's market pnce. Also note that according to the LOS, you are not responsible for this calculation. Working through this example, however, should ensure that you understand the concept of a zero-volatility spread well. 5.

A.

(

( ) ) ( s�0)

0.5 fJ.o 1+ = 2

s 1 + -.-!.:.2. 2 1+

3 2

=

:

1.025

1 .022

= 1.031 03

0 .5 f1.o = 0.03 103 x 2 = 0.0621 = 6.2 1%

B.

/1 here refers to the 1-year rate, one year from today, expressed as a BEY.

( �r ( ;r 1+

1+

£ 2

0.054 1 + -2

£ 2

1

f.

( ) ( �) 1+

=

2

X

0. 44

4 2

- 1 = 0.0320

0.0320 = 6.40o/o

Note that the approximation 2 bit less work.

Page 132

x

5.4 - 4.4

=

©2012 Kaplan, Inc.

6.4 works very well here and is quite a


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates C.

Discount each of the bond's cash flows (as a percent of par) by the appropriate spot rate: 2.25 2.25 + 0. 40 0. 44 1+ 1+

bond value =

A.

102.25 + -----:0. 54 1+

( �r ( �r ( �r

1+

o. so

102.25 2.25 2.25 = 98.36 +� + + 1 .02 1.0445 1 .0769 1 . 1 125

=

6_

2.25

+

( � r ( � )( � ) ( � )( � ) 1+

S o

S s

= 1+

1 + o.5 o. 5 = 1 +

0. 35

1+

0. 38

= l .0368

� = 1 .0368112 - 1 = 0.0182 2

S . IO

=

X

0.0 1 82

2

=

0.0364

3.64%

=

( � J ( � )( � )( � ) 1+

S

5

1+

=

S

5

1 + o.5 0.5

1 + o.5 1 .o

� = 1 .0576113 - 1 = 0.0188 2

s�.5

=

x

o.o 1 8 8

2

=

o.0376

3.76%

=

( � )( � )( � )( � )

= 1+

0. 35

1+

0. 38

1+

0. 40

1+

0. 44

= 1 .0809

s2· 0 = 1 .08091 14 - 1 = o.o 196 2 S2_0

=

B. 1+

7.

o.o 1 9 6 2 + 0. 35

x

2

=

o. o392 2

=

3.92% 102

( �r ( �r 1+

o.o 64

+

1+

0.0 76

= 1 00.35

Reinvestment income is most important to the investor with the 9o/o coupon bond, followed by the 8o/o coupon bond and the zero-coupon bond. In general, reinvestment risk increases with the coupon rate on a bond.

©20 12 Kaplan, Inc.

Page 133


The following is a review of the Analysis of Fixed Income Investments principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in:

INTRODUCTION TO THE MEASUREMENT OF INTEREST RATE RISK Study Session 1 6

EXAM FOCUS

This topic reviconcepts ew is aboutof theduration relationandofconvexi yield changes andisbond pricenothing changes,in thisprimarily based on the t y. There really study session that canofbeduration safely ignored; the calculation of duration, theimportant. use of duration, and the limitations as a measure of bond price risk are all You should work to understand what convexi t y i s and i t s relation to the interest rate risk of fi x ed­ incomethe securities. There are twotheimportant formulas: thed change formulabased for effecti ve duration and formula for estimating price effect of a yiel on both duration and convexi t y. Fi n al l y, you should get comfortable wi t h how and why the convexity of a bond is affected by the presence of embedded options. LOS 58.a: Distinguish between the full valuation approach (the scenario analysis approach) and the duration/convexity approach for measuring interest rate risk, and explain the advantage of using the full valuation approach. CPA® Program Curriculum, Volume 5, page 556

Theapplying full valuation or scenario analysisweapproach to measuring interest ratein theriskyield is based oncurve the valuation techniques have learned for a given change e., "ifforthea giYTM ven increases by 50 bp orFor100a sibp,nglewhatoption-free bond,onthisthecould beof thesim(i.ply, i s the impact value bond?" More compl i cated scenarios can be used as well, such as the effect on theshort-term bond value of a steepeni n g of the yield curve (long-term rates i n crease more than If ourin valuation model is good, theandexerciseesewhat is straightforward: plvalues ug inof thethe bonds. rates rates). described the interest rate scenario(s), happens to the For more complex bonds, such as cal l a bl e bonds, a prici n g model that incorporates yil valelduvolatil ity as well Ifasthespecifivaluation c yield models curve change scenarios is requigood,red tothis useis thethe fultheoreticall atioynpreferred approach. used are suffi c i e ntly approach. Appli e d to a portfolio of bonds, one bond at aaffect time,thewevalcanuegetof thea veryportfolio. good idUsing ea of how diapproach fferent interest rate change scenarios will this wi t h extreme changes i n interest rates is called stress testing a bond portfolio. The duration/convexity approach proviItsdesmaian napproximation ofsimplicity the actual compared interest rateto sensi t ivity of a bond or bond portfolio. advantage is its the full valuforationa portfolio approach.ofThemorefullthanvaluation approachespecially can getifquisomete complex and time consuming a few bonds, of the bonds have more complex structures, such shias fcallts andprovisions. ll see shortly, our scenarios to parallel yield curve settling Asforwean wiestimate of interestlimiting rate risk interest rate scenario).

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk

allowsprocess us toofuseestithematisummary convexiinty.yield. This greatly simplifies the ng the valmeasures, ue impactduration, of overalandl changes Comparedandtocanthebeduration/convexi tthey approach, the fulof lmore valuation approach is rate more precise used to eval u ate price effects complex interest scenarios. Strictly g, the duration-convexi estimating the effectsspeakiofnparallel yield curve shifts.ty approach is appropriate only for Example: The full valuation approach

Considerty, two option-free bonds. Bond X (Nis an= 8%5; PMT annual-pay bond with five years to maturi priced at 108. 4 247 to yiel d 6% = 8. 0 0; FV = 100; 1/Y = 6. 0 0%; CPT� PV = -108.4247). BondY is a 5% annual-pay bond wi t h 15 years to maturi t y, priced at 81. 7 842 to yield 7%. Assume a $10 million face-val u e position i n each bond and two scenarios. The fi r st ieslashiparalft of+lel shift in thes points. yield curve of+ 50thebasibonds points, and the4second scenario isperscenario a parall 100 basi Note that price of 108. 24 7 i s the price $100 of par value. Wi t h $10 mi l l i on of par value bonds, the market value wi l l be $10.84247 million. Answer:

fiThegure.full valuation approach for the two simple scenarios is illustrated in the following The Full Valuation Approach

Market Value of Scenario

Yield �

Bond X (in miiiions}

Bond Y (in miiiions}

Portfolio

Current

+0 bp

$ 1 0.84247

$8. 17842

$ 1 9.02089

1

+50 bp

$ 1 0.62335

$7.79322

$ 1 8.41657

-3. 1 8%

2

+ 1 00 bp

$ 1 0.4 1 002

$7.43216

$ 1 7.84218

-6.20%

Portfolio Value � %

N = 5; PMT = 8; FV = 100; 1/Y = 6% + 0.5%; CPT � PV = -106.2335 N = 5; PMT = 8; FV = 100; 1/Y = 6% + 1%; CPT � PV = -104.1002 N = 15; PMT = 5; FV = 100; 1/Y = 7% + 0.5%; CPT � PV = -77.9322 N = 15; PMT = 5; FV = 100; 1/Y = 7% + 1 %; CPT � PV = -74.3216 Portfolio value change 50 bp: (18.41657- 19.02089) 19.02089 = -0.03177 = -3.18% I

©20 1 2 Kaplan, Inc.

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #58

-

Introduction to the Measurement o f Interest Rate Risk

-6.Portfolio 20% value change 100 bp: (17. 84218 - 19.02089) 19.02089 = -0.06197 = It's worth noti nesg that, onforanBond individual bond basis, the(i.eeffect ofaan50 increase in yielin d on theyields, bonds' val u is l e ss X than for BondY . , wi t h bp increase theh aval100uebpofincrease, Bond X falls byls by2.03.2%,99%,whiwhile thele Yvaldrops ue ofbyBondY fallThis, s by 4.of7course, 1 %; and wi t X fal 9.12%). iofs total l y predictable since Bond Y is a longer-term bond and has a lower coupon-both which mean more interest rate risk. I

Professor's Note: Let's review the effects of bond characteristics on duration (price sensitivity). Holding other characteristics the same, we can state the following:

Higher (Lower) coupon means Lower (higher) duration. Longer (shorter) maturity means higher (Lower) duration. Higher (lower) market yield means Lower (higher) duration.

Finance professors Love to test these relations.

LOS 58.b: Describe the price volatility characteristics for option-free, callable, prepayable, and putable bonds when interest rates change. LOS 58.c: Describe positive convexity and negative convexity, and their relation to bond price and yield. CFA® Program Curriculum, Volume 5, page 560

We established earliAnerincrease that theinrelati on(discount between rate) price leads and yield for a straight coupon bond is negati v e. yield to a decrease in the value ofis aillbond. The precise nature of this relationship for an option-free, 8%, 20-year bond ustrated in Figure 1. 8%, Figure 1: Price-Yield Curve for an Option-Free, Price (% of Par) For an option-free bond the price-yield curve is co nvex toward the origin.

1 1 0.67 100.00 90.79

�----�--- YTM 7%

Page 136

8%

9%

©2012 Kaplan, Inc.

20-Year Bond


Study Session 16 Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk

First, note that the price-yi eldtherelationship isonegativel y sloped, so the price fallBecause s as the yithe eldcurve rises. Second, note that relation foll ws a curve, not a straight line. is convex (toward the origin), we say that an option-free bond has positi v e convexity. Because of its positive convexity, the priceInofFigure an option-free bondillustrated 1, we have that, for an 8%, 20-year option-free bond, a 1% decrease i n the YTM wi l l increase the price toto decrease 110.67, ato 90.79, a in price. Ain1%value.increase in YTM will cause the bond value relation were adeclstraight line,response there towoulequald bedecreases no difference between theIfin theyields. priceprice-yield increase and the price i ne in and increases Convexity i s a good thing for a bond owner; for a given volatility of yields, price are lsarger than price decreases. The convexity property is often expressed byrelationship sayiincreases ng, "atobond' pri c e falls at a decreasing rate as yi e lds rise. " For the price-yiel d as be convex, the slope (rate of decrease) of the curve must be decreasing we move from left to right (i.e., towards higher yields). Note that the duration (interest rate sensitivity) of a bond at any yield i s (absolute value of) the slope ofoption-free the price-yield function atyouthatremember yield. Thea convexi ty of the price-yield relation for an bond can help result presented earlier, that the duration of a bond is less at higher market yields. increases

more when yields fall than it decreases when yields rise. 10.67% increase 9.22% decrease

Callable Bonds, Prepayable Securities, and Negative Convexity

Widecreasing th a callable or prepayable debt, the upsi d e price appreciation in response to yiiseldcurrently s is limitedcall(sometimes calTheledfactpricthat e compression). Consider the caseat any of atimbond that a bl e at 102. the issuer can cal l the bond e for $1, 0 20 per $1, 0 00 of face val u e puts an effecti v e upper limit on the value of the bond.curve As Figriureses more 2 illustrates, as yields faloflanandidentical the pricebutapproaches $1,020, theWhenprice­the yield slowly than that noncallable bond. beginsbends to over to the left and exhibits in response to further decreases in yield, the price­ yiprieclde curve negative convexity. Thus, in Figure 2, however, so long asatyiyieldseldsremain those same callablcale lbonds will exhibit ablcalle options bonds wibecomes ll exhibit In other words, at higher yi e lds the val u e of the very small so that a callable bond will act very much l i k e a noncallable bond. It i s only at lower yields that the callable bond will exhibit negative convexity. rise at a decreasing rate

negative convexity; positive convexity.

below level y', above level y',

©20 1 2 Kaplan, Inc.

Page 137


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #58

-

Introduction to the Measurement o f Interest Rate Risk

Figure Price-Yield Function of a Callable vs. an Option-Free Bond 2:

Price (% of Par)

call option value 102

�r

- --- -- -- -

- ---.r�.. - .. .. - - .. .. ...

- - -_

.. - -

.. ..

r

callable bond '-------'-- Yield Negative Convexity Positive Convexity y'

In any termsparticular of price yisensitivi tsytheto interest rate that changes, thelds slope of slope the price-yield curve atcurve e ld tel l story. Note as yi e fall, the of the price-yield for the call a ble bond decreases, becoming almost zero (fl a t) at very low yields. This sinusterest howrate a calriskl feature affects price sensi tivitycloseto orchanges in yield. Atofhigher yields, thetelloption-free of a callable bond i s very identical to that a similar bond. At lower yields, the price volatility of the call a bl e bond wi l l be much lower than that of an identical but noncallable bond. The effect of a prepayment option is quite similar to that of a call; at low yi e lds i t wisecuri ll leadty. Note to negati vewhen convexiyieldsty andare low reduceandthecalprilablcee volatility (interestsecurities rate risk)exhibit of theless that and prepayable interest rate risk, rei n vestment risk rises. At l o wer yields, the probability of a cal l and the prepayment at the lower rate rates.both rise, increasing the risk of having to reinvest principal repayments The Price Volatility Characteristics of Putable Bonds

The value of a put increases at higher yields and decreases at l o wer yields opposite to the privaluece volatil of a callity option. an option-freeis ilbond, at higherCompared yields. Thitos comparison lustrateda putable in Figurebond3. will have less

Page 138

©2012 Kaplan, Inc.


Study Session 16 Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk

Figure 3: Comparing the Price-Yield Curves for Option-Free and Putable Bonds Price

putable bond /

- - - - - .. .. ... _ _ _ _ _ _ _

option-free bond Yield

y'

In Figure 3,y'thebecause price ofthethevalueputablof the e bondembedded falls moreputslrises owlyatinhigher responseyields.to increases inof yield above The slope theduration) price-yield relation is fl a tter, indicating less price sensi t i v ity to yi e ld changes (l o wer forandtheaputable bond ats prihigchere actsyields. Atthatyielofdans beloption-free ow y', thebond valueinofresponse the put is qui t e small, putabl e bond' li k e to yield changes. LOS 58.d: Calculate and interpret the effective duration of a bond, given information about how the bond's price will increase and decrease for given changes in interest rates. CPAÂŽ Program Curriculum, Volume 5, page 569

Inpercentage our introduction to the concept of duration, we described i t as the ratio of the change in pricechange to change in yield.to rising Now that weis smaller understand convexi ty, wechange knowinthat the price i n response rates than the price response to fallingduration rates forofoption-free bonds. The formula we willchanges use forin response calculating the effective a bond uses the average of the price to equal increases and decreases inegati n yieldvetoconvexity, account forthethispricefact.increase Ifwe ishave asmalcalllerablthan e bond that i s trading in the area of the price decrease, but using the average still makes sense.

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #58

The formula for calculating the effective duration of a bond is: yields fal -bond price when yields rise) effecti.ve duranon. (bond2 pri(inciteiawhen l price) (change in yield in decimal form) . wnte. as duranon. V_2V -V+ wh1c. h we w1 somenmes 0 (b..y) where: bond value iff the the yield yield increases decreases byby b..yy value i VVV bond initial bond 0y = change in yieprice ld used to get V and V Consider the following example of this calculation. =

Introduction to the Measurement o f Interest Rate Risk

--"--='--'-----' --=-'--

X

X

路11

=

-'-

b.

+

b.

_

+'

expressed in decimal form

Example: Calculating effective duration

Consider 20-year, semiannual-pay bondineswithby 50an 8% coupon that is currently pricedwill atincrease $908.0to0a $952. to yield30,9%. If the yield decl basis points (to 8.5%), the price and i f the yiel d i n creases by 50 basis points (to 9.5%), the pri c e widuration ll declinofe this to $866. bond.80. Based on these price and yield changes, calculate the effective Answer:

Let' s approachng thethisaverage intuitivofelytheto percentage gain a betterchange understanding of sthepriceformula. Weyieldbegin byincrease computi in the bond' for the and the percentage change in price for a yi e ld decrease. We can calcul a te this as: 30-$866.80) = 0.0471%, or 4.71% average pnce. change = ($952.2x$908. 00 The 2 in the denominator obtainchange the average price change,of theandcurrent the $908price.in the denominator is to obtain thiis stoaverage as a percentage Todivideget this the duration (to scal e our result for a 1% change in yield), the fi n al step i s to averagee, thepercentage pricewas change0.5%,by the change in interest ratesin decimal that caused it.as 0.In0the05. exampl yi e l d change whi c h we need to write form Our estimate of the duration is: 0路0471 = 4路7 1% = 9.42 =duration 0.005 0.50% Using the formula previously given, we have: 8) = 9.4 16 effective duration = (2$952.$9083 -$866. 0.005 percentage

X

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X

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Study Session 16 Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk

The interpretati on of thisanresult, as youmateshould beinconvinced byof this now,bond is thatof9.a 14o/o2o/o. change i n yi e ld produces approxi change the price Note,wilhowever, thatbestthisforestiyielmdatechanges of duration wasthisbased ontude. a change inweyiused eld of0.5o/ o and l perform cl o se to magni Had a yield change of0. 2 5o/o or 1 o/o, we would have obtained a slightl y di ff erent estimate of effective duration. This is an important concept, andunderstand you are required to learn theremember formula forit, consider the the calculation. To further help you thi s formul a and following. The price increase in response to a 0.5% decrease in rates was $4430 $908 4.879%. The price decrease in response to a 0.5% increase in rates was $41.$90820 4.537%. The average of thea 0.percentage price inelcrease andthethepricepercentage price decrease is 4.7thi1 o/o.s Because we used 5 % change in yi d to get changes, we need to double and get a 9.42% change in price for a 1 o/o change in yield. The duration is 9.42. =

=

For bonds witnearl h noyembedded options,to calculate modifiedeffecti duration and effectiforvea duration wianll be equal or very equal. In order v e duration bond wi t h embedded option, we need a pricing model that takes account of how the cash fl o ws change when interest rates change. LOS 58.e: Calculate the approximate percentage price change for a bond, given the bond's effective duration and a specified change in yield. CFAÂŽ Program Curriculum, Volume 5, page 570

Multiplyandeffecti vechange durationthebysigthen tochange indirection yield to getof thetheprice magnichange tude ofrigtheht (yield price up, change then get the price down). change in bond price = -effective duration change in yield in percent x

percentage

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Introduction to the Measurement o f Interest Rate Risk

Example: Using effective duration What the expected for apoints? bond with an effective duration of nine inisresponse to anpercentage increase inprice yieldchange of 30 basis Answer: -9 0.3% = -2.7% We expect the bond' s pri c e to decrease by 2. 7% in response to the yi e ld change. If the bond were priced at $980, the new price is 980 (1 - 0.027) = $953.54. X

x

LOS 58.f: Distinguish among the alternative definitions of duration and explain why effective duration is the most appropriate measure of interest rate risk for bonds with embedded options. CPAÂŽ Program Curriculum, Volume 5, page 576

The formula we used to calculate duration based on pri c e changes i n response to equal V- - V , is the formula for effective increases and decreases in YTM, 2V0(.measure 6.y) because it gives a good (option-adjusted) duration. This i s the preferred approximation of interest rate sensitivity for both option-free bonds and duration =

+

bonds with

embedded options.

Macaulay duration is ancash estimate ofwilla bond' s interest rate sensitivi ty basedbond on thehastime, ionen years, until promised fl o ws arrive. Since a 5-year zero-coupon only cash fltoowa 1%fivechange years from today,foritsa 5-year Macaulay duration ibond s five.isTheapproxi changematelinyvalue in response in yield zero-coupon 5%. A(the5-year coupon bond has some cash fl o ws that arri v e earl i e r than fi v e years from today s Macaulay durationtheis llessess than five. sensitivity This is consistent learnedcoupons), earlier: sotheithigher the coupon, the price (duration)withofwhat a bond.we Macaulay durationisisoften the earliest measure ofBecause duration,Macaul andabecause it wasis based basedononthe theexpected time, cash duration stated as years. y duration fl o ws for an option-free bond, i t i s not an appropriate esti m ate of the pri c e sensitivity of bonds with embedded options. Modified duration is deri v ed from Macaulay duration and offers a slight improvement over Macaulandayforduration in that it takesmodified the current YTMis notintoanaccount. Like measure Macaulay duration, the same reasons, duration appropriate ofhowever, interesteffecti rate sensi t ivity for bonds wi t h embedded options. For option-free bonds, be very similar. ve duration (based on small changes in YTM) and modified duration will Page 142

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Study Session 16 Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk

Professor's Note: The LOS here do not require that you calculate either Macaulay duration or modified duration, only effective duration. For your own understanding, however, note that the relation is Macaulay duration . . modified duratton = This accounts for thefact we + periodic market yield

1

.

Learned earlier that duration decreases as YTM increases. Graphically, the slope of the price-yield curve is Less steep at higher yields.

Effective Duration for Bonds With Embedded Options

noted earlier, inarecomparing thedivarious duration measures,cashbothfloMacaulay and with modified duration calculated r ectly from the promised ws for a bond nois calculated adjustmentfromfor expected the effectprice of anychanges embedded optionstoonchanges cash floiws.n yield Effectithatveexpl duration in response icitly take i n to account a bond' s option provisions (i. e . , they are i n the price-yield function used).

As

Interpreting Duration

We can interpret duration in three different ways. First, durationly,isthetheslslope ofthetheprice-yield price-yieldcurve curveisatthethefibond' s current YTM. Mathematical o pe of r st derivati v e of the price-yield curve with respect to yield. A secondofinterpretation of duration, as original lwy devel opedreceibyved.Macaulay, isghtsa weiareghted average the time (in years) until each cash fl o wil l be The wei the proportions comes years.of the total bond value that each cash flow represents. The answer, again, Aa 1%thirchange d interpretati on This of duration is the approximate percentage changetoina change price forin i n yield. interpretation, price sensi t i v ity i n response yield, is the preferred, and most intuitive, interpretation of duration. m

� �

Professor's Note: The fact that duration was originally calculated and expressed in years has been a source of confusion for many candidates andfinance students. Practitioners regularly speak of "longer duration securities. " This confusion is the reason for this part ofthe LOS. The most straightforward interpretation of duration is the one that we have used up to this point: '1t is the approximate percentage change in a bond's price for a I % change in YTM. Ifyou see duration expressed in years, just ignore the years and use the number. Questions might ask whether duration becomes longer or shorter in response to a change; longer means higher or more interest rate sensitivity. A duration of 6 82 years means that for a I % change in YTM, a bond's value will change approximately 6 82%. This is the best way to interpret duration. "

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #58

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Introduction to the Measurement o f Interest Rate Risk

LOS 58.g: Calculate the duration of a portfolio, given the duration of the bonds comprising the portfolio, and explain the limitations of portfolio duration. CPAÂŽ Program Curriculum, Volume 5, page 580

The concept ofmeasure durationof can alsorate be applied to portfolios. In fact, one of theisbenefi ts of durati o n as a interest ri s k i s that the simply theMathemati weightedcallaverage of the durations of the i n di v idual securities i n the portfolio. y, the duration of a portfolio is: duration of a portfolio

where: wD.i == market value ofofbond bond ii divided by the market value of the portfolio the duration N = the number of bonds in the portfolio I

Example: Calculating portfolio duration

youis $6,have000,a two-security portfolvalueio containing Bonds A andTheB.duration The market value ofASuppose Bond A and the market of Bond B is $4, 0 00. of Bond is 8.5, and the duration of Bond B is 4.0. Calculate the duration of the portfolio. Answer:

First,0fi00nd=the$6,wei market ivalue $10, 000g+hts$4,of0each 00, thebond.weightBecause of eachthesecurity s as follofothews:portfolio is $6' 000 = 60% weight in Bond A= $10, 000 $4,000 = 40% weight in Bond B = $10,000 Using the formula for the duration of a portfolio, we get: portfolio duration = (0.6 8.5) + (0.4 4.0) = 6.7 x

x

Limitations of Portfolio Duration

The l i mitations of portfolio durati o n as a measure of interest rate sensi t ivity stem from the fact thatthatyiincludes elds maybonds not change equally onmaturities, the bonds inrisks, the portfoli o. With a portfolio wi t h di f ferent credit and embedded there is nowhen reasonthetoyield suspect thatchanges. the yieldsAs anonexample, individuala steepening bonds will change byyioptions, equal amounts curve of the eld curve can increase yields on long-term bonds and leave the yield on short-term all

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk

bonds for thisto reason thatchanges we sayin that duration sensitivunchanged. ity of portfolItioisvalue the yield curve.is a good measure of the parallel

LOS 58.h: Describe the convexity measure of a bond and estimate a bond's percentage price change, given the bond's duration and convexity and a specified change in interest rates. CPA® Program Curriculum, Volume 5, page 581

is a measure of the curvature of the price-yield curve. The more curved the price-yield relation is, thewere,greater the aconvexi ty.line,A straitheghtconvexity line haswould a convexi ty ofThe zero. Ifreason the price-yi e l d curve i n fact, strai g ht be zero. we care about convexity is thatof thebondmorepriccurved theinprice-yield relachanges tion is, intheyield worse our duration-based esti m ates e changes response to are. Ashasana yield example, consider again an 8%, 20-year Treasury bond pricedve atduration $908 soofthatthisit to maturi t y of 9%. We previ o usly calculated the effecti bond as 9.42. Fiestiguremates 4 illustrates differences betweenyieldactual duration-based of price thechanges at different levels.bond price changes and Bond Convexity

Figure 4: Duration-Based Price Estimates vs. Actual

Prices

Price

$ 1 ,000.00 $993.53

f------+ Prices based on duration are underestimates of actual prices.

$908.00 $828.41 $822.47

' ' --------------- - - - - - - -------, , ' '

Actual price-yield curve

'

Price estimates based on a duration of9.42

�---�--�---- YTM 8%

9%

1 0%

Based onina yiel valued (toof 9.8%42andfor duration, we1.would estimate the new prices after 1% changes to 10%) as 0 942 908 = $993. 5 3 and (1 - 0.0942) 908 = $822. 4 7, respectively. These price estimates are shown in Figure 4 along the straight line tangent to the actual price-yield curve. The actual price ofofthe10%,8%thebondactualat aprice YTMofofthe8%bond is, ofiscourse, par1, about value $6($1higher ,000). than Based on a YTM $828. 4 our duration based estimate Note thatandpricea 1%estidecrease mates based on duration are less than the actual prices forofboth$822.a 41%7. increase in yield. Figure 4 illustrates why convexity i s important and why estimates of price changes based solely on duration are inaccurate. If the price-yield relation were a straight line x

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x

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #58

(i.e., if convexity werein zero), duration alone wouldTheprovide good estimates of bond pricethe changes for changes yiel d of any magnitude. greater the convexi t y, the greater error in price estimates based solely on duration. Introduction to the Measurement o f Interest Rate Risk

A Bond's Approximate Percentage Price Change Based on Duration and Convexity

Bypercentage combiningchange duration and convexity, we can obtain a more accurate estimate of the inmpriatingce ofa bond' a bond,s percentage especially price for relchange atively based large changes in yield. and The formula for esti on its convexity duration is: percentage change in price duration effect+ convexity effect = {[-duration (�y)J + [convexity (�y)2]} With 6.y entered as a decimal, the 100" is necessary to get an answer in percent. and Consider an 8% Treasury bond wi t h a current price of $908 and a YTM of 9%. Calculate of bothtya of1%68.increase YTM basedtheonpercentage a durationchange of9.42inandpricea convexi 33. and a 1% decrease in =

X

x

x 100

"x

Example: Estimating price changes with duration

convexity

Answer:

The durati o n effect, as we calculated earlier, i s 9. 4 2 0.01 = 0. 0 942 = 9. 4 2%. The 2 convexity effect is f68.33(from0.019% to1008%)= 0.is09.0683 1000.683% = 0. 6 83%. The total effect for aestimate 4 2% + = + 10.103%, and the of the new price of the bond is 1.10103 908 = 999. 74. This is much closer to the actual price of $1,000 than our estimate using only duration. decrease in yield o I %

x

x

x

x

x

The total effect for an f (from 9% to 1 0%) is -9.42% + 0. 6 83% = -8.this7is37%, andclotheser estimate of thepricebond($828. price4i0)s (1than-0.the08737)(908) = $828. 6 7. Again, much to the actual esti m ate based solely on duration. There are a few points worth noting here. First, the convexi t y adjustment i s al w ays 2 convexity isgurepositi4, vwhie because (6.y)thatisthealwduration-only ays positive. This goesestimate along of wiapositive tbond' h thes when illustration i n Fi c h shows based pri c e change suffered from being an underestimate of the percentage i n crease in theprice bondwhen price yiwhen yieldsRecall, fell, andthatanforoveresti mbleatebond, of theconvexi percentage decrease in vthee bond e lds rose. a call a t y can be negati at low yields. When convexity is negative, the convexity adjustment to the duration-only increase in yield o I %

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Study Session 16 Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk

basedyieestild mdecreases. ate of the percentage price change will be negative for both yield increases and Professor's Note: Different dealers may calculate the convexity measure differently. Often the measure is calculated in a way that requires an analyst to divide the measure by two to get the correct convexity adjustment.

LOS 58.i: Distinguish between modified convexity and effective convexity. CPA® Program Curriculum, Volume 5, page 584

Eff elctie modified ve convexiconvexi ty takesty idoes nto account changes in cash flowsmodifi due toedembedded options, whi not. The di f ference between convexi t y and effecti v e convexi t y mi r rors the di f ference between modifi e d duration and effecti vae bond's duration. Recal l that modi f i e d duration is calculated wi t hout any adjustment to cash flowiwsthforembedded embeddedoptioptions. Also recall that effecti ve were duration was appropriate for bonds o ns because the inputs (prices) calculated under the assumptionin thethatsecurities. the cash Clearl flows ycould varyve convexi at different yitheeldappropri s becauseateofmeasure the embedded options , effecti t y is to use foreffectbonds with embedded since sitcash is based of embedded optionsoptions, on the bond' flows.on bond values that incorporate the LOS 58.j: Calculate the price value of a basis point (PVBP), and explain its relationship to duration. CPA® Program Curriculum, Volume 5, page 584

The value of a basis point (PVBP) is thebydollar change in theor 0.01 price/value of acalcul bondprice or a portfolio when the yield changes one basis point, %. We can ate thethePVBP directly for aAsbond by changi ng theweYTM by duration one basis topointcalculate and computing change in value. a practi c al matter, can use the price value of a basis point as: price value of a basis point = duration 0.0001 bond value x

x

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #58

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Introduction to the Measurement o f Interest Rate Risk

The following example demonstrates this calculation. Example: Calculating the price value of a basis point Aofbond a market value of$100,000 and a duration of9.42. What is the price value a basishaspoint? Answer: the duration formula, the2 =percentage change incalculate the bond'0.0s 942% price forof athechange in yiUsing e$100,ld of0.01 o/o i s 0.01 o/o 9. 4 0. 0 942%. We can original 000 portfolio valuepoint, as 0.0the00942 100,000 = $94. 2 0. If the bond's yield increases (decreases) by one basis portfolio val u e l (rise) by $94.20. $94.20 is the (duration-based) price value of a basis point forwillthifals bond. We could altheso directl y calculate the0001) priceandvaluecalofculating a basis thepointchange for thisin bond bond value. by This increasing YTM by 0.01 o/o (0. would give us theestiPVBP for an induration crease in yield. Thisgoodwoulestidmbeateveryof interest close to rate our risk for duration-based m ate because is a very small changes in yiel d . We can ignore the convexity adjustment here because it i s of 2 2 very small magnitude: (�y) = (0.0001) = 0.00000001, which is very small indeed! x

x

LOS 58.k: Describe the impact of yield volatility on the interest rate risk of a bond. CPAÂŽ Program Curriculum, Volume 5, page 585

Earlier in thia lsotopic review, weis lessintroduced duration aschange a measurein yiofeldinthan terestaratebondriswith k. A bond with wer duration affected by a gi v en greater its interestduratirateon.risHere k. we combine a bond's duration with its yield volatility in assessing Consider a aTreasury bond wiBased th a durati on of 7alone, and a wesimilar singlsaye-Bthatratedthe Treasury corporate bond with durati o n of 5. on duration would bond has more interest rate risk.greater If, however, thevolatil volaitytiliofty theof themarket marketyieldyielond onthethe corporate bond i s suffici e ntly than the Treasury bond, the corporate bond can have greater price volatility due to yield (interest rate) changes thanvaltheuesTreasury bond. Investors mustwhenconsider both theinterest effectsrateofrisk. yield changes on bond and how volatile yields are estimating One measure of price risk that considers both these components is value-at-risk (VaR).

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Study Session 16 Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk

KEY CONCEPTS LOS 58 .a

The fultol valuation approachbonds to measuring interest ratefinrisk involves using aofpricing model value individual and can be used to d the price impact any scenario of interest rate/yield curve changes. Its advantages are its flexibility and precision. The duration/convexi tusey approach is based onbonds summary measures of interest rate riskis and, while simpler to for a portfol i o of than the ful l valuati o n approach, theoretically correct only for parallel shifts in the yield curve. LOS 58.b

Cal l abl e bonds and prepayable securities wi l l have less price vol a ti l i t y (l o wer duration) at low yields, compared to option-free bonds. Putable bonds. bonds will have less price volatility at high yields, compared to option-free LOS 58.c

Option-free bondssaidhave a price-yield relationship thatthiiss case, curvedbond(convex toward thein origin) and are to exhi b i t posi t i v e convexi t y. In prices fal l l e ss response to an increase in yield than they rise in response to an equal-sized decrease in yield. exhibitto anegati ve convexity at lowtheyyieldfalllevels. In thistocase,an equal-sized bond prices riCal sincrease ellablesseinibonds response decrease i n yield than i n response n yield. LOS 58.d

Eff ective duration ulated asithen yield, ratiotoofthethechange averageinpercentage equal-sized increaseisandcalcdecrease yield. price change for an enecuve. durauon. = 2Vv-0 -(.6.yv+) a:

LOS 58 .e

Approximate percentage change in bond price = -duration change in yield in percent. The tive interpretation of duration is as the percentage change in a bond's pricemost for aintui 1% change in yield to maturity. Macaulay duration and modified duration are based on a bond's promised cash flows. Effecti v e duration is appropriate for estimating price changes in bonds wi t h embedded options flows. because it takes into account the effect of embedded options on a bond's cash x

LOS 58.f

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #58

58.g of a bond portfolio is equal to a weighted average of the individual bond The duration durations, where the wei g hts are the proportions of total portfolio value i n each bond position. Portfolio duration it givines thetheportfolio, sensitivityanofunlikely portfolioscenario value onlyfor tomost yiportfolios. eld changes that areis limited equal forbecause all bonds 58.hof convexity, the duration measure is a poor approximation of price sensitivity Because eld changesof thethatpriarece-yield not absolutely small. The convexity adjustment accounts for thefor yicurvature relationship. Incorporating convexi ty, weas:can estimate the percentage change in price in responsebothto duration a change and in yield of (.6.y) {[(-duration)(�y )J + [( convexity)( �y )2 ]} Introduction to the Measurement o f Interest Rate Risk

LOS

LOS

x

100

58.iconvexity considers expected changes in cash flows that may occur for bonds Effective with embedded options, while modified convexity does not. 58. j Price value of a basis (PVBP) an estiminateyield. of the change in a bond's or a bond portfoli o's value for apoint one basis pointis change PVBP = duration bond (or portfolio) value YiUncertai eld 58.k volatil iabout ty is thea bond' standard deviprice ation due of theto changes inin theyieldyieldresultsof afrom bond.both a n ty s future changes sensitivity to yield changes (its duration) and also from the volatility of its yibond' eld ins prithecemarket. LOS

LOS

x

0.0001

x

LOS

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Study Session 16 Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk

CONCEPT CHECKERS

1. Why i s the price/yield profi l e of a call a bl e bond less convex than that of an idecreases. ncreaseidentical is cappedoption-free from above,bond?at orThenearprice:the call price as the required yield A.otherwise ncrease is capped from above, at or near the call price as the required yield B. imcreases. C. decrease mcreases.is limited from below, at or near the call price as the required yield 2. The 4. 6 5% semiannual-pay Portage Health Authority bonds have exactl y 17 years toapproach, maturitytheandinterest are currently priced to(inyipercent eld 4.39%.of value) Usingforthethese full valuation rate exposure given a 75 basis point increase in required yield, is to: A.bonds, -9.104%. B. -8.-9.3044%. 31%. 14% semiannual-pay coupon bond hass point six yearschange to maturity. The bondectivise 3. Acurrentl y tradi n g at par. Using a 25 basi i n yield, the eff 0.3.8389.89.of the bond is to: A.B.duration 3.970. Supposechange that thein yibond in Question 3 isvcallable at parassuming today. Usithatngitsa price 25 basis 4. point e l d , the bond' s effecti e duration exceed 100 is to: A.B.cannot1.972. 19.1.998. 72. modififoreda duration of a bond is 7.basis87. points The percentage change in price using 5. The duration yield decrease of 110 i s to: A.B. -8.+7.155%. 657%. +8.657%. a convexi t y of 57. 3 . The convexity effect if the yiel d decreases by 6. A110bondbasishaspoints is to: A.B. -1.+0.6673%. 93%. +1.673%. a bondmeasures, has an effecti ve durationpercentage of 10.5 andchangea convexity of97.3. Using 7. Assume both of these the estimated in price for thi s bond, to a decline in yield of 200 basis points, is to: A.iB.n response 19.05%. 22.989%. 5%. 24. closest

c.

closest

c.

closest

c.

closest

c.

closest

c.

closest

c.

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-

Introduction to the Measurement o f Interest Rate Risk

has determi ned thatbondif market yieladconvexity s rise by 100effectbasisof points, a 8. Ancertaianalyst n hi g h-grade corporate will have 1. 7 5%. Further, she' s found that the total esti m ated percentage change in price for thi s bond shouldchange be -13.35%. Given thisduration information, it follows that the bond's percentage in price due to is: A.B. -15.10%. +16.11.60%. 85%. 9. A.Theaddi totalngprithece bond' volatislitconvexity y of a typieffect cal noncallable bond can be found by: to i t s effecti v e duration. B.C. addi n g the bond' s negati v e convexi t y to i t s modified duration. subtracting the bond's negative convexity from its positive convexity. 10. The current pricbond' e of as$1,PVBP 000,is7-year, 5.5% semiannual coupon bond is $1, 0 29. 2 3. The to: A.B. $0.05. $5.$0.764.0. 11. The effectestionma ated bondbyportfol io's value of a decrease in yield would be using: approach. A.B. thethe prifullcevaluation value of C. both the portfolio'as basis duratipoint. on and convexity. 12. when An analyst has noticed latel y that the pri c e of a particular bond has ri s en l e ss the yiconclude eld falls bythat0.1theo/o bond: than the price falls when rates increase by 0.1 o/o. She could is ananoption-free bond. A.B. has embedded put option. C. has negative convexity. ch of the follduration. owing measures is for a currently callable bond? 13. A.WhiMacaulay B.C. Effecti v e duration. Modified duration. -

c.

closest

c.

most

accurately

lowest

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Study Session 16 Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk

CHALLENGE PROBLEMS

6. A bond dealer provides the following selected information on a portfolio offixed-income securities. Use the following information to answer Questions 1 through

Market Price

Coupon

Modified Duration

Effective Duration

Effective Convexity

$2 million

1 00

6.5%

8

8

1 54

$3 million

93

5.5%

6

$ 1 million

95

7%

8.5

8.5

130

$4 million

1 03

8o/o

9

5

-70

Par Value

1.

2. 3. 4. 5. 6. 7. 8.

50

What is the effective duration for the portfolio? Calculate the price value of a basis point for this portfolio. Which coupon)bond(s) likely has (have) no embedded options? (identify bonds by Which bond(s) is (are) likely callable? Which bond(s) is (are) likely putable? What is the approxi m ate pri c e change for the 7% bond if i t s yi e ld to maturity increases by 25 basis points? Why might two bond dealers differ in their estimates of a portfolio's effective duration? Why migforht portfolio effectiveeven duration beassume an inadequate measure ofdurati interest rate risk a bond portfolio i f we the bond effecti v e o ns are correct?

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #58 - Introduction t o the Measurement o f Interest Rate Risk

ANSWERS - CONCEPT CHECKERS 1.

A

As the required yield decreases on a callable bond, the rate of increase in the price of the bond begins to slow down and eventually level off as it approaches the call price, a characteristic known as "negative convexity."

2.

C

We need to compare the value of the bond today to the value if the YTM increases by 0. 75%. Price today = 103.092 4.65 N = 34 ; PMT = - = 2.325; FV = 1 00; 2 4.39 I I Y = -- = 2.195%; CPT ---. PV = - 1 03.092 2 Price after a 75 basis point increase in the YTM is 94.490 4.65 N = 34 ; PMT = - = 2.325; FV = 100; 2 5 14 1/Y = 路 = 2.57%; CPT --+ PV = -94.490 2 Interest rate exposure =

3.

c

v_

94.490 - 103 092 路 = -8 .344% 103.092

= 100.999

14.00 N = 12; PMT = -- = 7.00; FV = 100; 2 13.75 1 / Y = -- = 6.875%; CPT --+ PV = - 1 00.999 2 v+

= 99.014

14.00 N = 12; PMT = -- = 7.00; FV = 100; 2 14.25 1 / Y = -- = 7.125%; CPT --+ PV = -99.014 2 V0 = 100.000 b.y = 0.0025 duration =

Page 154

V_ - V+ 2V0 (b.y)

=

100.9 99 - 99 .014 2(100)0.0025

= 3.970

漏2012 Kaplan, Inc.


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk

4.

A

1 00

v

=

V+=

99.014

V0=

100

6.y=

0.0025

v_ - v+ . = duranon = 2V0 (6.y)

100-99.014 = 1 . 972 2(1 00)0.0025

5.

c

Est.[6. V_ o/o] = -7.87 x(-1.10%) = 8.657%

6.

B

convexity effect = convexity x ( 6.y )2 =

7.

c

Total estimated price change = (duration effect + convexity effect)

{[- 10.5 8.

A

X

[

(-0.02)] + 97.3 (-0.02)2 X

[57.3(0.01 1? ]

]}

x 100 = 0.693%

x 100 = 21.0o/o + 3. 8 9o/o = 24.89o/o

Total percentage change in price = duration effect + convexity effect. Thus:

- 13.35 = duration effect + 1.75 =? duration effect = -15. 10%· (Note: the duration effect must be negative because yields are rising.)

9.

A

Total percentage change in price = duration effect + convexity effect. Thus: Total percentage change in price = effective duration + convexity effect. (Note: since this is a noncallable bond, you can use either effective or modified duration in the above equation.)

10.

B

PVBP = initial price - price if yield is changed by 1 basis point. First, we need to calculate the yield so that we can calculate the price of the bond with a 1 basis point change in yield. Using a financial calculator: PV = -1,029.23; FV = 1 ,000; PMT = 27.5 = (0.055 x 1,000) I 2; N =14 = 2 x 7 years; CPT � IIY = 2.4999 8 , multiplied by 2 = 4.99995, or 5.00%. Next, compute the price of the bond at a yield of 5.00% + 0.01 o/o, or 5.01 o/o . Using the calculator: FV = 1 ,000; PMT = 27.5; N = 14; IIY = 2.505 (5.01 I 2); CPT � PV = $1,028.63. Finally, PVBP = $ 1 ,029.23 - $1,028.63 = $0.60.

11.

A

The full valuation approach is the most complex method, but also the most accurate.

12.

C

A bond with negative convexity will rise less in price in response to a decrease in yield than it will fall in response to an equal-sized increase in rates.

13.

B

The interest rate sensitivity of a bond with an embedded call option will be less than that of an option-free bond. Effective duration takes the effect of the call option into account and will, therefore, be less than Macaulay or modified duration.

©20 12 Kaplan, Inc.

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155


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #58 - Introduction t o the Measurement o f Interest Rate Risk

ANSWERS - CHALLENGE PROBLEMS 1.

Portfolio effective duration is the weighted average of the effective durations of the portfolio bonds. Numerators in weights are market values (par value Denominator is tOtal market value of the portfolio. 2 0.95 4.12 2.79 -- ( 8) + ( 1) + ( 8.5 ) + -- ( 5) 9.86 9.86 9.86 9.86 --

2.

=

price as percent of par).

. . 4 . 8 1 (we1ghts are m m1'll'wns)

Price value of a basis point can be calculated using effective duration for the portfolio and the portfolio's market value, rogether with a yield change of 0.01 o/o. Convexity can be ignored for such a small change in yield. 4.81

X

0.0001

X

9,860,000

=

$4,742.66

3.

The 6 . 5 % and 7o/o coupon bonds likely have n o embedded options. For both of these bonds, modified duration and effective duration are identical, which would be the case if they had no embedded options. (It is possible that these bonds have options that are so far out of the money that the bond prices act as if there is no embedded option. One example might be a conversion option tO common stock at $40 per share when the market value of the shares is $2.)

4.

The 8o/o bond is likely callable. It is trading at a premium, its effective duration is less than modified duration, and it exhibits negative convexity. Remember, call price can be above par.

5.

The 5.5% bond is likely putable. It is trading at a significant discount, its effective duration is much lower than its modified duration (close to zero in fact), and its convexity is positive but low. Note that a putable bond may trade below par when the put price is below par (also if there is risk that the issuer cannot honor the put). If it were callable, we would expect its modified and effective durations tO be closer in value because the market price is significantly below likely call prices.

6.

Based on the effective duration and effective convexity of the 7o/o bond, the approximate price change is: [-8.5

Page 156

--

x

X

0.0025]

+

[ 1 30

X

0.0025 2]

X

950,000

=

-$ 19,4 1 5 .63

7.

In order to estimate effective duration, the dealers must use a pricing model for the bonds and choose a specific yield change. Differences in models or the yield change used can lead tO differences in their estimates of effective duration.

8.

Effective duration is based on small changes in yield and is appropriate for parallel changes in the yield curve (or equal changes in the yields to maturity for all portfolio bonds). Other types of yield changes will make portfolio duration an inadequate measure of portfolio interest rate risk.

Š2012 Kaplan, Inc.


The following is a review of the Fixed Income Analysis and Valuation principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in:

FUNDAMENTALS OF CREDIT ANALYSIS Study Session 1 6

EXAM FOCUS

This topic revi e w introduces credit analysis, primarily for corporate bonds, but considerations foron credi t analysis ofcredithighspreads, yield, sovereign, and municipal bonds areratings also covered. Focus credit ratings, and the impact on return when and spreads change. LOS 59.a: Describe credit risk and credit-related risks affecting corporate bonds. CPA® Program Curriculum, Volume 5, page 606

isandthe fulriskl payments associatedofwiitnhterest lossesorstemming ure two of a components: borrower to make timelyand principal.from Credittherifailsk has i s the probabi l i t y that a borrower (bond issuer) fai l s to pay i n terest or repay principalorwhen due. refers to the value a bond investor will lose if the issuer defaults. Loss severi t y can be stated as a monetary amount or as a percentage of a bond's value (principal and unpaid interest). The equal astoathemonetary default value risk multiplied by the lossof severi loss can likewise beisstated or as a percentage a bond'ty.s Expected value. The Loss severity is theas percentage will receiverate.if the issuer defaults. a percentageofias bond' equal stovalue one anminusinvestor the recovery Bondsdifwith crediintyiriskeldtrade at hiagcredit-ri her yieldsskythanbondbonds thought to be freebond of credit risk. The ference between and a credit-risk-free of similar maturity i s called i t s For example, i f a 5-year corporate bond i s trading at a s pointsbond to Treasuries 6.5%.on 5-year Treasury notes is 4.0%, thespreadyieldofon+250thebasicorporate is 4.0% and2.5%the=yield Bond andpricesa narrower are inverselspread y relaimplies ted to spreads; widerThespreadsizeimplies a lowerreflbond price a higheraprice. of the spread ects the Credit risk

default risk

loss severity.

Default risk

Loss severity,

loss given default,

expected loss

recovery rate

yield spread.

+

©20 1 2 Kaplan, Inc.

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59

-

Fundamentals o f Credit Analysis

tworthinessthatofathebond'issuers spread and thewilliquidity for itsofbonds. thecredipossibility l widen dueof theto onemarket or both these factors. is or i s the possibil i ty that spreads will increase because the issuer hasg agencies becomeassign less credi tworthy. As weandwiissuers, ll see laterandinmaythisupgrade topic or revi e w, credit rati n ratings to bonds downgrade these ratingsis theoverrisktime.of receiving less than market value when selling a bond forandtheis reflbonds ectedofinlessthecredi sizetworthy of the biissuers d-ask spreads. Market liquidity risker issuers is greater and for the bonds of small with relatively little publicly traded debt. Spread risk

Credit migration risk

Market liquidity risk

downgrade risk

LOS 59.b: Describe seniority rankings of corporate debt and explain the potential violation of the priority of claims in a bankruptcy proceeding. CFA® Program Curriculum, Volume 5, page 609

Each category of debt Afrombond'thes same issuerof claims is rankedto theaccordi ngs assets to a and cash flows isin thereferred event of a default. priority issuer' to as its Debt canunsecured be eitherdebt or or represent a generalSecured debttheisissuer' backeds assets by collateral, while claim to cash flows. Secured debt has higher priority of claims than unsecured debt. and Secured debt can be further distinguished as debt.orUnsecured debt(where a specific asset i s pledged), or i s further divided into and rank ofdebt. unsecured debt is senior unsecured. Subordinated debtgradations. ranks belowTheotherhighest unsecured The general seniority rankings for debt repayment priority are the following: FiSenior rst liensecured or firstdebt. mortgage. Junior secured debt. Senior unsecured debt.debt. Senior subordinated Subordinated debt. Junior subordinated debt. Allclaims. debtAllwitsenior hin thesecured same category is saidfortoexampl rank e, are treatedor have same priority of debt holders, al i k e in a corporate bankruptcy. Recovery ratesrankareofhighest fory. Thedebtlower withthetheseni highest priority ofofclaims andthedecrease with each lower seniori t o rity ranki n g a bond, higher its credit risk. Investors require a higher yield to accept a lower seniority ranking. Inbefore the junior event oflenders a defaultandorequireorganizati o n, seni o r lenders have claims on the assets ty holdiers.n theory A strictthepriority always applied in practice. Although priorityofofclaims, claimshowever, is absolute,is notin many priority of claims

seniority ranking. secured debt

unsecured debt.

debentures

first lien senior secured, junior secured senior, junior, subordinated

first mortgage

• • • •

pari passu,

Page 158

©2012 Kaplan, Inc.


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis

cases lower-priori debt holders are notty debt paidholders in full. (and even equity investors) may get paid even if senior Bankruptciesthecanvalue be costly and take as long time todeteri settleo. rate Duringduebankruptcy proceedings, of a company' assets could to loss of customers and keyrmedemployees, whiamong le legalall clexpenses mount. Awibankruptcy reorgani zrecovery ation planrate.is confi by a vote a sses of i n vestors t h less than 100% Tomayavoid unnecessary delzation ays, negoti athattiondoesandnotcompromise among tovarious clgaiimholders result in a reorgani plan strictly conform the ori n al pri o rity of claims. By such from absolute prioriatvote y. or by order of the bankruptcy court, the final plan may differ LOS 59.c: Distinguish between corporate issuer credit ratings and issue credit ratings and describe the rating agency practice of "notching". CPAÂŽ Program Curriculum, Volume 5, page 616

Credit rating agenci eboth s assigntheratings toecategori es of bonds withthesimilar crediandt risk. Rating agenci e s rate issuer (i. . , the company issuing bonds) theratings debt issues, or the bonds themselves. Issuer credit ratings are called corporate family (CFR), arewhibased le issue-speci foverall ic ratingscrediaretworthi calledncorporate credit ratings (CCR). Issuerrated on ratings on the ess of the company. The issuers are their senior unsecured debt. Figure 1 shows ratinagenci gs scalees.s used by Standard & Poor's, Moody's, and Fitch, three of the major credi t rating Figure Credit Rating Categories 1:

(a) Investment grade ratings

Moody's Aaa Aal Aa2

Standard &Poor's, Fitch AAA AA+ AA

(b) Non-investment grade ratings

Moody's

Standard &Poor's, Fitch

Ba l

BB+

Ba2

BB

Ba3

B8-

81

8+

Aa3

AA-

Al

A+

82

8

A

83

8-

A3

A-

Caal

CCC+

Baal

8BB+

Caa2

CCC

Baa2

B8B

Caa3

CCC-

Baa3

88B-

Ca

cc

A2

c c

Š20 12 Kaplan, Inc.

c

D

Page 159


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59

-

Fundamentals o f Credit Analysis

Triarepconsidered le A or Aaa) is the highestBondsrating.ratedBonds with orratings ofareBaa3/BBBor higher Bal/BB+ lower considered and are often called or Bonds i n default are rated by Standard & Poor' s and Fitch and are i n cluded i n Moody' s lowestbonds,ratinprovisions g category,inC.bond Whenindentures a companymaydefaults ondefault one ofonitstheseveral outstanding tri g ger remaining issues as well. Such a provision is called a Abutborrower can haverating. multipl e debt issues thatdepend vary notononly by maturities and coupons also by credit Issue credit ratings the seniori t y of a bond issuengsandto itsbondscovenants. is the practice by rating agencies of assigning di f ferent rati of theitssame Notchingloisss based bonds and impactissuer.on potential severionty. several factors, including seniority of the Anratinexampl e of a factor that rating agenci es consider when structure, notching anbothissuethecredit g is In a holding company parent company andthethetransfer subsidiariof cash es mayor have outstanding debt.theAparent subsidcompany iary's debtbefore covenants may restrict assets "upstream" to theare subsidiary' s debt i s serviced. In such a case, even though the parent company' s bonds not junior to the subsidi a ry' s bonds, the subsidiary' s bonds have a priority claim to the subsidiary' flows. Thus the parent company's bonds are effectively subordinated to the subsidisary'cashs bonds. Notching is lesshigcommon forrihighl y rated issuerscantthandifferences for lower-rated issuers. Forrates lower足of rated issuers, her default s k leads to signifi between recovery debt with different seniority, leading to more notching. (AAA

investment grade. investment grade

non足

high yield bonds

junk bonds.

0

cross default provision.

Notching

structural subordination.

LOS 59.d: Explain risks in relying on ratings from credit rating agencies. CFA速 Program Curriculum, Volume 5, page 618

Relying on ratings from credit rating agencies has some risks. Four specific risks are: 1. update their default risk assessments Credit ratings change overof atime. RatiHigher ng agenci etsratings may during the l i f e bond. credi tend to be more stable than lower credit ratings. Ratingsweremistakes occurmuchfromhigher time ratings to time.thanFor they example, subprime mortgage securities assigned deserved. 3. difficultriskto ispredict and incorporateRisksintothatcredit are specific to a company or industry are ratings. Litigation such risk toas tobacco companies i s one example. Events that are di f fi c ult to anticipate, naturalin disasters, acquisitions, and equity buybacks using debt, are not easily captured credit ratings. Credit ratings are dynamic.

2. Rating agencies are not perfect.

Event

Page 160

difficult to assess.

息2012 Kaplan, Inc.


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis

4. faster Creditthan ratingscredilagt ratings. marketAdditional pricing. Market prices andwithcredit spreads changetrademuch l y , two bonds same rating can at didefault fferentrisyik.elds. Market prices reflect expected losses, while credit ratings only assess LOS 59.e: Explain the components of traditional credit analysis. CPA® Program Curriculum, Volume 5, page 623

Acredit common waycapacity, to categoricollateral, ze the keycovenants, componentsand ofcharacter. credit analysis is by the four Cs of analysis: Capacity

Capacityofrefers to a corporate borrower' s abilused ity repay its debtanalysi obligations on tianalysi me. s Analysis capacity i s simi l ar to the process in equity s . Capacity entai l s three l e vel s of assessment: (1) i n dustry structure, (2) industry fundamentals, and (3) company fundamentals. Industry Structure

The firstdescribed level of abycredit analyst' sforces: assessment isamong industryexististructure. Industry threat structureof can be Porter' s fi v e rival r y n g competitors, new entrants, threat of substitute products, bargai n ing power of buyers, and bargaining power of suppliers. � Professor's Note: We describe industry analysis based on Porter'sjiveforces in the � Study Session on equity valuation. Industry Fundamentals

The level of a credit analfactors yst's assessment is industry fundamentals, including the iIndustry nflunext ence fundamentals of macroeconomic on an industry' s growth prospects and profitability. evaluation focuses on: Industry cyclicality. Cycl i cal industries are sensitive to economic performance. Cyclcihcalmake industries tend toriskyhavethanmorenoncycl volatilicale earnings, revenues, and cash flows, whi them more industries. Industry growth prospects. Creditworthiness is most questionable for the weaker companies i n a slow-growing or declining industry. Industry published statistics. Industry statisti cs providedagencies by ratincan g agencies, investment banks, i n dustry periodicals, and government be a source for industry performance and fundamentals. •

• •

©20 1 2 Kaplan, Inc.

Page 1 6 1


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59

-

Fundamentals o f Credit Analysis

Company Fundamentals

The last level of credit analysts' assessment is company fundamentals. A corporate borrower should be assessed on: Markettoshare changes over time and cost structure relative to peers are some of theThefactors analyze. performance of the company over different phases of business cycle, trends in margins and revenues, and current management' s tenure. This includes the soundness of the thebondholders. ability to execute the strategy, and the effects of management's decisionsstrategy, on coverage ratios are importantAs wetoolswilforl discuss creditlater analyinsis.this topic review, leverage and •

Competitive position.

Operating history.

Management's strategy and execution.

Ratios and ratio analysis.

Collateral

Collateral analysis iss more important for lessto creditworthy companies. Theconsider marketwhen value of a company' assets can be difficult observe di r ectly. Issues to assessing collateral values include: Patents are considered high-quality intangible assets because they can beconsimorederedeasilya high-quality sold to generate cash flasset ows and thanisother intangibles. Goodwil l is not intangible usually written down when company performance is poor. expense relative to capital expenditures may signal High depreciation that management is notbe ipoor, nvestingwhichsuffimay cientlyleadintothereduced company. The quali tyflofowtheand company' s assets may operating cash potentially high loss severi t y. Equitycompany assets are of lowAqualistockty. that trades below book value may indicate that are difficult to value, but a company may have intellectual property that canThese function as collateral. •

Intangible assets.

Depreciation.

market capitalization.

Human and intellectual capital.

Covenants

Covenants are theissue.termsCovenants and conditions the borrowers and lenders have agreedfletoxibility as part of a bond protect lenders whi l e leaving some operating to the borrowers and (2) to run the company. There are two types of covenants: (1) require the borrower to takeon certain actions, suchmaintaining as paying icertain nterest,fiprincipal, and taxes; carrying insurance pledged assets; and nancial ratios within prescribed limits. restrict the borrower from taki n g certain actions, such as incurring additional debt or directing cash flows to shareholders in the form of dividends and stock repurchases. of anhand, issuer'covenants s operatingcreate activaitieslegally maybinding reduce theCovenants issuer's that abilityaretooverl repay.y restri On cthetiveother affirmative

covenants

negative covenants.

Affirmative covenants

Negative covenants

Page 162

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis

framework forcareful repayment of the debt obligation, whiassessment ch reducesofuncertainty forcontractual the debt holders. A credi t analysis should include an whetherthe the covenants protect the interests of the bondholders without unduly constraining borrower's operating activities. Character

Charactersuchrefersas management' to management' s integriqualifications ty and its commitment to repay theareloan. Factors s business and operating record important for evaluating character. Character analysis includes an assessment of: Management' s ability toindevelop a sound strategy.and operating Management' s past performance executing i t s strategy theled tocompany wi t hout bankruptcies, resrructurings, or other distress situations that additional borrowing. Use ofasaccounting policies andissues, tax frequent strategies that may be hidi n g problems, such revenue recognition restatements, and frequently changi nrecord g auditors. Any of fraud or other legal and regulatory problems. Benefi t s to equity holders at the expense of debt holders, such rating as debt-financed especiallythrough if they ledactiotonscredit downgrades.acquisitions and special dividends, • •

Soundness of strategy. Track record.

Accounting policies and tax strategies.

Fraud and malfeasance record.

Prior treatment of bondholders.

LOS 59.f: Calculate and interpret financial ratios used in credit analysis. CPA® Program Curriculum, Volume 5, page 628

Ratio analysis is part of capacity analysis. TwoCredit primaryanalysts categoricalculate es of ratios for credit analysi s are and company rati o s to assess viabilityandof apeers. company, to find trends over time, and to compare companies to industrytheaverages leverage ratios

coverage ratios.

Profits and Cash Flows

Profi t s and cash fl o ws are needed to servi c e debt. Here we examine four profit and cash flow merrics commonly used in ratio analysis by credit analysts. 1. EBITDA is a commonly used measure that is calculated as operating income plus depreciation and amortization. A drawback to using this measure for credit anal y sis is that areit doesnecessary not adjusesust forof funds capitalforexpenditures and changes in workiforngthesecapital, which a going concern. Cash needed uses is not available to debt holders. fromoperations plus(FFO). Funds from operations are net income from 2. continuing depreciation, amortization, deferred taxes, and noncash items. FFO i s similar to cash fl o w from operations (CFO) except that FFO excludes changes in working capital. Earnings before interest, taxes, depreciation, and amortization (EBITDA).

Funds

operations

©20 1 2 Kaplan, Inc.

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59

-

Fundamentals o f Credit Analysis

3. depreciation and amortization miFree cashtalfloexpendi w beforeturesdividends ins crease net income plus n us capi minus i i n working capital. Free cash flow before dividends excludes non-recurring items. i s free cash flow before dividends minus the 4. dividends. If free cash flow afterThis diviondendstheibalance s greatersheet. than zero, it outcome representsis cash that could pay down debt or accumulate Ei t her a form of deleveraging, a positive indicator for creditworthiness. Free cash flow before dividends.

Free cash flow after dividends.

Leverage Ratios

Analysts should adjas uunderfunded st debt reported on theplansfinancial statements by includi noff-balance­ g the firm's obligations such pension (net pension liabilities) and sheet liabilities such as operating leases. The threeratio,mostthecommon measures ofratio,leverage by credit analysts capital debt-to-EBITDA and theusedFFO-to-debt ratio. are the debt-to­ 1. capital ratio is Capital is the sumof theof total debtstructure and shareholders' equity. Thelowerdebt-to­ the percentage capital fi n anced by debt. ratio indicatessuchlessas credit risk.anIfanalyst the financial statements listsecond high values for intangible assets goodwill, should cal c ul a te a debt-to-capital ratio adjusted for a writedown of these assets' after-tax value. indicates higher leverage and higher credit risk. This 2. ratio is more volatilhie gforherfirratio ms inofcyclEBITDA. ical industries or with high operating leverage because of their high variability s ratiocredit dividrisk. es a cash flow measure by the value of debt, a 3. higher ratioBecause indicatesthilower Debt/capital.

A

Debt/EBITDA. A

FFO/debt.

Coverage Ratios

Coverage borrower'used s ability to generate cash flowsandto£BIT-to-interest. meet interest payments.ratiTheostwomeasure mostthecommonly are EBITDA-to-interest higher ratio indicates lower credit risk. Thi s rati o i s 1. used more often than the £BIT-to-interest expense ratiw measure, o. Becausethisdepreciation and amortization are sti l l included as part of the cash fl o ratio will be higher than the EBIT version. rati o indicates l o wer credi t ri s k. This rati o i s the 2. more conservative measurehigher because depreciation and amortization are subtracted from earnings. EBITDA/interest expense. A

£BIT/interest expense. A

Page 164

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis

1) Aselcredit anal y st is assessing Saxor, a U. S . multimedia company wi t h the followi n g ected financial information: Example: Credit analysis with financial ratios (Part

20X2

In $ millions

20Xl

Operating income

5,205

6,456

7,726

36,149

38,063

40,893

Depreciation and amortization

1,631

1 ,7 1 3

1 ,841

Capital expenditures

1,753

2, 1 1 0

3,559

Cash Row from operations

5,319

6,578

6,99 4

Total debt

12,701

12,480

1 3 ,977

Total equity

33,734

37,5 1 9

37,385

Dividends paid

648

653

756

Interest expense

300

33 0

360

Revenue

20X3

the cash flows and ratios listed below. Free cash flow (FCF) is after dividends forCalculate all calculations. 20Xl

20X2

20X3

EBITDA FCF after dividends Operating margin Debt/EBITDA EBITDNinterest FCF/debt Debt/capital

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59

-

Fundamentals o f Credit Analysis

Answer:

EBITDA = operating i n come depreciation and amortization: 20Xl: 5,6,240556 1,1,76 3113 == $8,169 $6,836 million 20X2: million 20X3: 7,726 1,841 = $9,567 million FCF = cash fl o w from operations capital expenditures dividends: 20Xl: 5,319 - 2,110 1,753 -- 648 == $2,$3,815 9 18 million 20X2: 6,578653 20X3: 6,994- 3,559 - 756 = $2,679 million million Operati5,n2g05margin = operating income revenue: 20Xl: 36,149 = 14. 4 % 20X2: 893 == 18.17 .O9o/o% 20X3: 6,7,742656 40,38,063 Debt/EBITDA: 20Xl: 12,701 6,836 = 1.9x 20X2: 12,13,497780 9,567 8,169 == 1.5x 1.5x 20X3: EBITDNinterest: 300 = 22. 8 x 20Xl: 6, 8 36 20X2: 360 == 24.26.68xx 20X3: 8,169 9,567 330 FCF/debt: 20Xl: 6, 8 36 12,701 = 23. 0 % 20X2: 20X3: 8,169 9,567 13,12,497780 == 30.19.26%% Debt/capital: 20Xl: 12,701 (12,701 + 33, 7 34) = 27.4% 20X2: 12, 4 80 (12, 4 80 + 37,519) = 25. 0 % 20X3: 13,977 (13,977 + 37,385) = 27.2% +

+

+

+

I

I I I

I I I

I

I I

I

I I

I I I

20Xl

20X2

20X3

EBITDA

6,836

8 , 1 69

9,5 67

FCF after djvidends

2,9 1 8

3,8 15

2,679

Operating margin

14.4%

17.0%

18 .9%

1.9x

1 .5x

1.5x

EBITDA/interest

22.8x

24.8x

26.6x

FCF/debt

23.0%

30.6%

19.2%

Debt/capital

27.4%

25.0%

27.2%

Debt/EBITDA

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis

2) 2.follCoyote Media is al s o a multimedia company and is a ri v al of Saxor. Gi v en the owing ratios forandCoyote over theon which same period, calculate the 3-year averagesto forhavebotha Saxor and Coyote comment mul t imedia company i s expected better credit rating. Example: Credit analysis with financial ratios (Part

Coyote Media

20Xl

20X2

20X3

Operating margin

18.0%

7.0%

9.5%

1 .9x

3.0x

2.0x

EBITDA/interest

27.5x

12.7x

18.3x

FCF/debt

15.0%

28.0%

26.6%

Debt/capital

28.7%

4 1 .2%

42.6%

Debt/EBITDA

Answer: 3-Year Averages

Saxor

Coyote

Operating margin

16.8%

1 1 .5%

1 .6x

2.3x

EBITDA/interest

24.7x

19.5x

FCF/debt

24.2%

23.2%

Debt/capital

26.5%

37. 5%

Debt/EBITDA

Allandratios support a higher credit(EBITDA/interest) rating for Saxor. Saxor hasdebt a better(FCF/debt). operatingLower margin better coverage for interest and for leverage as measured by debt-to-capital and debt-to-EBITDA also favor Saxor. LOS 59.g: Evaluate the credit quality of a corporate bond issuer and a bond of that issuer, given key financial ratios for the issuer and the industry. CPAÂŽ Program Curriculum, Volume 5, page 631

Ratings agenciclassifi es publish benchmark valystsuescanforevaluate financialtheratios that areforassociated with each ratings c ation. Credit anal potential upgrades and downgrades based on subject company ratios relative to these benchmarks.

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59

-

Fundamentals o f Credit Analysis

Example: Credit ratings based on ratios (Part 1 )

credit rati n g agency publishes the fol l o wing benchmark rati o s for bond issues ofaverages multimedia in eachto 20X3: of the investment grade ratings, based on 3-year over thecompanies period 20Xl

A

AAA

AA

A

BBB

24.5%

16.5%

1 O.Oo/o

7.5%

1 .3x

1 .8x

2.2x

2.5x

EBITDA/interest

25.0x

20.0x

17.5x

1 5 .0x

FCF/debt

30.0%

24.0%

20.0%

17.0%

Debt/capital

25.0%

30.0%

35.0%

40.0%

Credit Ratings Operating margin Debt/EBITDA

Based the ratioswhatcalculated in the previous exampl e andfortheCoyote industryandstandards the tableon above, are the expected issuer credi t ratings Saxor? in Answer: 3-Year Averages

Saxor

Coyote

Operating margin

16.8%

1 1 .5%

1.6x

2.3x

EBITDA/interest

24.7x

1 9.5x

BBB

FCF/debt

24.3%

23.2%

BBB

Debt/capital

26.6%

37.5%

BBB

Debt/EBITDA

BBB

A

Coyote

BBB

A A

Coyote

A A

Saxor

AA

AA

Coyote

AA

Coyote Saxor AA

AA

Saxor

AAA AAA

Saxor

AAA AAA

Saxor

AAA

Based on the rati o averages, it is most li k el y that Saxor' s issuer rati n g is AA and Coyote's issuer rating is 2) Coyote Medi decidesandtowillspinnotoffbeitsa televi sion division. Theof Coyote new company, Coy TV, wiis more l issueprofi newtaabldebt restricted subsidiary Media. Coy e and generates higher and less vol a tile cash fl o ws. Describe possible notching Media. for the new CoyTV issue and the potential credit rating change to Coyote A.

Example: Credit ratings based on ratios (Part

TV

Answer:

Because CoyTV may be a better credit ri s k due to a better profit potential, the new issue may have a credit rating one notch above Coyote Media. Coyote Medi a may now be less profitable and could have more volatil e cash fl o ws. This suggests an increase in credit risk that could lead to a credit rating downgrade. Page 168

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis

LOS 59.h: Describe factors that influence the level and volatility of yield spreads. CFA ® Program Curriculum, Volume 5, page 642

We caninterest thinkrate,of thetheyield on aninoption-free corporate bond as the asumliquidity of thepremium, real risk­ free expected fl a tion rate, a maturi t y premium, and a credit spread. All bond prices and yields are affected by changes in the fi r st three of these components. The last two components are the yield spread: yield spread = liquidity premium credit spread Yield spreads on corporate bonds are affected primarily by five interrelated factors: 1. the credit cycle,Thethemarket' s perception of overall credit risk i s cyclical. At the top of bondas themarket perceives low creditCredit risk and is generall yasbullish. Credi t spreads narrow credit cycle improves. spreads wi d en the credit cycle deteriorates. Creditmetrics spreadstonarrow as the economy strengthens and 2. investors expect firms' credit improve. Conversely, credit spreads widen as the economy weakens. CreditCredi spreads narrow in strong-performing markets 3. overall, including the equity market. t spreads widenity ofin returns, weak-performing markets. In steady-performing markets with low volatil credit spreads also tend to narrow as investors reach for yield. 4. broker-dealers to providBecause most bondscapitradetal foroverbond the counter, investors needYield e market-making markets to function. spreadsmarket-maki are narrowerngwhen when capitalbroker-dealers becomes scarce.provide sufficient capital but can widen 5. demand for bonds. Credit spreads supply.widenCrediin ttimes spreadsof low narrowdemand in timesfor bonds. of highExcess wisupply deninconditions, g spreads. such as large issuance in a short period of time, can lead to Yield spreads on l o wer-qual i t y issues tend to be more volatile than spreads on higher­ quality issues. +

Credit cycle.

Economic conditions.

Financial market performance.

Broker-dealer capital.

General market demand and

LOS 59.i: Calculate the return impact of spread changes. CFA ® Program Curriculum, Volume 5, page 646

The imchange pact of(�spread) spread changes is athecombination of twooffactors: (1)totheinterest magnirate tude ofchanges thereturn spread and (2) price sensitivity the bond (i.e., the bond's modified duration). ©20 12 Kaplan, Inc.

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59

-

Fundamentals o f Credit Analysis

For small spreadby:changes, the return impact (percent change in bond price) can be approximated return impact modified duration �spread The negati ve sign widen in the (the equation reflienctsspread the inverse relationship betweendecrease pricesandandthe yields. As spreads change i s positive), bond prices impact on return i s negati v e. As spreads narrow ( t he change in spread is negative), bond prices increase and the impact on return is positive. For spread changes, incorporating convexity improves the accuracy of return impactlargermeasurement. return impact modified duration �spread+ _!_2 convexity (�spread)2 �

-

-

x

x

x

Professor's Note: Make sure the value ofconvexity is scaled correctly. For option-free bonds, convexity should be on the same order ofmagnitude as modified duration squared. For example, ifyou are given that duration is 6 0 and convexity is 0.562, duration squared is 36 0 and the correctly scaled convexity is 562.

0 Also notice that convexity is divided in halfhere, but was not divided in half

when we adjustedfor convexity in an earlier topic review. This is because different authors calculate convexity differently. For the exam, use one-halftimes convexity ifa question asks for the return impact ofa change in spread.

Longer maturity bonds have higher duration and consequently higher spread sensitivity; theirhigher pricestheanduncertainty returns areofmore sensitive to tchanges inessspread. The longer theimplmaturi ty, the the future credi worthi n of the debt issuer, y i n g higherlarger credibid-ask t spreadsspreads for longer maturity bonds. Longer maturi tyinbonds also tend to have (i. e . , hi g her transaction costs), i m pl y g investors in longer maturity bonds would require higher spreads. ormaturity bondsshow theto have relationship betweencredispread and maturi ty.cally Because l o nger tend wi d er spreads, t curves are typi upward sloping. Bond performance is credit positivelspreads. y affected by narrowing credit spreads and negativel y affected by widening To enhance bond portfolio performance, active bond managers forecastbondspreadportfoli changeso. and expected credit losses for individual issues held and forneedthetooverall Credit curves

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis

Example: Impact on return

AnThis8-year semiannual-pay corporate bond wi t h a 5. 7 5% coupon i s pri c ed at $108. 3 2. bond'bys75duration and reported convexi ty are 6.upgrade. 4 and 0.Estimate 5. The bond' s creditimpact spread narrows basis points due to a credit rating the return with and without the convexity adjustment. Answer:

return impact (without convexity adjustment) -- 6.modifi ed0duration D.spread 4 -0. 075 0.0.00480 48 or 4.80% return impact with convexity adjustment - modified duration D.spread + _!_2 convexity (D.spread)2 -6.4 -0.0075 _!_2 (50.0) (-0.0075)2 0.0480 + 0.0014 0.0494 or 4.94% Notice that convexity needed to be corrected to match the scale of duration. We can calculate change inadjustment. the bond's price from the information given to illustrate the needtheforactual the convexity Beginning yield to maturity: NCPT= 16; PMT = 5.75 I 2 = 2. 8 75; FV = 100; PV = -108. 3 2; 1/Y = 2.25 2 = 4.50 Yield to maturity after upgrade: 4. 5 0 -0.75 = 3.75% Price after upgrade: 1/Y = 3.75 I 2 = 1.875; CPT PV = -113.71 The bondisprice is an intcrease of (113.71 I 108.32) - 1 = 4.98%. The calculated approximation closerofwi$113.71 th the convexi y adjustment. �

X

x

X

X

+

X

X

--t

X

--t

©20 12 Kaplan, Inc.

Page 1 7 1


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59

-

Fundamentals o f Credit Analysis

LOS 59.j: Explain special considerations when evaluating the credit of high yield, sovereign, and municipal debt issuers and issues. CFA ® Program Curriculum, Volume 5, page 650

High Yield Debt

Hignhgyield ores. These bonds are alsocorporate bonds arebecause rated below Baa3/BBB by credivedt rati agenci cal l ed of their higher percei credit risk. Reasons for non-investment grade ratings may include: . history. HiUnproven gh leverageoperating Lowghorsensinegati ve tofreebusiness cash flocycles w. . HiLow t ivity conficompetitive dence in management . Unclear advantages . Large off-balance-sheet Industry in decline . liabilities . Because hi g h yield bonds have higher default risk than investment grade bonds, credi t anal ystsinclude must paytheimore attention to lossprojections, severity. Special considerations for high yield bonds r liqui d i t y, fi n ancial debt structure, corporate structure, and covenants. Liquidity or avaitolability of cashborrowings, is critical forandhiavaigh lyield issuers.tendHighto yield issuers have limited access additional able funds be more expensi ve forcanhighquickly yield issuers. Bad company-specifi cmarkets. news andMany diffichiultghfinancial market conditions dry up the liquidity of debt yield issuers are privately owned and cannot access public equity markets for needed funds. Analysts focus on six sources of liquidity (in order of reliability): 1. Balance sheet cash. 2. Working capital. 3. Operating cash flow (CFO). 4. Bank credit. 5. Equity issued. 6. Sales of assets. For yielddueissuerwithin with afewshortor unreliable sources of liquidity, signifidefault. cant amounts ofoutdebtaofhigh coming ti m e frame may indicate potential Running cash with accesshighto external financing anceyielor dservice existing the primary reasonnowhy yield issuers default.to Forrefinhigh financial firmsdebt thatis non-investment grade

junk bonds

• • • • • • • •

Liquidity.

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis

are highlyislevered liquidity critical.and depend on funding long-term assets with short-term liabilities, Projforecting futurein earnings and cash flows,andincluding stress are scenari o s and accounting changes capital expenditures working capital, important for revealing potential vulnerabilities to the inability to meet debt payments. High yield i s suers' capital structures often include different types of debt with severaltypical levelslyofinclseniority and hence varying levelslienof potential loss unsecured severity. Capital structures u de secured bank debt, second debt, senior debt,may subordinated debt, and preferred stock. Some of these, especially subordi n ated debt, be convertible to common shares. Aancredit anal y st wil l need to calculate l e verage for each level of the debt structure when issuer has multiple layers of debt with a variety of expected recovery rates. High yieldarecompanies for which secured bank debt is a tohighborrow proportion of theincapital structure said to be and have less capacity from banks filiknelancially stressfulandperiods. top-heavy debt capitalissues. structures are more y to default have lowerCompanies recoverythat rateshavefor unsecured and Two European high yield companies in the same industry have the following financial information: Financial projections.

Debt structure.

top heavy

Example: Debt structure

In â&#x201A;Ź million

leverage

A

B

100.0

50.0

Interest expense

40.0

20.0

EBITDA

85.0

42.5

Secured bank debt

500.0

125.0

Senior unsecured debt

200.0

50.0

50.0

200.0

Cash

Convertible bonds

1. Calculate total leverage through each level of debt for both companies. 2. Calculate net leverage for both companies. 3. Comment on which company is more attractive to an unsecured debt investor.

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis

Answer:

Secured debt leverage: secured debt/EBITDA Senior unsecured leverage: (secured + senior unsecured debt)/EBITDA Total debt leverage: total debt/EBITDA Net leverage: (total debt - cash)/ EBITDA

A

B

500.0 I 85.0 = 5.9x

125.0 I 42.5 = 2.9x

(500.0

+

(500.0

200.0) I 85.0 = 8.2x + 200.0 + 50.0) I 85.0 = 8.8x

(750.0 - 1 00.0) I 85.0 = 7.6x

( 1 25.0

+

(125.0

50.0) I 42.5 = 4 . lx + 50.0 + 200.0) I 42.5= 8.8x

(375.0 - 50.0) I 42.5 = 7.6x

Company B has a l o wer secured debt leverage rati o than Company A, whi l e total and net leverage ratiosit iares lessabout theheavysame.andCompany Bsomeis more attractito vborrow e to unsecured debt holders because top may have capacity from banks, which suggests a lower probability of default. If i t does default, Company B may have a higherallypercentage availablebondsto unsecured holders than Company A, especi if holders ofof assets convertible have exercidebt sed thei r options. Many high-yield companies use aofholding company structure. A parent company recei v es di v idends from the earnings subsidiaries as its primary source of operatingto aincome. Because ofarestructural subordination, subsidiaries'These dividdiviendsdends paidcan upstream parent company subordinate to interest payments. beforidebt nsuffiholders cient toofpaythetheparent debt company. obligations of the parent, thus reducing the recovery rate Despite structural subordination, a parent company' s credit rating may be superi o r to subsidifrom aries'diratings because the parent can benefit from having access to multiple cash Hows verse subsidiaries. Someown complex corporate structures haveofintermedi ate holdingstock.companies that carryare their debt and do not own 100% their subsidiaries' These companies typically a result of mergers, acquisitions, or leveraged buyouts. Default of one subsidiary may not necessarily result in cross default. Analysts need to scrutinize bonds' indentures and Tootheranallegal documents to fullanal y understand thecalculate impact ofleverage complexratios corporate structures. y ze these companies, y sts should at each level of debt issuance and on a consolidated basis. Important covenants for high yield debt include: Changeto ofbuycontrol put. (typical This covenant givesvaluedebtor hola value ders sltheightly rightabove to requipar)reinthe issuer back debt l y for par the evently applies of an acquisition. For investment grade bonds,results a change of control pur typical only i f an acquisition of the borrower i n a rating downgrade to below investment grade. Corporate structure.

Covenants.

â&#x20AC;˘

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis

Restricted payments. The covenant protects lenders by limiting the amount of cash that may be pai d to equity holders. Limitations on liens. The covenant limits the amount of secured debt that a borrower canincreases carry. Unsecured debtamount holdersavailable prefer theto issuer toin have less secured debt, which the recovery them the event ofasdefault. Restricted versus unrestricted subsidiaries. Issuers can classifY subsidiaries restricted unrestricted. Restricted subsidiaries' cashThisflobenefi ws andts assets canofbeholding used tocompanies service orthebecause debt oftheirthedebt parent holding company. creditors is pari passu with thesubsidiaries debt of restri ctypically ted subsidiaries, rather than structurally subordinated. Restricted are the holding company' s larger subsidiaries thatof subsidi have signifi cant assets.status. Tax andA subsidiary' regulatorys issues can factor into the classifi c ation a ry' s restriction restriction status is found in the bond indenture. Bank covenants are often more restri c ti v e than bond covenants, and when covenants are violated, banks canbanksblockcanadditional loans until the eviolation If a violation is not remedied, trigger a default by accel rating theis fullcorrected. repayment of a loan. In terms ofinvestment the factorsgrade that affect their return,ty. Compared high yield bonds may be grade viewedbonds, as a hybri d of bonds and equi to investment high yi e ld bonds show greater price and spread volatil i ty and are more highly correlated with the equity market. Hisuchghasyielenterprise d analysisvalcanue.inEnterprise clude somevalue of the(EV)sameis equity techniques as equity market analysi s , market capitali zationtraded, plus total debt minus excess cash. For high yi e ld companies that are not publicly comparable public company equity data can be used to estimate EV. Enterprise val u e analysis that can imight ndicateresula firtm'from s potential for additional leverage, orcanthecompare potentialfirmscredibased t damage a leveraged buyout. An anal y st ona wider the didifffference erences between their EV/EBITDA and debt/EBITDA ratios. Firms wi t h therefore have less between credit risthese k. ratios have greater equity relative to their debt and •

Sovereign Debt

Sovereign debt is issued by national governments. Sovereign credi t analysis must assess both government' s abilitbecause y to service debt andusuall its willingness tolegaldo recourse so. The assessment ofnational wilthelingness i s important bondholders y have no if a government refuses to pay its debts. Afivbasic areas: for evaluating and assigning a credit rating to sovereign debt includes e keyframework 1. and Institutional effectiveness includes successful policymaking, absence of corruption, commitment to honor debts. 2. size Economic prospectsrelative includetogrowth demographics, income per capita, and of government the privtrends, ate economy. ©20 1 2 Kaplan, Inc.

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59

-

Fundamentals o f Credit Analysis

International includes ithen international country's foreign external debt, investment and the statusposition of its currency markets.reserves, its Fiscal flexibility includesturesthetogovernment' s servi willicne,gnessas wellandasability toinindebt creaseas a revenue or cut expendi ensure debt trends percentage of GDP. Monetaryobjflexibility includes thebeabillacking ity to with use monetary policy for domestic 5. economic e ctives (thi s mi g ht exchange rate targeting or membership in a monetary union) and the credibility and effectiveness of monetary policy. Credirating t ratingandagencies assigngn currency each national government twongsratings: (1) a localseparatel currency debt (2) a forei debt rati n g. The rati are assigned y because defaults on forei g n currency denominated debt have historically exceeded those currencyratingdebt.because Foreigthen currency debtmust typicpurchase ally has aforeign higher default ratein and aonopen lolocal wermarket credit government currency theof to make i n terest and principal payments, whi c h exposes it to the risk signifi currencydomestic depreciation. In contrast, localprinting currencymore debtmoney. can be Rati repaindgsby raicansingdifcferanttaxes,aslocalmuch controlling spending, or simply as two notches for local and foreign currency bonds. Sovereign defaults can be caused by events suchin theas war,pricespolitical icountry' nstability,s export severe devaluation of the currency, or large declines of the commodities. Access to debt markets can be difficult for sovereigns in bad economic times.

3. 4.

Municipal Debt

Municipal bonds are issued by state and local governments or their agencies. Municipal bonds usually have lower default rates than corporate bonds with same credit ratings. Most muni c ipal bonds can be classified as or (GO) entity, bonds whi are cunsecured by thebyfullitsfaitaxing th credit theGeneral issuingobligation governmental h is to saybonds they arebacked supported power.of Unlikey soverei gns, municipalities cannot use monetary policy to serviceability their debt and usuall must balance their operating budgets. Municipal governments' to service their general obligation debt depends ultimatel y on the local economy (i. e . , the tax base). Economic factors todimensions assess include employment, trends in perdemographics, capita income andand perabilitycapita debt, tax base (depth, breadth and stability), to attract new jobs (location, i n frastructure). Credit anal y sts must also observe revenuetovariability through economic cycles. Relns yandingsaloneshitaxes, ghly vari asignal ble taxeshigthat are subject economic cycles, such as capi t al gai can her credit risk. Municipalitiesbenefits. may have long-termreporting obligations such as underfunded pensionsareandalso post-retirement Inconsistent requirements for municipalities an ISSUe. Revenue c projects. often tohaveservice higherthecredit than GO bonds bonds finance becausespecifi the project is theRevenue sole sourcebondsof funds debt.risk general obligation bonds

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revenue bonds.


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis

Analysis revenueng corporate bonds combines using techniques similar to those forofanalyzi bonds, analysis with analofysistheofproject, the financing of the project. Athekeyratiometric forprojrevenue bondsrevenue is thetodebt service coverage ratio (DSCR),payments which is of the e ct' s net the required interest and principal onservithece bonds. Many revenue bonds incl u de a covenant requiri n g a minimum debt protect thelowerlenders' Lenderscreditworthiness). prefer higher debt service coveragecoverage ratios, asratithiso torepresents defaultinterests. risk (better

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis

'

KEY CONCEPTS

LOS Credit riskorrefers to oftheprincipal. possibilityCredit that ariskborrower fails toofmake therisk, scheduled interest payments return i s composed default which is the probability of default, and losswillseveri ty,thewhiborrower ch is thedefaults. portion ofThetheexpected value oflossa bond orprobability loan a lender or i n vestor lose if is the of default multiplied by the loss severity. Spread the possibilitySpread that aribond loses valcredit ue because itson credit spread wiridskensand relmarket ative riliquidity toskitsis benchmark. s k includes migrati or downgrade risk. LOS Corporate debt isassets rankedandbyhasseniority oroverpriority of claims. Secured debt is a directdebt claim onmay specifi c fi r m priority unsecured debt. Secured or unsecured be further ranked as senior or subordinated. Priority of claims may be summarized as follows: FiSecond rst mortgage or first lien. or subsequent lien. Senior secured debt. debt. Senior subordinated Senior unsecured debt. Subordinated debt. debt. Junior subordinated LOS Issuer credit nratings, corporateapplfamily reflectunsecured a debt issuer' creditworthi ess andortypically y to a ratings, firm's senior debt.s overall Issue credi t ratings, or corporate credit ratings, refl e ct the credit risk of a specifi c debt issue. Notching refers to thecredit practirating ce oftoadjusting an issue creditandrating upward or of a downward from the issuer reflect the seniority other provisions debt issue. LOS Lenders and bond investors should not rely exclusivel y on credit ratings from rating agencies forratithengsfolcanlowingchange reasons: Credit during the credit life ofriska debtaccurately. issue. Rati n g agencies cannot al w ays judge Firms areprices subjectof bonds to riskoften of unforeseen creditcrediratitnratings. gs do not reflect. Market adjust moreeventsrapithat dly than 59 .a

59.b

• • • • • •

59.c

59 .d

• •

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis

59.e of traditional credit analysis are known as the four Cs: Components Capaci t y: The borrower' s ability to make timel y payments on its debt. The value of assets pledged against a debt issue or available to creditors if theCollateral: issuer defaults. Covenants: Provisi o ns of a bond i s sue that protect credi t ors by requi r ing or prohibiting actions by anof anissuer'issuer's management. Character: Assessment past treatment of bondholders. s management, strategy, quality of earnings, and 59.f Credi t analysts use profi t abi l i t y, cash fl o w, and leverage and coverage ratios to assess debt issuers'Proficapacity. tabitypi litycrefers to noperating incomebefore and interest operatingandprofitaxest margin, with operating income all y defi ed as earnings (EBIT). Cash fl o w may be measured as earni n gs before interest, taxes, depreciation, and amortizati oorn (EBITDA); funds from operations (FFO); free cash flow before divi d ends; free cash fl o w after dividends. Leverage ratios include debt-to-capital, debt-to-EBITDA, and FFO-to-debt. Coverage ratios include EBIT-to-interest expense and EBITDA-to-interest expense. 59.gleverage, higher interest coverage, and greater free cash flow imply lower credit Lower risk andinclude a higherincredit ratis totalng fordebta fiitsrm.obligations When calculating leverage ratios,pensions analystsand should a fi r m' such as underfunded off-balance-sheet financing. For a specifdebt, ic debtandissue,highersecured collaimplies teral implies risk compared unsecured seniority lowerlower creditcredit risk compared to lowerto seniority. 59.h bond yields comprise the real risk-free rate, expected inflation rate, credit Corporate spread, maturity liquidity An issue's yield spread to its benchmark includespremium, its crediandt spread and premium. liquidity premium. The l e vel and volatil i ty of yield spreads are affected by the credit and business cycles, the performance of and financial markets as a iwhole, availability oftend capitalto narrow from broker­ dealers, and supply demand for debt s sues. Yield spreads when theinvestor creditdemand cycle isforimprovi n g, the economy i s expanding, and fi n ancial markets andthe new debt issues are strong. Yiel d spreads tend to widen when credit cycle,oftheneweconomy, nanciaorl markets are weakening, the supply debt issuesandisfiheavy broker-dealer capital is andinsuffiin cperiods ient forwhen market making. LOS •

LOS •

LOS

LOS

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59

-

Fundamentals o f Credit Analysis

59.ican use duration and convexity to estimate the impact on return (the Analysts percentage change in bond price) of a change in credit spread. For small spread changes: return impact -duration �spread For larger spread changes: return impact -duration �spread 2_2 convexity (�spread)2 Hiincreases gh 59.yieldjthebonds are more likely to default than investment grade bonds, which importance of estimati ngperformance, loss severity. Analysis ofs corporate high yieldanddebtdebtshould focus on l i qui d i t y, projected fi n ancial the i s suer' structures, and debt covenants. Credit riskityoftosovereign debtforincludes the issuing country' s sability and willingness todebt pay. Abil pay i s greater debt issued i n the country' own currency than for issued a foreign currency. Willingness refers to the possibility that a country refuses to repay iints debts. Analysis ofongeneral obligation municipal debt isandsimilar to analonytaxsis ofrevenues. sovereigAnalysis n debt, of focusing the strength of the local economy its effect municipal revenue bonds is si m i l ar to anal y si s of corporate debt, focusing on the ability of a project to generate sufficient revenue to service the bonds. LOS

:=:;j

:=:;j

x

x

+

LOS

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x


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis

CONCEPT CHECKERS

1. A.Expected lossrisk.can decrease with an increase in a bond's: default B.C. loss severirate. ty. recovery 2. A.Absolofuthete priority of clprinciple. aims in a bankruptcy might be violated because: negotiatemusta dibefferent outcome. B.C. creditors available funds distributed equally among creditors. is ratidescribed as issue a difference between a(n): 3. A."Notching" issuer credit n g and an credi t rating. B.C. company average credit grade rating.credit rating. investmentcredit graderating creditandratianngindustry and a non-investment of thet ratifollngoagencies? wing statements is a limitation of relying on ratings 4. Which from credi A.B. Credit ratingsc riaresksdynami cc. ult to rate. Firm-specifi are diffi C. Credit ratings adjust quickly to changes in bond prices. o analtyy.sis is used to assess a borrower's: 5. A.Raticapaci C.B. character. collateral. 6. A.HigherFFO/debt credit riratio. sk is indicated by a higher: B.C. debt/EBITDA EBITDNinterestratio.expense ratio. Compared tohave othera lower: firms in the same industry, an issuer with a credit rating of 7. AAA should A.B. FFO/debt ratio. operating margin. C. debt/capital ratio. 8. A.Creditthespreads tend to wi d en as: credit cycle improves. B.C. economic conditions broker-dealers becomeworsen. more willing to provide capital. 9. A.Compared to shorter duration bonds, longer duration bonds: lertbid-ask spreads.spreads. arehavelesmal sslesssensicertainty ive toregarding credit B.C. have future creditworthiness. pari passu

best

least likely

most likely

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Page 1 8 1


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59

-

Fundamentals o f Credit Analysis

10. sovereign One key difference between sovereign bonds and municipal bonds is that Issuers: A.B. have can print money. governmental taxingconditions. power. C. are affected by economic

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis

CHALLENGE PROBLEM

Woden, Inc., ibalance s a highsheet yield forbondtheissuer th a credi ng ofBa2/BB. Woden presents the following mostwirecent year t(irati n millions of dollars): Cash

10

Accounts payable

10

Accounts receivable

15

Short-term debt

5

Inventories

...5.2

Current portion of long-term debt

_.2 18

80

Current liabilities

Land

10

Long-term bank loans

30

Property, plant, and equipment, net

85

Secured bonds

10

Current assetS

Goodwill

..22

Unsecured bonds

Non-current assets

120

Total long-term debt

Total assetS

200

Net pension liability Total liabilities Paid-in capital Retained earnings Total shareholders' equity Total liabilities and equity

_.1.Q

60

_n 100 10 _..2.Q

100

200

For the year,were Woden' earnings before interest, taxes, depreciation, and amortization (EBITDA) $45smillion. For fi r ms i n Woden' s i n dustry, credit rating standards for an investment grade (Baa3/ BBB-)(based creditonrating includeofafinanci debt-to-EBITDA ratio lessOnthan 1.8x and cala debt-to-capital ratio all sources n g) less than 40%. a conference l wiinvestment th analysts, Woden' s management states that they believe Woden shoul d be upgraded to grade, based on its debt-to-EBITDA ratio of l.Sx and its debt-to-capital ratio of 34%. Why might a credit analyst disagree with management's assessment?

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Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59

-

Fundamentals o f Credit Analysis

ANSWERS - CONCEPT CHECKERS

Page 184

1.

C

An increase in the recovery rate means that the loss severity has decreased, which decreases expected loss.

2.

B

A negotiated bankruptcy settlement does not always follow the absolute priority of claims.

3.

A

Notching refers to the credit rating agency practice of distinguishing between the credit rating of an issuer (generally for its senior unsecured debt) and the credit rating of particular debt issues from that issuer, which may differ from the issuer rating because of provisions such as seniority.

4.

c

Bond prices and credit spreads change much faster than credit ratings.

5.

A

Ratio analysis is used to assess a corporate borrower's capacity to repay its debt obligations on time.

6.

B

A higher debt/EBITDA ratio is sign of higher leverage and higher credit risk. Higher FFO/debt and EBITDA/interest expense ratios indicate lower credit risk.

7.

c

A low debt/capital ratio is an indicator of low leverage. An issuer rated AAA is likely to have a high operating margin and a high FFO/debt ratio compared to its industry group.

8.

B

Credit spreads widen as economic conditions worsen. Spreads narrow as the credit cycle improves and as broker-dealers provide more capital to bond markets.

9.

c

Longer duration bonds usually have longer maturities and carry more uncertainty of future creditworthiness.

10. A

Sovereign entities can print money to repay debt, while municipal borrowers cannot. Both sovereign and municipal entities have taxing powers, and both are affected by economic conditions.

Š2012 Kaplan, Inc.


Study Session 1 6 Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis

ANSWERS - CHALLENGE PROBLEM The debt ratios calculated by management are based on the firm's short-term and long-term debt: Total debt

=

5

+

Debt/EBITDA Debt/capital

=

3

=

+

30

+

68 I 45

6 8 I 200

10 =

=

+

20

68

=

1.5x

34o/o

A credit analyst, however, should add Woden's net pension liability to its total debt: Debt + net pension liability Adjusted debt/EBITDA Adjusted debt/capital

=

=

=

68

+

90 I 45

90 I 200

22

=

=

=

90

2.0x

45o/o

Additionally, a credit analyst may calculate what the debt-to-capital ratio would be ifWoden wrote down the value of its balance sheet goodwill and reduced retained earnings by the same amount: Adjusted capital

=

200 - 25

=

175

Adjusted debt I adjusted capital

=

9 0 I 175

=

5 1 o/o

These adjustments suggest Woden does not meet the requirements for an investment grade credit rating.

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SELF-TEST : FIXED INCOME INVESTMENTS

14 questions, 21 minutes

1. Anin itestimate of the price change for an option-free bond caused by a 1% decline s yieldthat:to maturity based only on its modified duration will result in an answer A.B. iiss too small. C. maytoobelarge. too small or too large. 2. Three companies the same industry have exhibited the following average ratios over a 5-yearinperiod: 5-Year Averages

Alden

Barrow

Collison

Operating margin

1 3 .3%

1 5.0%

20.7%

Debt!EBITDA

4.6x

0.9x

2.8x

EBIT/Interest

3.6x

8.9x

5.7 x

FFO/Debt

12.5%

14.6%

1 1 .5 %

Debt/Capital

60.8%

23.6%

29.6%

Based onlycrediont ratitheninformation given, the company that is expected to have the highest g is: A.B. Alden. Barrow. C. Collison. 3. Which statement about the theories of the term structure of interest rates is A. sloped. Under the liquidity preference theory, the yield curve will be positively B. Amarket yield segmentation curve that slopestheoryup and then down (humped) is consistenttheory. with the but not wi t h the pure expectations C. bonds Evidencesupports that lifthee insurance companies havetheory. a strong preference for 30-year market segmentation 4. Which of the following is a common form of external credit enhancement? A.B. APortfolio insurance. corporate guarantee. C. A letter of credit from a bank. bond wiofth6anandembedded put option has a modifi e d duration of 7, an effecti v e 5. Aduration a convexity of 62. 5 . If interest rates rise 25 basis points, the bond' s price wi l change by A.B. 1.1.50%. 46%. 1.54%.

most

accurate?

least likely

approximately:

c.

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Self-Test: Fixed Income Investments

of thebyfoll50obasis wing points bonds would be the best one to own if the yield curve 6. Which shifts down at all maturities? A.B. 4-year 8%, 8% YTM. C. 5-year 5-year 8%, 8.5%,7.58%% YTM. YTM. ofy onthea folldebtowisecurity? ng provisions would decrease the yield to 7. Which maturi t A.B. Conversion Call option. option. C. Cap on a floating-rate security. 8. theOtherbondthingsis rated: equal, a corporate bond's yield spread is likely to be volatile if A.B. AAA AA withwith5 3years totomaturity. years C. BBB with 15 years tomaturity. maturity. 9. The effects ofwith a decrease in interestoption rate (yiandeld)onvolatility on thewith marketa putyieoption ld of a debt security a prepayment a debt security are Prepaymenta(n):option Put option Decrease A.B. Decrease Increase Increase Decrease C. Decrease A has an embedded option, a nominal yi e ld spread to Treasuries of 1.6%, 10. Bond aB zero-volatil ityto spread ofexcept 1.4%,that anditandoesoption-adjusted spread of 1.2%. Bondhas a is identical Bond A not have the embedded option, nomioption-adjusted nal yield spreadspread to Treasuries ofThe1.4%, a zero-volatility spread ofin1.3Bond %, andA, anand of 1. 3 %. option embedded the bond thatoption is the better valBetter ue, are:value Embedded A.B. Put Bond A Bond Call C. Call Bond AB most likely

most

most likely

most likely

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Page 187


Self-Test: Fixed Income Investments

11. Atobank loantwodepartment is tryi ngIftocurrent determiimplied ne the Treasury correct rateeffectiforvae2-year loan be made years from now. annual spot rates are: 1-year = 2%, 2-year = 3%, 3-year = 3.5%, 4-year = 4. 5 %, the base forward rate for the loan before adding a risk premium is to: A.B.(risk-free) 4.5%. 6.9.00%.%. to mortgage passthrough securities, CMOs created from them 12. Compared have: A.B. greater less prepayment ri s k. C. a differentaverage claimyields. to the mortgage cash flows. 13. A.Thecanarbitrage-free approach to bondsecurities. valuation only be applied to Treasury B.C. requires each cash fl o w to be discounted at a rate specifi c to its time period. that value discounting each cash flow at the yield to maturity must result in theshowscorrect for a bond. 14. Which of thewithfollinvesting owing statements describes a form of risk associated in fi x ed income securities? A.B. Credit risk hasequal, only atwobondcomponents, defaulttoriansk and downgrade risk. Other things is more valuable i n vestor when it has less liquidi t y risk. C. riBonds are callable, amortizing more reinvestment sk thanthatotherwise equivprepayabl alent bondse, orwithout thesehave features. closest

c.

most

likely

most likely:

least accurately

Page 1 8 8

Š2012 Kaplan, Inc.


Self-Test: Fixed Income Investments

SELF-TEST ANSWERS: FIXED INCOME INVESTMENTS

1.

A

Duration is a linear measure, but the relationship between bond price and yield for an option-free bond is convex. For a given decrease in yield, the estimated price increase using duration alone will be smaller than the actual price increase.

2.

B

Four of the five credit metrics given indicate that Barrow should have the highest credit rating of these three companies. Barrow has higher interest coverage and lower leverage than Alden or Collison.

3.

C

The market segmentation theory is based on the idea that different market participants (both borrowers and lenders) have strong preferences for different segments of the yield curve. If expectations are that future short-term interest rates will be falling enough, then the yield curve could be downward sloping even given rhar there is an increasing premium for lack of liquidity at longer maturities. A humped yield curve is consistent with expectations that short-term rates will rise over the near term and then decline.

4.

A

External credit enhancements are financial guarantees from third parties that generally support the performance of the bond. Portfolio insurance is not a third party guarantee.

5.

A

Effective duration must be used with bonds that have embedded options. �p

=

(-) (ED)(�y)

+

.6.P (-) (6)(0.0025) -1.461% =

(C)(�y) 2 +

(62.5)(0.0025) 2

=

-0 . 0 1 5

+

0.00039

=

-0.014610% or

6.

B

The bond with the highest duration will benefit the most from a decrease in rates. The lower the coupon, lower the yield to maturity, and longer the time to maturity, the higher will be the duration.

7.

B

A conversion provision is an embedded option that favors the buyer, not the issuer, so buyers will accept a lower YTM with a conversion option. Call options and caps favor the issuer and increase the YTM that buyers will require.

8.

C

Spread volatility is typically greatest for lower quality and longer maturities. The BBB rated 15 -year corporate bond has the lowest credit quality and longest maturity of the three choices.

9.

B

A decrease in yield volatility will decrease the values of embedded options. The security holder is short the prepayment option. The decrease in the value of the prepayment option increases the value of the security, and the required yield will decrease. The security holder is long the pur option so the value of a putable bond will decrease with a decrease in yield volatility and the required yield will increase.

10. C

Since the OAS is less than the Z-spread for Bond A, the effect of the embedded option is to increase the required yield, so it must be a call option and not a put option. The OAS is the spread after taking out the effect of the embedded option. Since the OAS is higher for Bond B, it represents the better value after adjusting for the value of the call in Bond A.

©20 1 2 Kaplan, Inc.

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Self-Test: Fixed Income Investments 11. B

The forward rate is [ 1 .045 4 I 1 .03 2] 112 - 1 [4.5(4) - 3(2)]/2 6.

=

6.02%, or use the approximation

=

Page 190

12. C

CMOs are created to have different claims to the cash flows (principal, scheduled repayments, prepayments) than those of the underlying mortgage passthrough securities. On average, the yield will likely be lower on the CMO, since the reason to create them is to lower overall funding costs. They can have more or less prepayment risk, but on average will have the same prepayment risk as the underlying MBS.

13. B

The arbitrage-free valuation approach discounts each cash flow at a discount rate specific to its maturity. For Treasury securities these discount rates are theoretical Treasury spot rates. For non-Treasury securities, these discount rates are Treasury spot rates plus a spread to account for liquidity risk, credit risk, and any other relevant risks that differ from those of a Treasury bond of similar maturity.

14. A

Even if a bond does not default and is not downgraded, it still faces credit spread risk as the premium in the market for the bond's credit risk may increase. Lower liquidity risk (i.e., higher liquidity) is preferred by investors, reduces a bond's required rate of return, and increases its value, other things equal. Reinvestment risk is higher for callable, prepayable, or amortizing bonds as all these features lead to a greater probability of receiving principal repayment earlier, which means there are more funds to be reinvested over the life of the bond.

Š2012 Kaplan, Inc.


The following is a review of the Derivatives principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in:

DERIVATIVE MARKETS AND INSTRUMENTS Study Session 1 7

EXAM FOCUS

This topic revieDerivatives-specifi w contains introductory material forterminology the upcomingarerevipresented ews ofspecifi c types ofinformation derivatives. c defi n itions and al o ng wi t h vativesconcepts markets.thatUponunderlie completion ofvthies sandreviethew, candidates should beframework. familiar There wiabout th theideri basic derivati general arbi tragethe s li t tle contained i n thi s revi e w that wil l not be elaborated upon i n five reviews that follow. LOS 60.a: Define a derivative and distinguish between exchange-traded and over-the-counter derivatives. CFAÂŽ Program Curriculum, Volume 6, page 5

derivative is a security that its value from the value or return of another asset or security. physical exchangederivatives exists foraremanystandardi optionszedcontracts contracts. Exchange-traded and backedandbyfutures a clearinghouse. and are custom instruments and are traded/created by deal e rs in a market with no central location. dealeraremarket with no centralmarkets locationandiseach referred to as isanwith over-the-counter market. They l a rgel y unregulated contract acounterparty counterparty,doeswhinotch may owner of a derivative to default risk (when the honorexpose their thecommitment). Some trade in the over-the-counter market, notably bond options. A

derives

A

Forwards

swaps

A

options

LOS 60.b: Contrast forward commitments and contingent claims. CFAÂŽ Program Curriculum, Volume 6, page 6

forwardForward commitment is a legallinclude y binding promise to perform some actionandin theswaps. future. commitments forward contracts, futures contracts, Forward contracts and futures contracts can be wri t ten on equities, indexes, bonds, physical assets, or interest rates. contingent claim i s a clai m (to a payoff) that depends on a particular event. Options arefutures, contingent claimshavethatpayments depend that on aarestockmadepricebasedat some le forwards, and swaps on a future price ordate.rateWhi outcome

A

A

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #60

-

Derivative Markets and Instruments

whether the movement isbroken up or down, contingent claims onlyorrequi rratee a payment if a It certain threshol d pri c e is (e. g . , i f the price is above the i s below takes two options to replicate a future or forward. Y).

X

LOS 60.c: Define forward contracts, futures contracts, options {calls and puts), and swaps and compare their basic characteristics. CFA® Program Curriculum, Volume 6, page 6

Inasseta or a security at a specifi one party agrees to buy, and the counterparty to sell, a physical date inhastheafuture. the asset increases, the buyerc(atpricetheonolder,a specilowerfic price) gain, andIf thethefuture seller aprice loss.of Amain differences wiisthaforwards forward contract that is standardized and exchange-traded. The are that futures are traded i n an active secondary market, arelosses.regulated, backed by the clearinghouse, and require a daily settlement of gains and Ashort-termis a (flseries of forward contracts. In the simplest swap, one party agrees to pay the oating) rate(fixofed)interest oninterest some iprincipal amount, and the counterparty agrees to pay a certain rate of n return. Swaps of different currencies and equity returns are also common. Anthe option tohasbuyan an asset attoa particular priceat isthetermed a call price, iThe sellcallerbuyer of option sell the asset agreed-upon f the chooses to exercise the right to buy the asset. Anoptionoptionhas toansell an assettoatpurchase a particularthe price is termed a price,Theif thesellerputofbuyer the asset at the agreed-upon chooses to exercise the right to sell the asset. forward contract,

futures contract

swap

option.

obligation

put option.

obligation

Professor's Note: To remember these terms, note that the owner ofa call can "call the asset in" (i. e., buy it); the owner of a put has the right to "put the asset to" the writer of the put.

LOS 60.d: Describe purposes of and controversies related to derivative markets. CFA® Program Curriculum, Volume 6, page 17

The is that they are "too riBecause sky," especially to investors winvolth vlimied inted knowl e dge of someti m es complex instruments. of the high l e verage i derivatives payoffs, they are sometimes likened to gambling. The markets are that they: Provide price information. AlReduce low ritransactions sk to be managed costs.and shifted among market participants. criticism ofderivatives

benefits ofderivatives

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©2012 Kaplan, Inc.


Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #60 - Derivative Markets and Instruments

LOS 60.e: Explain arbitrage and the role it plays in determining prices and promoting market efficiency. CFAÂŽ Program Curriculum, Volume 6, page 20

Arbitrage is an important concept i n val u ing (pricing) deri v ati v e securities. In its purest sense, arbia portfolio trage is riskless. Ifthat a return greatera certain than the(riskl risk-free rate canthenbe anearned byrage holding of assets produces e ss) return, arbi t opportunity exists. Arbitrage opportunities arisesupply whenandassetsdemand are mispriced. Tradi ngasset by arbitrageurs willcient continue until they affect enough to bring prices to effi (no-arbitrage) levels. There are two arbitrage arguments that are particularly useful i n the study and use of derivatives. The fiflrostwsisinbased on the regardless law of futureTwoevents, securishould ties orhave portfolios thatprice. have identical cash the future, the same IfB.AYouand Bhavehaveantheimmediate identicalprofit, futureandpayoffs, and A is priced l o wer than B, buy A and sel l the payoff on A will satisfy the (future) liability of being short on B. The secondintypea portfolio of arbitrage is lused where two securities wia portfolio th uncertainconsisting returnsofcanA beand combined that wi l have a certain payoff. If Bcondition has a certain payoff,inthethatportfol io shouldreturnyieldoftheA andrisk-free rate. Ifis this no-arbitrage is violated the certain B together higher than the ririssk-free rate, anbuyarbithetrage opportunity exists.earnAnarbiarbitrageur couldwhenborrow at the payoff k-free rate, A B portfolio, and t rage profits the certain occurs. The payoff wi l l be more than i s requi r ed to pay back the l o an at the risk-free rate. of one price.

+

Professor's Note: We will discuss arbitrage further in our review of options.

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Page 193


Study Session 17 Cross-Reference to CFA Institute Assigned Reading #60

-

Derivative Markets and Instruments

KEY CONCEPTS

LOS 60.a A derivative has a value that is derived from the value of another asset or interest rate. Exchange-traded derivatives, notably futures and some options, are traded i n centralized locations and are standardized, regulated, and default risk free. Forwards and swaps are customized contracts (over-the-counter deri v ati v es) created by dealers andmarkets by financial institutions. There is very of these contracts in secondary and default (counterparty) risk limited must betrading considered. LOSforward 60.b commitment is a binding promise to buy or sell an asset or make a Apayment i n the future. Forward contracts, futures contracts, and swaps are al l forward commitments. A(e.contingent claim is an asset that has value only i f some future event takes pl a ce g., asset price is greater than a specified price). Options are contingent claims. LOS 60.ccontracts obligate one party to buy, and another to sell, a specific asset at a Forward predetermined price at a specific time in the future. Swaps contracts are equivalent currencies, or equity returns. to a series of forward contracts on interest rates, Futuresrequire contracts are much likeof anyforward and daily settlement gainscontracts, or losses. but are exchange-traded, quite liquid, Apredetermined call option giprice ves theatholder not the obligation, to buy an asset at a some titheme right, in thebutfuture. Apredetermined put option giprice ves theatholder not the obligation, to sell an asset at a some titheme right, in thebutfuture. LOS 60.d markets are criticized for their risky nature. However, many market Derivative participants use derivatives to manage and reduce existing risk exposures. Derivative securities play an important role i n promoting effi c ient market prices and reducing transaction costs. LOS 60.ss arbi e trage refers to earning more than the risk-free rate of return with no risk, or Riskl e earning an immediate gain with no possible future liability. Arbi be expected forcefuture the prices securitiesoforfuture portfolios to betrage equalcanif they have thetosame cash flofowstworegardless events.of securities Page 194

Š2012 Kaplan, Inc.


Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #60 - Derivative Markets and Instruments

CoNCEPT CHECKERS

1. AWhich of the foll o wi n g describes a deri v ati v e security? A.B.derihasalwvatiaysnove:increases risdate. k. expi r ati o n C. has a payoff based on another asset. 2. Which of the following statements about exchange-traded derivatives is A.B. They are liquid. They arecarrystandardi contracts.risk. C. They significzanted default 3. A customized agreement to purchase a certain T-bond next Thursday for $1,000 A.B. ana futures option.contract. C. a forward commitment. is: regulated. 4. AA.swap highly of forward B.C. thea series exchange of onecontracts. asset for another. givselles theat aholder: 5. A.A calltheoption right to speci f i c price. right to buyto atsella atspecific C.B. antheobligation a certaiprice. n price. 6. Arbitrage prevents: A.B. market effi c iency. higherwitthan the risk-free return. at different prices. C. profit two assets h identical payoffsratefromof selling are to provide or improve: 7. A.Derivatives liquidi t y. B.C. price information. inflation reduction. most accurately

least

accurate?

lS:

least likely

Š20 12 Kaplan, Inc.

Page 195


Study Session 17 Cross-Reference to CFA Institute Assigned Reading #60

-

Derivative Markets and Instruments

ANSWERS - CoNCEPT CHECKERS

Page 196

1.

C

A derivative's value is derived from another asset.

2.

C

Exchange-traded derivatives have relatively low default risk because the clearinghouse stands between the counterparties involved in most contracts.

3.

C

This non-standardized type of contract is a forward commitment.

4.

B

A swap is an agreement to buy or sell an underlying asset periodically over the life of the swap contract. It is equivalent to a series of forward contracts.

5.

B

A call gives the owner the right to call an asset away (buy it) from the seller.

6.

C

Arbitrage forces two assets with the same expected future value to sell for the same current price. If this were not the case, you could simultaneously buy the cheaper asset and sell the more expensive one for a guaranteed riskless profit.

7.

C

Inflation is a monetary phenomenon, unaffected by derivatives.

Š2012 Kaplan, Inc.


The following is a review of the Derivatives principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in:

FORWARD MARKETS AND CONTRACTS Study Session 1 7

EXAM FOCUS

This topic revi e w introduces forward contracts in general and covers the characteristi c s ofmaterial forward, andcontracts ondvarious fintime ancialto securities, as This well asmaterial interestonrates. It iscontracts not easy you shoul take the l e arn i t well. forward provides a good basis for futures contracts and many of the characteristics of both types the same. Take the time to understand the intuition behind the valuation ofof contracts forward rateare agreements. FO RWARD CONTRACTS

Ato forward contract i s a bil a teral contract that obl i gates one party to buy and the other sell aly,specifi c quantity oftheancontract asset, at pays a set anything price, on toa specific datethe contract. in the future. Typical neither party to get into If theto buy expected future price of the asset i n creases over the life of the contract, the ri g ht atnegati thevcontract price will have positi v e value, and the obli g ation to sel l wil l have an equal e value. Ifthetherigfuture price(atofantheabove-market asset falls below thewillcontract price,positive the result iThe s opposite and ht to sell pri c e) have the value. parties may enter i n to the contract as a speculation on the future price. More often, a party seeks to enter into a forward contract tothehedgefuturea riprice sk it already has. itTheplansforward contract i s used to el i minate uncertainty about of an asset to buy orhavesellexisted at a laterfor date. Forward contracts on physical assets, such as agricultural products, The Level however,andfocuses their (more recent) use for ficenturies. nancial assets, such asI CPA T-bills,curriculum, bonds, equities, foreignoncurrencies. LOS 61 .a: Explain delivery/settlement and default risk for both long and short positions in a forward contract. CFAÂŽ Program Curriculum, Volume 6, page 28

The to theposition forwardandcontract that agrees toThebuyparty the financial or physical assetthathas aagrees longparty forward i s cal l e d the to the forward contract to sell or deliver the asset has a short forward position and is called the We illustrateandthesalemechani cs of the bill. basicNote forward contract throughandanfutures examplecontracts based onon T-bi thewillpurchase of a Treasury that whi l e forward usuallto make y quotedthe inexampl termse ofeasya discount percentage fromconventions face value, weandwill usecalculations dollarlls areprices to fol l ow. Actual pricing are among the contract characteristics covered later in this review. long.

short.

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts

Considerbilla contract underB 30whichdaysParty Anowagreesat atoprice buy ofa $1,$990. 000 Party face value, 90-day Treasury from Party from A is the longwiland Party B is the short. Both parties have removed uncertainty about the price they l pay/recei veshort for themustT-bidelllivaterthethefuture date. Iflong 30 daysin exchange from nowforT-bills arepayment. trading atIf $992, the T-bill to the a $990 T-bills are trading at $988 on the future date, the long must purchase the T-bill from the short for $990, the contract price. Each party to a forward contract i s exposed to default risk (or counterparty risk), the probabil iforty that the other party (the counterparty) wiinception l not perform as promised. It is unusual any cash to actually be exchanged at the of a forward contract, unl i ke futures contracts i n which each party posts an initial deposit (margin) as a guarantee of performance. Atcontract any point in time, including the settl e ment date, only one party to the forward wiofll theowecontract money, meani ng that side ofvaltheuecontract has amount. a negativFole value. Thethe other si d e wi l l have a positive of an equal l o wing example, i f the T-bill price i s $992 at the (future) settlement date and the short does not deliver the T-bill for $990 as promised, the short has defaulted. LOS 61.b: Describe the procedures for settling a forward contract at expiration, and how termination prior to expiration can affect credit risk. CPAÂŽ Program Curriculum, Volume 6, page 29

The previous example was for a deliverable forward contract. The short contracted to deliver the actual instrument, in this case a $1,000 face value, 90-day T-bill. Thi is one eprocedure for settling a forward contract at the or expiration dates specifi d in the contract. Anhas alternati ve wisettlement method iiss cash settlement. Underamount this method, the party that a position t h negati v e value obligated to pay that to the other party. Inshortthewould previoussatisfyexampl e , i f the pri c e of the T-hill were $992 on the expi r ation date, the thesame contractresultbyaspaying $2 tovery.theIflotheng. short Ignoring transactions costs, this method yi e lds the asset deli had the T-hill, i t could besubtracting sold in thethemarket for $992. The short' s net proceeds, however, woul d be $990 after $2 payment to the long. If the T-hi l l price at the settlement date were $988,ce ofthe$988, longtogether would make athi$2s payment to thewould short.makePurchasing aT-bill at thejustmarket priwould with $2 payment, the total cost $990, as it be if it were a deliverable contract. Onpricetheofexpiration (orabovesettlement) date of the(forward) contract,price; the long receivesreceiavpayment if the the asset is the agreed-upon the short es a payment if the price of the asset is below the contract price. settlement date

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts

Terminating a Position Prior to Expiration

Aintopartyan opposite to a forward contract can with an expiration dateprior totoexpithertime ationremai by entering forward contract equal ning on the original contract. Recall our theexample andforward assumeprice thatoftena days afterfaceinception (it wasT-hil originally a 30-day contract), 20-day $1, 0 00 value, 90-day l i s $992. The short,contract. expectinSigncethethepriceshortto beis obli evengated higherto sellby thethedeliT-hillvery20date, wishes tofuture, termihenatecan the days i n the effecti exit the(a long contract by enteri into a new (20-day) identicalvelyT-hill position) at thengcurrent forward priceforward of $992.contract to buy an The position of the original short now is two-fold, an obligation to sell a T-hill in 20 days forin $990 (under the original contract) anda $2anloss,obligati on toeffecti purchase antedidentical T-hill 20 days for $992. He has locked i n but has v ely exi theof the contract since the amount owed at settlement i s $2, regardless of the market price T-hill at the settlement date. No matter what the pri c e of a 90-day T-hill is 20 days from now, $990.he has the contractual right and obligation to buy one at $992 and to sell one at However,contract, if the short' s new forwardremains. contractIfisthewitprice h a different partyl atthanthe theexpiration first forward some of the T-hil date i s above $992, and the counterparty to the second forward contract fai l s to perform, the short's losses could exceed $2. alternative is toThisenterwould into avoi the dsecond (offsetti ng)thecontract with themakesamea $2partypayment as the original contract. credit ri s k since short could to theorigcounterparty at contract expiration, thetheamount ofposition his netinexposure. In fact, if the i n al counterparty were wil l i n g to take short the second (20-day) at theunti$992 price, a payment of the present valuevalentof thetransaction. $2 (discounted fornal thecontract 20 days l the settlement date) would be an equi The origi counterparty would be wi l l i ng to allow termi n ati o n of the ori g i n al contract for an immediate payment of that amount. Ifto theexitoriginal counterparty requi r es a payment larger than the present value of $2 thethecontract, thesk heshortbearsmustby enteri weightngthisintoadditional cost tocontract exit thewithcontract agai n st defaul t ri the off s etting a different counterparty at a forward price of $992. terminate the position

credit risk

An

LOS 61 .c: Distinguish between a dealer and an end user of a forward contract. CPAÂŽ Program Curriculum, Volume 6, page 30

The is ritypical ly wish a corporation, government unit, or nonprofit institution that has existing s k they to avoid by l o cking i n the future price of an asset. A U.S. corporation that has an obligation to make a payment i n Euros 60 days from now can eliminate its exchange rate risk by entering into a forward end user of a forward contract

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts

contract towithpurchase the required payment a settlement date 60amount days inoftheEuros future.for a certain dollar-denominated Dealers areIdealoften banks,wilbutl balance can alsotheibe rnonbank financial institutions suchoverall as securities brokers. l y , dealers overall long positions with their short positions by entering forward contracts with enda buying users whopricehave(atopposite exiswiltingl risk exposures. A deal e r' s quote desk wi l l quote which they assume a long position) and a slspread ightlybetween higher selthelingtwopriceis the(atdeal whiecr'hs they will assume aforshort position). The bid/ask compensation administrative costs aspositions. well as bearing default risenter k andinto any contracts asset pricewiriskth other from unbalanced (unhedged) Dealers wil l also dealers to hedge a net long or net short position. LOS 61 .d: Describe the characteristics of equity forward contracts and forward contracts on zero-coupon and coupon bonds. CPAÂŽ Program Curriculum, Volume 6, page 32

Equity forward contracts wherein themuchunderlying asset is a assingle stock, a portfolio of An stocks, or a stock index, work the same manner other forward contracts. itonvestor who wishes to sellabout10,0the00 stock sharesprice of IBMon that stockdate, 90 days fromdo sonowbyandtakiwishes avoid the uncertainty could ngthea short position i n a forward contract coveri n g 10, 0 00 IBM shares. ( W e wil l leave motivation for this and the pricing of such a contract aside for now.) A10,deal000ershares might90quote a price of $100 per share, agreei n g to pay $1 mil l i o n for the daysstock fromselnow.ler hasThelocked contractin themayselling be deliprice verablofe orthesettled inandcashwilas described above. The shares getactualnolymore i f the pri c e (i n 90 days) i s actually hi g her, and wi l l get no l e ss if the price lower. Acanportfoli o manager who wi s hes to sel l a portfolio of several stocks 60 days from now similofaeach rly request a quote, giviniog. The the dealer the companybetween namesthiands typetheofnumber of shares stock in the portfol only difference forward contract and several forward contracts each covering a si n gle stock, i s that the pricing would be better higherbetotal the portfoli o because origination costs(awould less forprice)theforportfol io forward contract.overall administration/ Anotiforward contractandonwila stock except that thecontract. contract will be based on a onal amount l veryindex likelyibes similar a cash-settlement

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts

Example: index forward contracts Aportfolio portfolithat o manager desires to generate $10 million 100 days from now from a is quite similarin ain1 00-day composition to contract the S&Pbased 100 index. Sheindexrequests a quote on a short position forward on the wi t h a notional amount of $10 mi l lion and gets a quote of 525. 2 . If the index level at the settlement the contract.date is 535.7 , calculate the amount the manager will pay or receive to settle Answer: The actual index level is 2% the contract price, or: 535.7 I 525.2 1 = 0.02 = 2% the short party, the portfoli o manager must pay 2% of the $10 million notional amount, $200,000, to the long. Alternati velvye, ifa payment the indexfwere 1 o/olong belowofthe$100,contract level,ch would the portfoli o manageroffset woul d recei r om the 0 00, whi approximately any decrease in the portfolio value. Equity

above

-

As

Divi d ends are usual l y not included i n equity forward contracts, as the uncertai n ty about divi dendprices. amounts andforward paymentcontracts dates isaresmalcustom l compared to the theuncertainty aboutspecify future equity Since instruments, parties could aeffecti totalvreturn valuedi(including dividends)asrather ely remove vidend uncertainty well. than simply the index value. This would Forward Contracts on Zero-Coupon and Coupon Bonds

Forward contracts onngshort-term, zero-coupon bonds (T-bills in the However, United States) and coupon i n terest-payi bonds are quite similar to those on equities. whil e equities do not have a maturity date, bonds do, and the forward contract must settle before the bond matures. we The notedpercentage earlier, T-bidiscount ll pricesforT-bills are often iquoted as a percentage discountT-bill fromquoted face at value. s annualized so that a 90-day a 4% discount pricedofat(1a-(900.0 1)360)$1,04%00 == $990 1 o/o discount face value. equival ent to a wiprillcebequote per $1,0from 00 offace value.This is

As

I

x

x

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts

Example: Bond forwards Ato forward contract covering a $10 mill i on face val u e ofT-bi l ls that wi l l have 100 days at contract settlement at 1.96 foron athediscount thematurity dollar amount the long must payis priced at settlement T-bills. yield basis. Compute Answer The 1.96% annualized discount must be "unannualized" based on the 100 days to maturity. 0. 0 196 (1 00 I 360) = 0.005444 is the actual discount. The dollar settlement price is (1 - 0.005444) $10 million = $9,945,560. Please fall. noteAthatlong,whenwhomarket interest rates increase, discountswillincrease, andonT-hill prices i s obli g ated to purchase the bonds, have losses the forward and gains on the contract when interest rates fall. Thecontract outcomeswhen for theinterest shortrates wil rise, be opposite. x

x

The specifieasd inofforward contractsdate,onexclusive coupon-bearing bondsinterest. is typical ly stated as a yiis eonldprice tobonds maturity the settlement of accrued If the contract with the possibility of default, there must be provisions in the contract to defi ne defaultmustandalsospecify the obliigfations of thehaveparties in the event ofsuch default.as callSpecial provisions be included the bonds embedded options features conversion features. Forward contracts can be constructed covering individual bonds ororportfoli os of bonds. LOS 61 .e: Describe the characteristics of the Eurodollar time deposit market, and define LIBOR and Euribor. CFAÂŽ Program Curriculum, Volume 6, page 36

Eurodollar deposit is the term for deposits in large banks outside the United States denominated intheU.London S. dollars.Interbank The lending rateRate on dollar-denominated loansas between banks is called Offered (LIBOR). It is quoted anLIBOR is annualized rate based on a 360-day year. In contrast to T-hill discount yields, anas aadd-on certificate loans of deposit. LIBOR is used referencerate,ratelikefora flyield oatingquoterateonU.S.a short-term dollar-denominated worldwide.

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts

Example: LIBOR-based loans

Compute the amount that must be repaid on a $1 million loan for 30 days i f 30-day LIBOR is quoted at 6%. Answer:

The add-onwould interestrepayis $1,calc0ul00,ated000as $1$5,000 million= $1,0.0005,6 000(30at the360)end= $5,of30000.days.The borrower +

x

x

I

isompublia number shed dailofylabyrgethebanks; BritishsomeBanker' sargeAssociation and isbanks compiled from quotes f r are l multinational based in other countries that have London offices. There i s also an equivalent Euro lending rate called Euribor, or Europe Interbank Offered Rate. Euribor, established in Frankfurt, is published by the European Central Bank. The floating rates are forLIBOR various(orperiods and90-day are quoted as such. For example, the termi n ol o gy i s 30-day Euribor), LIBOR, and 180-day LIBOR, depending on the term of the loan. For l o nger-term fl o ating-rate loans, the interest rate is reset periodically based on the then-current LIBOR for the relevant period. LIBOR

LOS 61.f: Describe forward rate agreements (FRAs) and calculate the gain/loss on a FRA. LOS 61 .g: Calculate and interpret the payoff of a FRA and explain each of the component terms of the payoff formula. CFAÂŽ Program Curriculum, Volume 6, page 35

Amoney at a certain rate at some (FRA)future can bedate.viewed as a forward contract to borrow/lend Indate.practice, these contracts settle in cash, but no actual loan i s made at the settlement This means that the creditworthiness ofessentially the partiesriskless to therate,contract need not be considered in the forward interest rate, so an as LIBOR, in the contract. (The parties) to the contract may still besuchexposed to defaulcant ribeskspecifi on theedamount owed at settlement. The ltheongcontract positionprice in anbeing FRA theis theinterest party rate that onwould borrowIfthethemoney (long theat contract loan with the loan). fl o ating rate expiration Euribor)canisbeabove the asratethespecifi etod inborrow the forward agreement, the landongthepositilongo(LIBOR nwiinllthereceiorcontract vi e wed right at below market rates ve a payment. Ife thea cashreference ratefromat thetheexpiration daterightis below the contract rate, the short wil l recei v payment long. (The to lend at rates market rates would have a positive value.) forward rate agreement

higher than

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts

Tocalculcalculate thevaluecashas payment at settlement formaki a forward rateatagreement, weis eineed toabove a te the of the settlement date of n g a loan a rate that t her orperiod, belowthethecashmarket rate. Since the i n terest savings would come at the end of the loan payment atatesettlement of thevalue forwardat theis thesettlement present date valueofofthetheinterest interest savings. We need to cal c ul the discounted savings or excess i n terest at the end of the loan period. An example wi l l il l ustrate the calculation of the payment at expiration and some terminology of FRAs. FRAs Consider an FRA that: res/settl esnotional in 30 days.principal amount of $1 million. IsExpi based on a IsSpecifi basedesona forward 90-day rate LIBOR. of 5o/o. Assume thatthethecashactual 90-daypayment LIBOR 30-days from now (at expiration) is 6o/omakes . Compute settlement at expiration, and identify which party the payment. Example:

• •

Answer:

If6o/othe, thelonginterest couldsaved borrowonata 90-day the contract rate ofloan5o/o,woul ratherd be:than the market rate of $1 million (0.06 - 0.05)(90 360) 1 million = 0.0025 1 million = $2,500 The $2,500 in interest savings would not comevaluntil thetheseendsavings. of the 90-day loan period. The value at settlement is the present u e of The correct discount rate to use is the actual rate at settlement, 6o/o, not the contract rate of 5o/o. The payment at settlement from the short to the long is: 2' 500 1 [(0.06) (90 360)] $2,463.05 Inanddoing the calculation of the settlement payment, remember thatarethe term of the FRA the term of the underlying "loan" need not be the same and interchangeable. Whil the settlement date can berateanyonfuture date, in practicetheitvalue is usually some multiple oftypi30caledays. The specifi c market which we calculate of the contract will l y be similar, 30-day, 60-day, 90-day, or 180-day LIBOR. If we describe an FRA asthea payment 60-day FRA on 90-day LIBOR, settlement or expi r ati o n i s 60 days from now and at settlin (30-day) ement is months, based onand90-daywoulLIBOR 60 days asfroma 2-by-5 now. Such an(orFRA could be quoted d be described FRA 2 5to FRA). The 2 refers to the number of months until contract expiration and the 5 refers the total time until the end of the interest rate period (2 3 = 5). I

+

X

I

x

x

=

not

x

+

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts

The general formula for the payment to the long at settlement is: days ) (floating -forward ) ( { notional principal) [ ( days 1 (floating) 360 where: days number of days in the loan term The factor.numerator is the interest savings in percent, and the denominator is the discount Notespecified that if thein the contract, rate underl ying the agreement turnsisoutnegati to beve below theshort rate the numerator in the formula and the receives a payment from the long. FRAs for non-standard off-the-run FRAs. periods (e.g., a 45-day FRA on 132-day LIBOR) are termed +

T

=

floating

forward

LOS 61 .h: Describe the characteristics of currency forward contracts. CFAÂŽ Program Curriculum, Volume 6, page 38

Under theofterms of a for a certain amount of another one partycurrency agrees toat aexchange a certain amount one currency future date. This type of forward contract in practice wi l l specify an exchange rate at whi c h one party can10 millbuyiona fiEuros xed amount of. dolthelarscurrency underlying the contract. Ifrecei we vneed to exchange for U. S 60 days in the future, we mi g ht e a quote of5 USD0. 9 5. The forward contract specifi e s that we (the l o ng) wi l l purchase USD9. million for EURI 0 mi l lion at settlement. Currency forward contracts can be del i v erable oramount settlednecessary in cash. Asto compensate with other forward contracts, the becashdisadvantaged settlement amount is the the party who would by the actual change in market rates as of the settlement date. An example will illustrate this. currency forward contract,

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts

Example: Currency forwards Gemco expects to recei v e EUR50 million three months from now and enters i n to a casheuro. settlement currencyexchange forwardrateto exchange thesepereuroseuroforat U.S. dollarswhat at USD1. 23 per If the market is USD 1.25 settlement, is the amount of the payment to be received or paid by Gemco? Answer: Under the terms of the contract Gemco would receive: USD 1.23 = USD61.5 million EUR50 million EUR Without the forward contract, Gemco would receive: USD 1.25 = USD62.5 million EUR50 million EUR The counterparty would beamount disadvantaged bythetheadvantage differencethatbetween thehavecontract rateto and the market rate i n an equal to would accrued Gemco had they not entered into the currency forward. Gemco must make a payment of USD 1.0 million to the counterparty. A direct calculation of the value of the long (USD) position at settlement is: ( USD 1.23- USD 1.25) EUR50 million= -USDI.O million EUR EUR x

x

x

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts

KEY CONCEPTS

LOS 6 l .a

Aa certai deliverable forward contractdateontoantheassetshort,specifiwhoes that the longa certain (the buyer) will ofpayan n amount at a future wil l deliver amount asset. Default riatsksettlin aement, forwardbecause contracttypical is thely risk that thechanges other party toatthethecontract willofnotthe perform no money hands initiation contract. LOS 6 l .b

Aasset,forward contract with cash settlement does not require del i v ery of the underlying paymentpricate andthe thesettlement based buton thea cashcontract market date pricefrom of theoneassetcounterparty at settlement.to the other, Early termination oftha theforward contract can beat accomplished by entering into a newprice. forward contract wi opposite position, the then-current expected forward This early termination wi l l fi x the amount of the gain or loss at the settlement date. s newriforward is withsiandiceffoneerentofcounterparty than the original, there is creditits orIfoblithidefault s k to consider the two counterparties may fai l to honor gation under the forward contract. LOS 6 l .c

end user of a forward contract is most often a corporation hedging an existing risk. Forward deal ers, large banks,andor thebrokerages origi nothers, ate forward contracts andpricing take theto long side i n some contracts short si d e i n wi t h a spread i n compensate must bear. them for actual costs, bearing default risk, and any unhedged price risk they ty forward contract may betheon riassiknofgleequity stock,prices a customized portfolio, or an equityequi index, and is used to hedge at some future date. Equity forward contracts cany based be wrisolel ttenyonon aantotalindexreturn basis (including divi d ends), but are typi c all value. Index forwards notionalcontract amountandandthetheactual percentage diatffsettlement. erence betweensettletheinincash dex based value ionn thetheforward index level Forward contracts i n whi c h bonds are the underlying asset may be quoted in terms of the discountbonds. on zero-coupon bonds (e.g., T-bi lls)must or incontain terms ofspecial the yieldprovisi to maturi tdeal y onwithcoupon Forwards on corporate bonds o ns to the possibility or conversion Forward contracts may also beofwridefault tten onas well portfolias wiostofh anyfixedcallincome securitiesfeatures. or on bond indexes. An

LOS 6l.d

An â&#x20AC;˘

â&#x20AC;˘

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts

LOS 6l.lear time deposits are USD-denominated short-term unsecured loans to large Eurodol money-center banks outside the United States. The London Interbank Offered Rate (LIBOR) is an international reference rate for Eurodol ar deposits and is quoted for 30-day, 60-day, 90-day, 180-day, or 360-day (1-year) lterms. Euribor is the equivalent for short-term Euro-denominated bank deposits (loans to banks). For rates are ofexpressed basedbothon LIBOR the loanandtermEuribor, as a proportion a 360-dayas annual year. rates and actual interest is LOS 6Lf Forward agreements (FRAs)thatserve to hedgein thethe uncertainty aboutrise,short-term rates (e.a payment g., 30-rateorat90-day LIBOR) wil l prevail future. If rates the l o ng receives settlement. below the contract rate. The short receives a payment if the specified rate falls to a level LOS 6I.g The payment to the long at settlement on an FRA is: [ days in loan term (reference rate at settl e ment-FRA rate) 360 ] . p amount notion pnnct [ d a , y _ _ s m_o _ an _t _ e _ rm _ 1 reference rate at settlement _ 360 ] The numerator isratethe and difference between the rateandon atheloandenominator for the specifiis toeddiscount period atthithes forward contract the rate at settlement, interest differential back to the settlement date at the market rate at settlement. LOS 6l h . Currencyatforward that oneforpartya certain will deliver amountcurrency. of one currency the settlcontracts ement datespecify in exchange amounta certain of another Under cashbetween settlement, a single cashratepayment is made at settlement based onexchange the rate difference the exchange fi x ed in the contract and the market at the settlement date. .

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts

CONCEPT CHECKERS

1. A.Thehasshortnoindefaul a delit vrisk. erable forward contract: B.C. makes is obligaatedcashtopayment deliver theto thespecifilongedatasset. settlement. 2. A.On thethe settlement date of a forward contract: may besellrequired toorsellmaketheaasset. B.C. theat leastshort longonemust the asset cash payment. party must make a cash payment to the other. of the foll o wi n g statements regardi n g early termination of a forward 3. Which is who enters into an offsetting contract to terminate has no risk. A.contract A party partytermination who terminthrough ates a forward contract early mustwimake aoriginal cash payment. C.B. AEarly an offsetti n g transaction t h the counterparty eliminates default risk. 4. AA.dealcannot er in betheaforward contract market: bank. B.C. may enter into a contract wi t h another dealer. gets a small payment for each contract at initiation. 5. Which of the following statements regarding equity forward contracts is A.B. Dividends Equity forwards may be settled i n cash. are neverin anincluded in indexcould forwards. C. Aofshort position equi t y forward not hedge the risk of a purchase that equity in the future. of the foll o wi n g statements regarding forward contracts on 90-day T-bills 6. Which A.B.is The faceis novaluedefault mustribesk paid by theforwards long atbecause settlement. There on these T-bills are government-backed. C. will If short-term s increase unexpectedly after contract initiation, the short profit on yiel thedcontract. lar ontimaediscount deposit: basis. 7. AA.Eurodol i s priced B.C. may be issued a Japanesedenominated bank. in Euros. is a certi ficate ofbydeposit differenceis forbetween LIBOR and Euribor is that: 8. A.OneLIBOR London deposits. B.C. they currencies. LIBORare isforslidightlfferent y higher due to default risk. most accurate?

least

accurate?

most accurate?

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts

9. Which of the following statements regarding a LIBOR-based FRA is short wi l l settl e the contract by making a loan. A.B. The can beincreases based onunexpectedly interest ratesoverforthe30-,contract 60-, orterm, 90-daytheperiods. C. FRAs Ifrequired LIBOR long will be to make a cash payment at settlement. 10. 60-day ConsiderLIBOR a $2 million FRA with a contract rate of 5o/ o on 60-day LIBOR. If is 6o/o at settlement, the long will: A.B. pay $3,333. recei v e $3,300. C. receive $3,333. A hasrateentered a 8currency forward contracttheto purchase 10 mill ion97atperan 11. Party exchange of $0. 9 per euro. At settlement, exchange rate i s $0. If thea payment contract iofs settled in cash, Party A will: A.B.euro.make $100,000. C. recei receivvee aa payment payment ofof $100, $103,0090.00. 12. 3.15o/o If the quoted discount yield onhasa the128-day, $1ofmillion T-billgaineddecreases from to 3. 0 7o/o, how much holder the T-bill or lost? A.B. Lost $284.$284. Gained C. Gained $800. 13. maturi 90-daytLIBOR is quoted as 3. 5 8o/o. How much i n terest woul d be owed at y6for12.a 90-day loan of $1.5 million at LIBOR 1.3o/o? A.B. $17, $18,3900.25. $32, treasurer needs toandborrow 10 million euros fortake180to days, 60thedays 14. Afromcompany now. The type of FRA the position he should hedge interest rate riskPosition of this transaction are: FRA A.B. 22 x 68 Short Long 2 8 Short most

accurate?

â&#x201A;Ź

+

c.

c.

Page 2 1 0

X X

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts

ANSWERS - CONCEPT CHECKERS 1.

B

The short in a forward contract is obligated to deliver the specified asset at the contract price on the settlement date. Either party may have default risk if there is any probability that the counterparty may not perform under the terms of the contract.

2.

A

A forward contract may call for settlement in cash or for delivery of the asset. Under a deliverable contract, the short is required to deliver the asset at settlement, not to make a cash payment.

3.

C

Terminating a forward contract early by entering into an offsetting forward contract with a different counterparty exposes a party to default risk. If the offsetting transaction is with the original counterparty, default risk is eliminated. No cash payment is required if an offsetting contract is used for early termination.

4.

B

Forward contracts dealers are commonly banks and large brokerage houses. They frequently enter into forward contracts with other dealers to offset long or short exposure. No payment is typically made at contract initiation.

5.

B

Index forward contracts may be written as total return contracts, which include dividends. Contracts may be written to settle in cash, or to be deliverable. A long position is used to reduce the price risk of an expected future purchase.

6.

C

When short-term rates increase, T-bill prices fall and the short position will profit. The price of a T-bill prior to maturity is always less than its face value. The deliverable security is a T-bill with 90 days to maturity. There is default risk on the forward, even though the underlying asset is considered risk free.

7.

B

Eurodollar time deposits are U.S. dollar-denominated accounts with banks outside the United States and are quoted as an add-on yield rather than on a discount basis.

8.

B

LIBOR is for U.S. dollar-denominated accounts while Euribor is for euro-denominated accounts. Neither is location-specific. Differences in these rates are due to the different currencies involved, not differences in default risk.

9.

B

A LIBOR-based contract can be based on LIBOR for various terms. They are settled in cash. The long will receive a payment when LIBOR is higher than the contract rate at settlement. x

(60 I 360)

x

1 I (1

+

0.06 I 6) = $3,300.33.

(0.06 - 0.05)

11. A

($0.98 - $0.97) x 10 million = $ 100,000 loss. The long, Party A, is obligated to buy euros at $0.98 when they are only worth $0.97 and must pay $0.01 x 1 0 million = $ 1 00,000.

12. B

The actual discount has decreased by: (0.03 1 5 - 0.0307) x

128

-

360

=

$2 million

x

10. B

0.0284% of $ 1 ,000,000, or $284.

A decrease in the discount is an increase in value.

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts

13. B

(0.0358

+

0.013)

( ) 90

360

1 . 5 million = $ 1 8,300. Both LIBOR and any premium to LIBOR

are quoted as annualized rates. 14. B

Page 2 1 2

This requires a long position in a 2

x

8 FRA.

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The following is a review of the Derivatives principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in:

FUTURES MARKETS AND CONTRACTS Study Session 1 7

EXAM FOCUS

Candidatestheshould focusofonmargi the terminology of futures markets, how futures differOther from forwards, mechanics n deposits, and the process of marking to market. concepts herefinancial includefutures limit pricontracts. ce moves,Learn delivtheery options, and theposition characteristi cs ofimportant the basic types of ways a futures can be to contract expiration understand how cash settlement is accomplished byterminated the finalprior mark-to-market at contractandexpiration. LOS 62.a: Describe the characteristics of futures contracts. LOS 62.b: Compare futures contracts and forward contracts. CFA® Program Curriculum, Volume 6, page 43

Futures are very much l i k e the forward contracts we learned about in the previous topic review. They are in that both: Canpribeceiedtherto have delivzero erablevalue or cashat thesettlement contracts.enters into the contract. Are time an investor Futures contracts from forward contracts in the following ways: Futures contracts trade on organized exchanges. Forwards are private contracts and doFutures not trade. contracts areofhighl y standardized. Forwards are customized contracts satisfyi n g the needs the parties invol v ed. Acontracts single clearinghouse ins atithengcounterparty to all futures contracts. Forwards are with the origi counterparty. The government regulates futures markets. Forward contracts are usually not regulated. contracts

similar

differ

Characteristics of Futures Contracts

A major diffcontract erence between forwardscontracts and futures is that futuresand contracts have standardized terms. Futures specify the quality quantity of goods that can be delivered, the deli v ery time, and the manner of deli v ery. The exchangethealsobasic sets price the minimum priceor fltick,uctuation (whi ch is calledgrainthecontract tick size).is a For example, movement, for a 5, 0 00-bushel quartera dailof ay point (1mpoint =ch$0.sets0 1)thepermaximum bushel, orprice $12.movement 5 0 per contract. Contracts alsoe have price li i t , whi allowed in a si n gl day. For example, wheat cannot move more than $0.20 from its close the preceding day. Standardization.

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #62

-

Futures Markets and Contracts

The pricemonth. limits expand duringalperiods gh volatitimes lity andfor each are notcontract. in effect durinmaximum g the delivery The exchange so sets ofthehitrading Ittrading. wouldWhy? appearStandardization that these rulestells wouldtraders restrictexactltrading actiisvbeing ity, buttraded in fact,andtheythe stimulate y what conditions of the transaction. The purchaser of a futures contract is said to have gone long or taken a whileach e thecontract seller of traded, a futurestherecontract is saidandto have goneTheshortlongorhastakencontracted a to buy For is a buyer a sel l er. the asset atprice. the contract price at contract expiration, and theto gain shortexposure has an obligation toin sell at that Futures contracts are used by to changes thecontracts price ofto thereduceassetexposure underlyingto price a futures contract. Aasset (hedgein contrast, wilpril usece risk). futures changes i n the thei r asset Anthe exampl e i s a wheat farmer who sells wheat futures to reduce the uncertainty about price of wheat at harvest time. Clearinghouse. Each exchange hasll honor a their obligations. The clearinghouse guarantees thatthis traders in the futures market wi The clearinghouse does by splitting each trade once itbuyer is madeto and actiselnlgerasandthetheopposite sideeveryof each position. The cl e ari n ghouse acts as the every sel l er to buyer. By doing this, the havi clearingnghouse allowsthe eiother ther side ofof thethe trade totrade. reverseThispositions at a future date withethout to contact si d e initial al l ows traders to enter market knowing that they wi l l be able to reverse their position. Traders are also freed from having to worryIn theabouthistory the counterparty defaulting since the counterparty is now thedefaulted clearinghouse. of U. S . futures trading, the clearinghouse has never on a trade. Uniformity promotes market Liquidity.

Long position, short position.

speculators hedger,

clearinghouse.

Professor's Note: The terminology is that you "bought" bond futures ifyou entered into the contract with the Long position. In my experience, this terminology has caused confusion for many candidates. You don't purchase the contract, you enter into it. You are contracting to buy an asset on the Long side. "Buy" means take the Long side, and "sell" means take the short side in futures.

LOS 62.c: Distinguish between margin in the securities markets and margin in the futures markets, and explain the role of initial margin, maintenance margin, variation margin, and settlement in futures trading. CFAÂŽ Program Curriculum, Volume 6, page 48

In usecurities markets,Initialmargin on ofa stock or bond purchase is a percentage of the market valthe eremai of theningasset. l y, 50% the stock purchase amount may be borrowed, and amount, theamount, equity ithen themargin account,loan.must bemargin paid ipercentage, n cash. Theretheispercent interest charged on the borrowed The ofminimum the security value thatof market is owned,value.will vary over time and must be maintained at some percentage Page 214

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Study Session 1 7 Cross-Reference t o CFA Institute Assigned Reading #62 - Futures Markets and Contracts

In thethefutures markets, margiThere n is a performance guarantee. Itconsequentl is money deposited by both l o ng and the short. i s no l o an i n vol v ed and, y , no i n terest charges. Each futures exchange has a clearinghouse. To safeguard the clearinghouse, the exchange requitrader res traders todeposi postt margin andledsettle thein)rwith accounts on a(who, daily inbasis.turn,Before trading, themargin must funds (cal margi a broker wil l post with the clearinghouse). In securities markets, theprice cashprovi deposited isthepaidbroker. to theThis sellerisofwhythethesecuriunpaid ty, withbalance the is a balance of the purchase d ed by loan, with interest charged to the buyer who purchased on margin. Initial margin is the money that must be deposited i n a futures account before any trading Itequal is sets about for eachonetypeday'ofs maximum underlyingprice asset.fluInitial margionnthepertotal contract iofs reltheaticontract' vtakes ely lowplace. and ctuation value s underlying asset. Maintenance margin isbalance the amount ofaccount marginfalthatls below must bethemaintained in margin a futuresdue account. If the margi n i n the maintenance to a changetoinbring the contract e for thebackunderlup ytoingtheasset, funds must be deposited the marginpricbalance initialadditional margin requirement. This is ipercentage n contrast toupequi margimargin, ns, whichnotrequire to bringlevel.the margin to thety account maintenance back toinvestors the initialonlymargin Variation is theamount. funds Ifthataccount must bemargin deposited intothetheinitial account to bring it back tofundsthe can initialmargin margin exceeds margin requirement, be withdrawn or used as initial margin for additional positions. The settlement price is analogous to the closing price for a stock but i s not simply the priof trading, ce of thecalled last trade. It is anperiod, averagewhich of theisprisetcesbyofthetheexchange. trades during thefeaturelast ofperiod the closing This themake settlement price prevents manipulation by traders. The settl e ment price i s used to margin calculations at the end of each trading day. Initial and minimum margi n s in securities accounts are set by the Federal Reserve, althoughmarket brokerage houses canclearinghouse require more.andIniaretialbased and maintenance margi nprice s in the futures are set by the on historical dail y volMargiatilityn inoffutures the underlying asset sincelymargin is resettl epercentage d daily in futures accounts. accounts is typical as a of the value of the assets covered byis much the futures s means that the leverage, based on the actual cash required, highercontract. for futuresThiaccounts. much lower

How a Futures Trade Takes Place

Into thecontrast to forward contracts i n whi c h a bank or brokerage i s usually the counterparty is a buyerthatandwiallseller futures oftrade. The futures exchangecontract, selects there the contracts trade.onTheeachasset,sidetheof aamount the asset, and the Š20 1 2 Kaplan, Inc.

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #62

-

Futures Markets and Contracts

settlement/delivery date areamount standardized in this manner (e.gthere ., a Juneis afutures contract on 90-day T-bills wi t h a face of $1 million). Each time trade, the del i very price for that contract i s the equi l i b ri u m pri c e at that point i n ti m e, which depends on supply (by those wishing to be short) and demand (by those wishing to be long). The mechanismlocation by whionch supply and demand determine thiEachs equilibrium is opentooutcry atexchange a particular the exchange fl o or called a trade i s reported so that the equilibrium price, at any point in time, is known to all traders.the pit.

LOS 62.d: Describe price limits and the process of marking to market, and calculate and interpret the margin balance, given the previous day's balance and the change in the futures price. CPAÂŽ Program Curriculum, Volume 6, page 48

Many futures contracts have price limits, whi c h are exchange-imposed limits on how much the arecontract price from can change fromtrades the previous day'outside s settlement price.IfExchange members prohibited executing at prices these limits. the or (equilibrium) price at which traders woul d wil l i n gl y trade is above the upper limit below the lower limit, trades cannot take place. Consider a futures contract that has daily price limits of two cents and settled the previousofdaychanges at $1.0in4.market If, on theconditions followinorg tradi ng day, traders wishwitolltrade at $1.0The7 because expectations, no trades take place. settlement pril bece saiwildl tobe have reported asa$1.lim0it6 (for theandpurposes of marking-to-market). The contract wil made move, the price i s sai d to be li m it (from theareprevious day).tradeIf imarket conditions had changed such that theprice, priceandat whithech traders wi l ling to s below $1. 0 2, $1. 0 2 wil l be the settlement priup core idown, s said tothebeprilimit down. If trades cannot take pl a ce because of a l i mit move, ei t her is said topositions. be locked limit since no trades can take place and traders are locked into theirceexisting Marking-to-market is theinprocess ofofadjusting the margi n from balancetheinprevious a futurestrading accountday, each day for the change the value the contract assets based on the new settlement price. The futures exchanges can require a mark-to-market more frequently (than daily) under extraordinary circumstances. up

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #62 - Futures Markets and Contracts

Computing the Margin Balance

Example: Margin balance ConsiderAssume a long position ofcontract five Julypricewheatis $2.contracts, eacheachof whicontract ch coversrequi5,r0es00an bushels. that the 0 0 and that initial margi n deposit of $150 and a maintenance margi n of $100. The total initial margin requi red forCompute the 5-contract trade is $750.forThethismaintenance margin fordecrease the account i s $500. the margi n balance position after a 2-cent ionn price on Day 1, a 1-cent increase in pri c e on Day 2, and a 1-cent decrease in price Day 3. Answer: Each contractvalisufore by5,$50, 000 bushels change of(0.01)(5)(5, $0. 0 1 per0bushel changes00. the contract or $250soforthattheafiprice ve contracts: 00) = $250. The followingchanges figure ileach lustrates the change in initial the margibalanncebalaisncetheasinitial the price of thirequis contract day. Note that the margin change.rement of $750 and that the required deposit is based on the previous day's price Margin Balances Day

Required Deposit

Price/Bushel

Daily Change

Gain/Loss

Balance

$750

$2.00

0

0

$750

0

$ 1 .98

-$0.02

-$500

$250

2

$500

$ 1 .99

+$0.01

+$250

$ 1 ,000

3

0

$ 1 .98

-$0.01

-$250

$750

0 (Purchase)

Atmaintenance the close onmargin Day 1,leveltheofmargi n balance has gone beloofw the$500minimum or to bring $500. Therefore, a deposit is required thebalamargi nanybackpoint to theas initial marginthelevelinvestor of $750. Wereali canzinterpret the margin nce at the amount would e i f the position were closedmargioutnbybalance. a reversing trade at the most recent settlement price used to calculate the

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #62

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Futures Markets and Contracts

LOS 62.e: Describe how a futures contract can be terminated at or prior to expiration. CPAÂŽ Program Curriculum, Volume 6, page 53

There are 1. Atheshort can termi n ate the contract by del i veri n g the goods, and a long can terminate by The accepting deliforverydeliandverypayi(forngphysical the contract pricetermsto the delshort.ivery,Thisandis caldetails ledcontract location assets), of exactly what i s to be del i vered are al l specified in the contract. Deli v eries represent less than 1% all contract terminations. 2. Inmarked-to-market a account is based on thedelivery settlementis notpricean onoption. the laThest dayfutures of trading. 3. You maywemakedescribed a exiting or a forward trade in thepriorfutures market. This isfutures, similar to thehowever, way contract to expiration. Wi t h the othertrade side of(maturi yourtposition is held bygood)the clearinghouse-if you makethe anclearinghouse exact opposite y, quantity, and to your current position, will positions net your positions out,Theleaving youprice withcana zerodifferbalance. Thistheis how most futures are settled. contract between two contracts.sellIf you initially areposition long onein)contract at $370golperd contract ounce ofwhen goldtheand subsequently (take the short an i d entical is deducted $350/oz.,from $20 tithemesmargi the nnumber of ounces ofaccount. gold specified in ofthethecontract wilprice l be deposit(s) in your The sale futures contract hasendsbeen the exposure orto future pricebyfluactuationstrade. on the first contract. Your position positionwithmayanalsoopposite be settled through an own and deliver the goodsHere,andyousettlfinde up 4. Aa trader position to your between yourselves, off the fl o or of the exchange (call e d an ex-pit transaction). This isthetheflosole exception to theYoufederal lawthenthatcontact requiresthethatclearinghouse all trades takeandplace on or of the exchange. must tel l them what happened. Antheexchange forcontract physicalsisdiffers from a delitheveryfloorinofthatthetheexchange, traders actually exchange goods, the not cl o sed on and the two traders pri v ately negotiate the terms of the transaction. Regular del i very involves only one trader and the clearinghouse. four ways to terminate a futures contract:

delivery.

of

of

cash-settlement contract,

reverse,

offsetting,

reversed,

closed out,

closing

exchange for physicals.

Delivery Options in Futures Contracts

Some tofutures contracts grant bond contractstogivthee theshort;shortoptions one ofwhat,severalwhere, and when deliver. Some Treasury a choi c bonds that are Physi acceptabl e to delsuch iver andgoloptions as tomaywhenoffertoadelichoice ver during the expiration month. c al assets, d or corn, of del i very locations toin the short. These options can be of signifi c ant val u e to the holder of the short position a futures contract. delivery options

as

Page 2 1 8

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Study Session 1 7 Cross-Reference t o CFA Institute Assigned Reading #62 - Futures Markets and Contracts

LOS 62.f: Describe the characteristics of the following types of futures contracts: Treasury bill, Eurodollar, Treasury bond, stock index, and currency. CFA® Program Curriculum, Volume 6, page 57

Let' s introduce fi n ancial futures by first examining the mechanics of a T-hill futures contract. Treasury billsettlfutures contracts are based onarea $1100million facethe valannualized ue 90-day (13-week) T-hi l l and e in cash. The price quotes minus discount in percent on the T-bills. Afrompricefacequote of98. 5 2(90represents an annualized discount of 1.48%, an actual discount of 0. 0 148 360) = 0. 0 037, and a delivery price of (1 - 0. 0 037) 1 million = $996,300. T-hill futures contracts are not as important as they once were. Their prices are heavi l y influencedhavebylostU.S.importance Federal Reserve operations and overall monetary policy. T-hill futures in favor of Eurodollar futures contracts, which represent aborrowers more free-market and more global measure of short-term interest rates to top quality for U.S. dollar-denominated loans. Eurodoiiar futures are based on 90-day LIBOR, whi c h is an add-on yield, rather than a discount yielared. calculated By convention, however, the priLIBOR ce quotesinfollow theThese same convention as e T-bills and as (100 annualized percent). contracts settl i0.01 n cash,%, representi and the minimum price change i s one which is a price change of 0. 0 001 = ngof$25(1 00per- $197 .million contract. A quote of 97.60 corresponds to an annualized LIB OR 6 ) = 2.4% and an effective 90-day yield of 2.4 4 = 0.6%. x

x

I

tick,

I

Professor's Note: Eurodollar futures are priced such that the long position gains value when interest rates decrease. This is different from forward rate agreements and interest rate call options, where the long position gains when interest rates mcrease.

Q

One of the first things a new T-bill futures trader learns is that each change in price of 0. 0I in the price ofa T-bill futures contract is worth $25. Ifyou took a long position at 98.52 and the price fell to 98.50, your loss is $50 per contract. Because Eurodollar contracts on 90-day LIB OR are the same size and priced in a similar fashion, a price change ofO.OI represents a $25 change in value for these as well.

Treasury bond futures contracts: Are traded for Treasury bonds with maturities greater than 15 years. Are a deli v erable contract. Havequoted a face asvaluea percent of $100,and000.fractions of 1% (measured in 1132nds) of face value. Are The shortthatinwiallTreasury bonddelifutures contract hascontract. the option tois deliver anydelivery of several bonds satisfy the very terms of the This cal l ed a option and is val u able t o the short because at expiration, one particular Treasury bond will be the cheapest-to-deliver bond. •

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #62

-

Futures Markets and Contracts

Each whichreceiis used to adjustpayment. the long'These s payment ataredelmultipl ibond very isoiesrsgithatforventhethea more valuable bonds v e a higher factorsat futures price at settlement. The long pays the futures price expiration times the conversion factor. Stocktrades indexinfutures. most popular futureonis thea multiplier S&P 500ofIndex that Chicago.TheSettlement is in stock cash andindexis based 250. Future The val u e of a contract i s 250 times the level of the i n dex stated in the contract. Wi t h anfutures indexpricelevelrepresents of 1,000, athegaivalue of each contract is $250,000. Eachstockindexindexpointfutures in the n or loss of $250 per contract. A long position on S&P 500 i n dex futures at 1,051 would show a gain of$1,750 i n the trader' s account iifs thetradedindexonwere 1,058index at theandsettlhasement date ($250 contract the same a multipli er of 50.7 = $1,750). A smaller Futurescontract contracts covering severalsame,otheralthough populartheindices are traded, andfromthe contract pricing to and val u ation are the multiplier can vary contract. Currency futures. The currency futures market is smaller i n volume than the forward currency market wetrade described ineurothe previous topic revipeso ew. In(MXP), the UniandtedyenStates, currency contracts on the (EUR), Mexican QPY), among others. Contracts are set i n units of the forei g n currency, and the price i s stated inon USD/unit. The sizechange of theinpeso contractof theis MXP500,000, and the euro0001contract is EUR125, 0 00. A the price currency unit ofUSD0. translates into a gain or unit loss ofUSD50 EUR125,000 contract. on a MXP500,000 unit contract and US012.50 on a conversion foetor,

x

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Study Session 1 7 Cross-Reference t o CFA Institute Assigned Reading #62 - Futures Markets and Contracts

KEY CONCEPTS

LOS 62.a

Like forward and contracts, futures contracts aredate mostandcommonly for delivery delivery ofor settlement commodities fi n ancial assets at a future can require in cash. Compared to forward contracts, futures contracts: Are more liquid, trade on exchanges, and can be closed by an offsetting Dothe contract. not have counterparty risk; the clearinghouse acts asoutcounterparty to eachtrade. side of Have lower transactions costs. Requi r e margin deposits andas areto asset markedquantity, to market daity,ly.settlement dates, and delivery Are standardi z ed contracts qual i requirements. LOS 62.b

LOS 62.c

Futures deposits are not loans, but deposits to ensure performance under the terms ofmargin the contract. Initial margin is the deposit required to initiate a futures position. Maintenance is the minimum marginvariation falls belowmargin. this amount, it mustmargin be brought back up tomargin its initialamount. level byWhen depositing Margin calculations based onset theby thedailyexchange. settlement price, the average of the prices for trades during a closingareperiod Trades cannotthe take place atandpricesare saithatd todifbeferlifrom the previous day'thes settlement prices by more than pri c e limit m i t down (up) when new equilibrium price is below (above) the minimum (maximum) price for the day. Marki addingingaisettlement ns to or subtracting fromtothethe next. marginng-to-market account daily,is thebasedprocess on theofchange prices fromlosses one day The mark-to-market adjustment either adds the day' s gains in contract value to the long' s margin balance andvalsubtracts them froms margin the short'balance s marginandbalance, or subtracts the day' s loss i n contract u e from the long' adds them to the short's margin balance. A futures positiontrade, can beenteri terminated iann theopposite followiposition ng ways:in the same contract. AnCashoffsetting n g i n to payment atassetexpiration (cash-settlement contract). Deli v ery of the specifi e d in the contract. An exchange for physicals (asset delivery off the exchange). LOS 62.d

LOS 62.e •

• •

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #62

-

Futures Markets and Contracts

LOS 62.lfar futures contracts are for a face value of $1,000,000, are quoted as 100 minus Eurodol annualized 90-day LIBOR in percent, and settle in cash. Treasury bond contracts are for a face value of $100, 0 00, give the short a choice of bonds iver, and use conversion factors to adjust the contract price for the bond that is todelidelvered. Stock indexvalue,futures haveeainmultiplier contract and settl cash. that is multiplied by the index to calculate the Currency futures are for delivery of standardized amounts of foreign currency.

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Study Session 1 7 Cross-Reference t o CFA Institute Assigned Reading #62 - Futures Markets and Contracts

CONCEPT CHECKERS

1. A.WhichHedgers of thetrade followito nreduce g statements about futures markets is some that preexisting risk exposure. clearinghouse guarantees traders in the futures market will honor B. The their obligations. C. deposit If an account to ornexceeds variationrisesmargi . the maintenance margin, the trader must 2. A.Thevaridailaytionprocess ofn.adjusting the margin in a futures account is called: margi marking-to-market. C.B. maintenance margin. buysat 98.14 (takes and a longclosesposition in)at aa price Eurodollar futures contract ($1 million 3. Afacetrader value) it out of98. 2 7. On this contract, the trader has: A.B. gained lost $325.$325. C. gained $1,300. 4. Innotthepermifutures market, a contract does not trade for two days because trades are tted at the equilibrium price. The market for this contract is: A.B. limit up. limit down. C. locked limit. existence of a delivery option with respect to Treasury bond futures means 5. The that the: A.B. short short has can thechooseoptionwhichto settl bonde iton cash deliver.or by delivery. C. long chooses which of a number of bonds will be delivered. 6. Assume thefutures holderposition ofa longtofutures position tonegotiates privatel y with theandholder ofshorta short accept delivery close out both the long positions. Which of the fol l owing statements about the transaction is The transaction is: as del i very. A.B. alalssoo known known as an exchange for physicals. C. the most common way to close a futures position. factortheinnumber a Treasuryof bonds bond contract is:vered. 7. A.A conversion used to adjust to be deli i ed by the face value to determine the deli v ery price. B.C. multipl multiplied by the futures price to determine the delivery price. least accurate?

most

accurate?

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #62

-

Futures Markets and Contracts

125,pric0e00settleuroes atfutures contracts are sold at a priceforofthi$1.s account 0234. Thechanges next 8. Three day the $1.0180. The mark-to-market the previous day' s margin by: A.B. -$675. +$675. +$2,025. futureswhimarket, the clearinghouse is to: 9. A.In thedecide ch contracts will margins. trade. and maintenance B.C. setact initial as the counterparty to every trade. to meet a margi n cal l are termed: 10. A.Fundsdaideposited margin.costs. B.C. vari settllyaetion ment margin. 11. A.Compared to forward contracts, futures contracts are to be: standardiin size. zed. B.C. larger less subject to default risk. c.

least likely

least likely

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Study Session 1 7 Cross-Reference t o CFA Institute Assigned Reading #62 - Futures Markets and Contracts

ANSWERS - CONCEPT CHECKERS 1.

C

If an account rises to or exceeds the maintenance margin, no payment needs to be made, and the trader has the option to remove the excess funds from the account. Only if an account falls below the maintenance margin does variation margin need to be paid to bring the level of the account back up to the level of the initial margin.

2.

B

The process is called marking-to-market. Variation margin is the funds that must be deposited when marking-to-market draws the margin balance below the maintenance margtn.

3.

B

The price is quoted as 100 minus the annualized discount in percent. Remember that the gains and losses on T-hill and Eurodollar futures are $25 per basis point of the price quote. The price is up 1 3 ticks, and 13 x $25 is a gain of $325 for a long position.

4.

C

This describes the situation when the equilibrium price is either above or below the prior day's settle price by more than the permitted (limit) daily price move. We do not know whether it is limit up or limit down.

5.

A

The short has the option to deliver any of a number of permitted bonds. The delivery price is adjusted by a conversion factor that is calculated for each permitted bond.

6.

B

When the holder of a long position negotiates directly with the holder of the short position to accept delivery of the underlying commodity to close out both positions, this is called an exchange for physicals. (This is a private transaction that occurs ex-pit and is one exception to the federal law that all trades take place on the exchange floor.) Note that the exchange for physicals differs from an offsetting trade in which no delivery takes place and also differs from delivery in which the commodity is simply delivered as a result of the futures expiration with no secondary agreement. Most futures positions are settled by an offsetting trade.

7.

C

It adjusts the delivery price based on the futures price at contract expiration.

8.

C

(1 .0234 - 1 . 0 1 80) x 125,000 x 3 $2,025. The contracts were sold and the price declined, so the adjustment is an addition to the account margin.

9.

A

The exchange determines which contracts will trade.

=

10. C

When insufficient funds exist to satisfY margin requirements, a variation margin must be posted.

11. B

Size is not one of the things that distinguishes forwards and futures, although the contract size of futures is standardized, whereas forwards are customized for each party.

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Page 225


The following is a review of the Derivatives principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in:

OPTION MARKETS AND CONTRACTS Study Session 17

EXAM FOCUS

Thi s deri v ati v es revi e w introduces options, descri b es their terms and trading, and provides deri vations nofg how severalthe options valuati on results. Candidates should spendThisome tidesme understandi payoffs on several types of options are determined. s incl u options on stocks, bonds, stock i n dices, i n terest rates, currencies, and futures. The assi g ned material on must establlearn ishingatupper and oflowerthe bounds iparity s extensirelations ve, so iand t should notto construct be ignored.an Candidates l e ast one put-cal l how arbi tinragethestrategy. The notation,whatformulas, andonrelisasayi tionsngmay(andseem daunting, but if youthe put ti m e to understand the notati why), you can master important points. LOS 63.a: Describe call and put options. CFA® Program Curriculum, Volume 6, page 72

Antransaction involvinggianvesunderlying its owner theassetrigatht,a butpredetermined not the legalfuture obligation, to conduct a date (the exercise date) and at a predetermined price (the or Options give the option the righasht tothedecide whetherto perform or not theif thetradebuyerwil exercises eventuallthey takeoption. place. The seller ofbuyer the option obligation The owner of a ed time period. has the right to purchase the underlying asset at a specific price for a specifi The for aowner specifieofd atime period. has the right to sell the underlying asset at a specific price For mustpossible be a seloptions ler. Thepositions: seller of the option is also calledeverythe owner of an option, Therethere are four 1. Long call: the buyer of a call option-has the right to buy an underlying asset. 2. asset. Short call: the writer (seller) of a call option-has the obligation to sell the underlying 3. Long pur: the buyer of a put option-has the right to sell the underlying asset. 4. asset. Short put: the writer (seller) of a put option-has the obligation to buy the underlying To acquire these rights, to the owners seller ofoftheoptions option.must buy them by paying a price called the option contract

exercise price

call option

put option

option writer.

option premium

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strike price).


Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts

Listed After stock issuance, option contracts trade contracts on exchanges andustedare normally for 1 00butshares of stock. stock option are adj for stock splits not cash dividends. To$55seeandhowhasana caloption contract works, consider the stock of ABC Company. It sells for that sells fordatea inpremium of $10. This call option has an exercise pricel option of $50avaiandlablhase onanitexpiration five months. Professor's Note: The option premium is simply the price of the option. Please do not confuse this with the exercise price of the option, which is the price at which the underlying asset will be bought/sold if the option is exercised.

If theoption ABCselcallleroption is purchased for $10,forthe$50.buyerThecansellpurchase ABC stock from the over the next fi v e months er, or wri t er, of the option gets keep thebuyer$10exercises premiumthenooption, matterthewhatsellerthe wistock doesveduring thisstritikme price e period. Ifmustthetodeloption l l recei the $50 andor i v er to the buyer a share of ABC stock. If the pri c e of ABC stock fall s to $50 below, the buyer i s not obli g ated to exerci s e the option. Note that option holders wi l l y exercise thei act if it ofis profitable do so. The option writer, however, has anonlobligation to actr rigathttheto request the optiontoholder. option onhasABCthestock itos thesellsame as aofcallABCoption, except thetime buyerduring of thetheputnext A(loputng position) right a share for $50 at any fiexerci ve months. The put wri t er (short position) has the obligation to buy ABC stock at the se price in the event that the option is exercised. The ofhasthevalue, optiontheis thebuyeronemaywhoeither decidexerci es whether oroption not toorexerci se theoptionoption. Ifanother theowner option s e the sell the to buyer in the secondary options market. LOS 63 .b: Distinguish between European and American options. CFA® Program Curriculum, Volume 6, page 73

American expiration options date. may be exercised at any time up to and including the contract's European options can be exercised only on the contract's expiration date. � Professor's Note: The name ofthe option does not imply where the option trades­ � they arejust names.

Atsameexpiration, an Ameri c an option and a European option on the same asset wi t h the strike however, price are identical. They mayandeither behaveexercised orvalalluoes,wedsotoyouexpire. Before expiration, they are di f ferent may different must distinguish between the two. ©20 12 Kaplan, Inc.

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #63

If two opti oone ns areis aidentical (maturity, underlying stock, strike price,option, etc.) intheallvalways,ue of except that European option and the other i s an American theearlyAmerican option wi l l equal or exceed the val u e of the European option. Why? The Americanmore. option gives it more flexibility, so it should be worthexercise at leastfeature as muchofandthe possibly Option Markets and Contracts

LOS 63.c: Define the concept of moneyness of an option. CPA® Program Curriculum, Volume 6, page 75

refersoption to whether an optiona positive is payoff,orit is in the money. IfIfimmediate immediate exercise of the would generate exercise would resultthe inexerci a lossse price, (negativeexercise payoff), igenerate t is out ofneither the money. When theandcurrent asset pri c e equals wi l l a gain nor loss, the option is The following describe the conditions for a call to be in, out of, or at the money. Ifholder S - X would 0, a calreceive l optionfromis inimmediate the money.exercise, S X isbuyitheng a amount of the payoff a call share for and selling it in theIfmarket for a greater price S. a callisoption money. If S = X,S -Xa call 0,option said toisbeoutatofthethemoney. The following describe the conditions for a to be in, out of, or at the money. If iXS 0, aexercise, put option is inathesharemoney. X-Sexercisi is theng amount of the payoff from m mediate buying for Sand the put to receive for the share. the stock'IfsX-priceS is0,greater amoney. put option is said to be out When of the money. a put than optiontheisstrioutkeofprice, the If S = X, a put option is said to be at the money. Moneyness

in the money

out ofthe money.

at the money.

option

In-the-money call options.

>

X

-

<

Out-ofthe-money call options. At-the-money call options.

put option

In-the-money put options.

>

X

Out-ofthe-money put options.

<

At-the-money put options.

Example: Moneyness

Consi der a Calculate July 40 calhow l andmuch a Julythese 40 put,options bothareon ianstock $37/share. or outthatof theis currently money. selling for Professor's Note: A july 40 call is a call option with an exercise price of$40 and an expiration date in july. Answer:

The becausecallX-is $3S out= $3.of0the0. money because S-X= -$3.00. The put is $3 in the money Page 228

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts

LOS 63.d: Compare exchange-traded options and over-the-counter options. CPA® Program Curriculum, Volume 6, page 76

Exchange-traded orCorporation listed optionsfor Chi are cregulated, standardized, liquid,transactions. and backed byMostthe Options Clearing ago Board Options Exchange exchange-l isted options have expiration datesanticipatory within twosecurities to four months of the current date. Exchanges al s o li s t long-term equity (LEAPS), which are equity options with expiration dates longer than one year. Over-the-counter (OTC) options on stocks for1970s. the retail trade all buthowever, disappeared with themarket growthin OTC of theoptions organized exchanges i n the There is now, an active onmarket, currencies, swaps,options and equities, pris largel mariylyunregulated, for institutional buyers. Like the forward the OTC market i consists customwayoptions, much theofsame forwardsinvolves marketscounterparty are. risk, and is facilitated by dealers in LOS 63.e: Identify the types of options in terms of the underlying instruments. CPA® Program Curriculum, Volume 6, page 80

The types of options and (3)threecommodity options.we consider are (1) financial options, (2) options on futures, Financial optionsinterest includerates, equityandoptions and other optionspricebasedfor fionnancial stock indices, Treasury bonds, currencies. The strike options can be in terms of yield-to-maturi ty on bonds, an indexhavelevelpayoffs , or anbased exchange ratedifference for LIBOR-based on the between LIBOR at expiration and the strike rate in the option. aretivelmost often based on Treasury bonds because of their active trading. There are rel a y few l i sted options on bonds-most are over-the-counter options. Bond options can beoptions, deliverable or settle inoncash.bondThepricesmechanics of bondfaceoptions areof the lbond. ike those of equity but are based and a specific value The buyer of a call option on a bond wi l l gai n if i n terest rates fal l and bond pri c es rise. A put buyer will gain when rates rise and bond prices fall. settle i n cash, nothi n g is deli v ered, and the payoff is made directly to the option holder' s account. The payoffexceeds on an ithendexincalldex (long) is theedamount (if any) (the by whi c h the i n dex level at expiration level specifi in the option strifromketheprice),account multiplied by the An equal amount wi l l be deducted of the index call option writer. foreign

currency options.

interest rate options

Bond options

Index options

contract multiplier.

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #63

-

Option Markets and Contracts

Example: Index options

Assume thatmultipl you ownieraforcallthisoption on theis 250. S&P Compute 500 Indexthewithpayoff an exercise price equal toassuming 950. The contract on this option that the index is 962 at expiration. Answer:

This is a call, so the expiration date payoff is (962-950) $250 = $3,000. x

sometimes give theat aholder the rightprice,to buythe orstrisellke price. a specified futures contractcalled on orfutures beforeoptions, a given date given futures on futures contracts give the holder the right to enter into the long side ofonaafutures contractat 98at a(percent given futures price. Assume that you hold a callpriceoption bond future of face) and at expiration the futures onfutures the bond contract i s 99. By exercising the call, you take on a long position i n the contract, and the account is i m mediately marked to market based on the settlement accountof thewouldbondsbe credited wittheh cashcontract. in an The amountsellerequal to exerci 1 o/o (99sed- call98) ofwiprice.lthel takeYour faceonvalue covered by of the the short position i n the futures contract, and the mark-to-market value of this position will generate thegicash deposited to your account. on futures contracts v e the holder the option totertake on aobligation short futuresto position at a futures price equal to the stri k e price. The wri has the take on the opposite (long) position if the option is exercised. holder theprice.right to either buy or sell a fixed quantity of some physical asset atgiavfiextheed (strike) Some capital investment projectswhilehaveit isprovisions that(forgivexample, e the company flexitobilabandon ity to adjust the project' s cash Rows i n progress an option the project beforea completion). have value that should be considered when evaluating project's NPV.Such Options on futures,

Call options

Put options

Commodity options

real options

� Professor's Note: Evaluating projects with real options is covered in the Study � Session on corporate finance at Level II. LOS 63.f: Compare interest rate options with forward rate agreements (FRAs). CPA® Program Curriculum, Volume 6, page 81

are similar asset to theisstock optionsrateexcept that the exercise pricerateis an ioptions nterest rate and the underlying a reference such as LIBOR. Interest are also simil a r to FRAs because there is no deli v erabl e asset. Instead they are settl ed in cash, a notional amountareandEuropean the spreadoptions. between the strike rate andin antheamount referencethatrate.is based Most oninterest rate options Interest rate options

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts

Tointerest see how interest ratewith optionsa notional work, consider aoflo$1,ng 0position in a a1-year LIBOR-based rate call option amount 00, 0 00 and stri k e rate of 5%. For our example, l e t' s assume that this option is cosdess for simplicity. If at expiration, LIBOR is00greater(LIBORthan 5%,5%).theIfLIBOR option canis belessexercised andthetheoption ownerexpiwillresrecei ve ess $1, 0 00, 0 than 5%, worthl and the owner receives nothing. Now,samelet'sfeatures considerasatheshortcallposition injusta LIBOR-based interest rate putis option withto be thecostless, that we discussed. Again, the option assumed withs below a strik5%, e ratetheofoption 5% andwrinotional amount ofpay$1,the000,put000.holderIf atanexpiration, LIBOR fall t er (short) must amount equal to $1, 0 00, 0 00 (5%LIBOR). If at expiration, LIBOR is greater than 5%, the optiononeexpires worthlpayoff ess andis adjtheusted. put wriForterexample, makes noif thepayments. Ifrate the rate is foroption less is than year, the reference for the 60-day LIBOR,ratetheandpayoff be $1,are000,annualized 000 (5%actual LIBOR the would strike rate rates. LIBOR)(60/360) because the Noti c e the one-sided payoff on these interest rate options. The long call recei v es a payoff when LIBOR exceedshand,thethestrishort ke rateputandposition receivesmakes nothingpayments ifLIBORif LIBis below thebelowstrikethe rate. On the other OR i s strike rate, and makes no payments when LIBOR exceeds the strike rate. The ofasthea forward long interest rate call option plusToaseeshortthis,interest ratetheput option hasfixed-rate thecombination samepayerpayoff rate agreement (FRA). consider in thea 5%fixfied-rate xed-rate,payer$1,will 000,receive 000 notional, LIBOR-based FRA.5%).LikAnd, e our long cal l position, $1, 0 00, 0 00 (LIBORlike our short put position, the fixed-rate payer will pay $1,000,000 (5%- LIBOR). x

x

x

x

x

� Professor's Note: For the exam, you need to know that a long interest rate call � combined with a short interest rate put can have the same payoffas a long position in an FRA.

LOS 63.g: Define interest rate caps, floors, and collars. CFA® Program Curriculum, Volume 6, page 83

Ancorrespond to the resetis adates seriesonofainterest rate callloan.options, having expirati onprotect dates thata fl o ating-rate Caps are often used to fllimit) oating-rate from an increase in interestloan. rates. Caps place a maximum (upper on theborrower interest payments on a floating-rate Caps pay when rates risel above thewicapth strirate.ke Inratesthisequal regard,to thea capcapcanrate.be Each viewedoption as a in a seri e s of interest rate cal opti o ns cap is called a Ancorrespond to thefloorresetisdates a seriesonofa flinoterest rate put dates that ating-rate loan.options, Floors arehaving oftenexpiration used to protect interest rate cap

caplet.

interest rate

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #63

-

Option Markets and Contracts

a floating-rate nder from a decline limit) on the inleterest payments that arein interest receivedrates. fromFloors a floatiplace ng-ratea minimum loan. (lower Anminimum interestraterateonfloortheonpayments a loan operates just the opposite on a floating-rate loan. of a cap. The floor rate is a Floorsofpayinterest when rate ratesputfalloptions below thewithfloorstrikerate.ratesIn this regard, aflflooororrate. can beEachviewed as ina series equal to the option a floor is called a Anmayinteresta caprateforcollar combines a cap and a fl o or. A borrower wi t h a fl o ating-rate loan some of the cost ofprotection the cap. against rates above the cap and a floor in order to defray Let'oor.s reviOneweachthereset information infloFigure 1, which illtheustrates theforpayments from a cap(e.g.and, 90a fldays) date of a ating-rate loan, interest the next period is determined Here,onwetheassume the reference rate andonthatthe webasishaveof some quarterlreference y paymentrate.dates loan. that LIBOR is The fig10%, ure shows thewieffect of aacappayment that istosettheatcap10%.buyerIn theto offset event any thatinterest LIBO Rexpense rises above the cap l l make inof periods excess oforanforannual rate oflife10%. Aloan.capThemaycapbe will structured topayment cover a certain number the entire of a make a at any future interest payment due date inwhenever thethereference rate (LIBOR in our example) exceeds thebetween cap rate. As indicated the fi g ure, cap' s payment i s based on the difference the reference rate and the cap rate. The amount of the payment will equal the notional amount specifi ed in theusedcapto contract timesthethenotional differenceamount betweenis usually the cap equal rate and the reference rate. When hedge a loan, to the loan amount. 1 also iratellustrates a loan floorfallofs5%belowfor our LIBOR-based loan. Forpayment any payment where thebyFigtheurereference on the 5%, there i s an additional required floor toNotebringthatthethetotalissuerpayment toating-rate 5% (1.2 note 5% quarterly ona acap90-day LIBOR­ based loan). of a fl o wi t h both and a floor when (a collar) is long a cap and (has sold) a fl o or. The note issuer recei v es a payment rates are above the cap, and makes an additional payment when rates are below the floor (compared to just paying the reference rate). jloorlet.

buy

sell

short

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts

Figure 1: Interest Rate Caps and Floors Loan Rate Loan Rate without Caps or Floors

1 Oo/o -

5%

0%

- --

-

-- --

- -

- - -- - -- -- - -- -

-- - -

- -

- --

-

--

1 0% Cap

5% Floor

5%

LIB OR

10%

LOS 63.h: Calculate and interpret option payoffs and explain how interest rate options differ from other types of options. CFA® Program Curriculum, Volume 6, page 83

or other typea callof option wireceives th a monetary­ based exerci s e pri c e, i s strai g htforward. At expiration, owner any amount bywillwhich the asset price exceeds the strike price, and zero otherwise. The holder ofanda put recei v e any amount that the asset price is below the stri k e price at expiration, zero otherwise. While areandquoted in termsas ofanyield-to-maturi tthey, T-bill s principle in discountapplies. yield,That indicesis, iinn each indexbonds points, currencies exchange rate, same theandpayofftheperstrikeunitpriceof the(orrelevant asset, weto aneeddollarto strike translaprice. te theWeasset valcanuethentocase, amuldoltotliply argetvalue rate, or yield) options contract. this payoff times however many units of the asset are covered by the For a stock index option,levelweandsawthethatstrithese dollarby thevalumultipli es were eobtained from multiplying the index k e l e vel r specifi e d in the contract. Theonresulting dolfutures lar payoffsis thearecashper thecontract. The payoff options on optionis holder when he exercises the option and the resulting futures position markedreceives to market. Calculating the payoff for a stock option,

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #63

The areondifaferent. Fornotional example, a callandoption based on 90-day LIBOR makes a payment based stated amount the difference between 90-day LIBOR and the option' s stri k e rate, times 90 360 to adj u st for the interest rate period. Thetermpayment is made, not atForoption expiration, but based at a future date corresponding to the of the reference rate. example, an option on 90-day LIBOR wil l make a payment 90 days after the expiration date of the option. This corresponds date on which a LIBOR-based borrower wouldpayment make thedatenextofteninterest paymenttoonthea loan. Option Markets and Contracts

payoffs on interest rate options

I

Example: Computing the payoff for an interest rate option

Assume you bought a 60-day call option on 90-day LIBOR with a notional principal of $190-day millionLIBOR and aisstri6%keatratecontract of 5%.expiration, Compute and the payment thatwhenyouthewillpayment receive ifwill be determine received. Answer:

The interest savings on a $1 million 90-day loan at 5% versus 6% is: 1 million (0.06-0.05)(90 360) = $2,500 This is the amount that will be paid by the call writer 90 days after expiration. x

I

LOS 63.i: Define intrinsic value and time value, and explain their relationship. CFAÂŽ Program Curriculum, Volume 6, page 88

Anamount optiothat n's the optionvalueowneris thewould amount byve which the option isexercised. in-the-money. It is thehas recei i f the option were An option zero intrinsic value i f it is at the money or out of the money, regardl e ss of whether i t i s a call or a put option. Let' s look at the value of a call option If the expiration date price of the stock exceeds theIf thestrikepricepriceof theof thestockoption, thethancallorowner wiltheexercise the option and recei v e S -X. i s less equal to strike price, the call holder will let the option expire and get nothing. The option is the greater of (S -X) or 0. That is: = max[O, S -X] Similarly, the option is {X - S) or 0, whichever is greater. That is: P = max[O, X- S] intrinsic

at expiration.

intrinsic value ofa call

C

intrinsic value ofa put

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts

Example: Intrinsic value

Consider call option h a stri$50,ke priandce$45. of $50. Compute the intrinsic value of this option forastock prices wioft$55, Answer:

stock price = $55: C = max[O, S -X] = max[O, (55 - 50)] = $5 stock price = $50: C = max[O, S -X] = max[O, (50- 50)] = $0 stock price = $45: C = max[O, S -X] = max[O, (45 - 50)] = $0 NoticeBecause that at expiration, if the stock iswiworth $50exercior sbele theow,calltheoption call option is worth $0. Why? a rati o nal option holder l l not and take the loss. Thi s one-sided feature of call options i s i l l u strated i n the option payoff di a gram presented in Figure 2 for the call option we have used in this example. Professor's Note: Option payoffdiagrams are commonly used tools to illustrate the value ofan option at expiration.

Figure 2:

Call

Option Payoff Diagram

Value Long call

$5

o �n-r............ . .... . ........ . .... . ,.,.,

'.... ' .· ' ·

-$5

I ----------------------------

· . . . .

' '

·. I

j_ - - - - - - - -

�·•.

· · · · · · ·.

.

..

·

Short call

'------'---'- Srock p ri �e ar exp1ranon X = $50 $55

indicated intheFigure 2,isthein theexpiration dateFor payoff to the wriowner is eitherthezeropayoff or theis amount that option money. a call option t er (seller), eioption ther zero or mi n us the amount it i s i n the money. There are no positive payoffs for an optiongaiwriter whateverwriter. the callTheowner ns. receives the premium and takes on the obligation to pay

As

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #63

With reference to Figure 2, you should make the following observations: The payoff call position (thethesolidstrike line)price, is a flat line which angles upward toThethepayoff right totoat athea long 45writer degree angl e from ofangl a calle from (dottedtheline), isprice, a flat line which angles downward toOptitheonsrigareht ata zero-sum a 45 degreegame. strike If youpayoff addofthezero.long call option's payoff to the short option' s payoff, you will get a net At a stock price of $55, the payoff to the long is $5, which is a $5 loss to the short. Similarvaltououres forpayoff dioption. agram forAs aindicated call option,here,Figure 3price illustrates thestockat-expiration payoff a put i f the of the ithes lessprithan thethe strike price, the put owner wil l exerci s e the option and receive ( X S). If c e of stockreisandgreater than or (0).equalAttoa thestockstrike price, thetheputpayoff holderonwilallong let theputputis $1option expi get nothing price of $40, 0;stock the selat l$50er ofandtherecei put v(the short) would have a negati v e payoff because he must buy the e stock worth $40. 3: Option Markets and Contracts

X.

X.

Figure

Put Option Payoff Diagram

Value X

$10

0 I

-$10

· ..·· ..

• • •

- - - - - - - - - - - - �·· .. ..·· · · .· .

-X

· .· . . .

Short

put $40

Stock price

X = $50

The of an option i s the amount by which the option premium exceeds therelationshi intrinsicp canvaluebeandwritten is sometimes as: called the speculative value of the option. This option value = intrinsic value time value Asoption we discussed earlier, theAt anyintrinsic valduring ue ofthean option is theoptions amountcontract, by whiitschvaltheue i s in the money. point l i f e of an withatll typi cstock ally bepricegreater than its inintrinsic value.thatThigis visesbecause therea ipositive s some probability the wil l change an amount the option payoff at expiration greater than the (current) intrinsic value. Recall that an option's intrinsic time value

+

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts

value (toan aoption buyer)reaches is the amount of thetherepayoff attimeexpiration andandis bounded byvaluezero.is When expiration i s no remaining the time zero. For American options and in most cases for European options, the longer the time to expiration, premium (price).the greater the time value and, other things equal, the greater the option's LOS 63.j: Determine the minimum and maximum values of European options and American options. CFAÂŽ Program Curriculum, Volume 6, page 91

The following is some option terminology that we will use when addressing these LOS: s{ = the price of the underlying stock at time exerci se expiration price of the option XT == the the ti m e to cr = thetimeprice of a European call at any time prior to expiration at = T = thetimeprice of an American cal l at any time prior to expiration at = thetimepri==cTTe of a European put at any time prior to expiration at = thetimepri= cTe of an American put at any time prior to expiration at RFR = the risk-free rate t

t

c{

t

t

Pr

Pr

t

Professor's Note: Please notice that lowercase letters are used to represent European-style options.

Theoreti c all y , no option wi l l sell for less than its intrinsic value and no option zero. can take on a negative value. This means that the lower bound for any option is Thetime-t maximum valueofoftheeitherunderlying an American orThisa European option at any ti m e tis the share price stock. makesthe sense because no one would pay a price for the ri g ht to buy an asset that exceeded asset's boundary value. It woul d be cheaper toexpressed simply buyrespectivel the underlyi ng asset. AtandtimeEuropean t = 0, thecall upper condition can be y for American options as:

Lower bound.

The lower bound ofzero applies to both American and European options.

Upper bound for call options. call

Theexerci priceseforvaluean American puttheoption cannotstock be moreprice than its stri k e price. This i s the in the event underlying goes to zero. However, since European puts cannot be exercised prior to expiration, the maximifumthevalstockue isprice the present of theis expected exercise price Even goes to value zero, and to staydiscounted at zero, theat theintririnssick-freevalue,rate. Upper bound for put options.

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #63

X,condition will notcanbe recei ved untilfortheAmeri expiration At timeputt = options, 0, the upper boundary be expressed can anddate.European respectivel y, as: X X and (1+ RFR) The minimum and maximum boundary any time tare summari zed in Figure 4. conditions for the various types of options at P0 :S

Option Markets and Contracts

T

Po :S

Figure 4: Option Value Limits Option

Minimum VaLue

Maximum VaLue

European call

c, 2: 0

c, :::; s,

American call

c, 2: 0

c, :::; s,

European put

p, 2: 0

American put

P, 2: 0

P, :::; X/(1

+

RFR)tT-•l

p, _ <X

Professor's Note: The values in the table are the theoretical limits on the value of options. In the next section, we will establish more restrictive limits for option prices.

LOS 63.k: Calculate and interpret the lowest prices of European and American calls and puts based on the rules for minimum values and lower bounds. CFA® Program Curriculum, Volume 6, page 91 Professor's Note: The option boundary conditions that we discuss below will be important when you study option pricing models. For now, ifyou follow the logic leading up to the results presented in Figure 5, you will be prepared to deal with these LOS. Knowing and understanding the results in Figure 5 satisfy the requirements of these LOS; the following derivation of those results need not be memorized.

Atexercithissed,point,the weminimum know thatpriceforhasAmerican-style options, whichvalue. can For be immediately to be the option' s intrinsic at-the-money and out-of-the money options, thi s minimum i s zero, because options cannot haveintrinsic negati v e values. For in-the-money American options, the minima are simply the valoption ues Sfor- Xlessforthancalls,itsandintrinsic X- S value for puts.and Ifimmediately this were notexerci the scase, youa guaranteed could buy theprofit. e it for So,priorfor toAmerican options, we can express the at any time expiration as: = max[O, S,-X] = max[O, X- S ] however, Tothedetermine minima arethenotlower so obvious these options areFor notEuropean exercisabloptions, e immediately. boundsbecause for European options, lower bound on the option price

t

Cr P,

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,

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts

weshortcanposition examineinthethevalstock ue ofanda portfolio in whichbond. the option is combined with a long or a pure discount For a construct the following portfolio: At =loT.ng at-the-money European call option with exercise price X, expiring at time Aexpiration. long discount bond priced to yield the risk-free rate that pays X at option A short position in one share of the underlying stock priced at S0 = X. The current value of this portfolio is c0 -S0 + X (1 + RFR)T. At =expiration time, t on= T,thethicals portfoli o wipayll pay - ST our+ X.short Thatstock is, weposition, will collectand max:[O, S -X] l option, S to cover T collect X fromTthe maturing bond. IftheSTcall� pays X, theS call-X,is thein-the-money, andandthe portfolio willtohave a our zeroshort payoffposition. because bond pays +X, we pay -S cover T t= T payoff is: ST -X+ X- ST = 0. T is, the time That call istheout-of-the-money, and theweportfoli oXhason thea posibond, tive payoff equal Ifto X>X-SST thebecause cal l value, c , is zero, collect and pay to cover Tthe short position. So, theT time t = T payoff is: 0 +X-ST =X- ST . -ST Note that nothematter whether thewiloption expiresto orin-the-money, at-the-money, or out-of­ the-money, portfolio value l be equal greater than zero. We will never have to make a payment. To prevent possibili of a negative have a negatiarbitrage, ve value.anyThus,portfol we canio that statehasthenovalue of thetyportfoli o payoff= cannot as: c0 -S0 + X ( 1 + RFR)T � 0 which allows us to conclude that: European call option,

I

Cr

Cr

at time t 0

I

Combining this result with the earlier minimum on the call value of zero, we can write: T is the present value of a pure discount bond with a face value Note that X (1 + RFR) of Basedas:on these results, we can now state the lower bound for the price of an American call C0 � max[O, S0 -X (1 + RFR?J X.

I

I

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #63

-

Option Markets and Contracts

How can we say this? This conclusion follows from the following two facts: se feature 1. The equivalearlyentexerci European call (i.one.an, CAmerican t ;::: ct) . call makes it worth at least as much as an 2. The lower bound for theforvaluean American of a European calForl isexampl equal eto, max[O, or greater thanX I the theoretical lower bound cal l . max[O, (1 + RFR) T] ;:::

S0 -

S0 - X] .

Professor's Note: Don't get bogged down here. We just use the fact that an American call is worth at least as much as a European call to claim that the lower bound on an American call is at least as much as the lower bound on a European call.

Derive theat time t = 0: by forming the following portfolio AA long at-the-money European put option with exercise price X, expi r ing at t = T. short nposition on a riequal sk-freetobond priced at X I (1 + This is the same as borrowi g an amount X I (1 + A long position in a share of the underlying stock priced at At= max[O, expiratiX-on timeont =theT, put this option, portfolioreceiwilvlepay from+ the-X.stock,Thatandis,paywe-Xwilloncollect the bond issue (loan). IfIf X,X,thethepayoff payoffwilwilllequal: be zero. + -X = X. Again, a no-arbitrage argument can be made that the portfolio val u e must be zero or greater, because there are no negative payoffs to the portfolio. At time t = 0, this condition can be written as: minimum value of a European put option

• • •

50 .

S T]

RFR) T.

RFR) T_

ST

ST > S T :::;

PT

ST

PT

ST

PT

ST -

and rearranged to state the minimum value for a European put option at time t = 0 as: X I (1 + We as: have now established the max[O, X I (1 + Po ;:::

RFR) T - S0

minimum bound on the price of a European put option

Po ;:::

Page 240

RFR) T - S0]

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts

Professor's Note: Notice that the lower bound on a European put is below that of an American put option (i.e., max[O, SJ). This is because when it's in the money, the American put option can be exercised immediately for a payoff of

X-

X-50. FiandgureEuropean 5 summarizes now know the boundary optionswhat at anywetime prior regardi to expinrgation at time t =prices T. for American t

Figure 5 : Lower and Upper Bounds for Options Option

Minimum Value

Maximum Value

European call American call

Cr 2: max[O, Sr -X I (1

European put

Pr 2: max[O, X I ( 1

+

+

r RFR)T- ]

r RFR) T- - Sr]

X I (1

+

r RFR) T-

X

American put

Professor's Note: For the exam, know the price limits in Figure 5. You will not be asked to derive them, but you may be expected to use them.

Example: Minimum prices for American vs. European puts

Compute the lowest possible price for 4-month Ameri c an and European 65 puts on a stock that is trading at 63 when the risk-free rate is 5%. Answer:

American put: :2: max[O, = max[0,2l = $2 European put: $0.95max[O, (1 RFR)T - = max[O, 65 1 1.05°·333-631 = P0

X - S0l

Po :2:

XI

+

S0l

Example: Minimum prices for American vs. European calls

Compute lowestatpossible 3-monthrateAmeri stock that theis trading 68 whenprithece forrisk-free is 5%.can and European 65 calls on a Answer:

C max[O, c max[O, 0 :2:

S0 - X I

0 :2:

S0 - X I

(1 RFR)Tl = max[O, 68-65 1 1.05°·251 = $3.79 (1 + RFR)T] = max[O, 68-65 1 1.05°·25] = $3.79 +

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts

LOS 63.1: Explain how option prices are affected by the exercise price and the time to expiration. CPA® Program Curriculum, Volume 6, page 96

The result we are aft e r here i s a simple and somewhat intui t i v e one. That is, gi v en two putsse prithatce wilarelidentical inastallasrespects exceptas exercise price, theloonewerwiexerci th these price. higher exerci have at l e much value the one wi t h the Thi is because the underl ying stock canexcept be soldexerciat asehigher price. Similarl y, gilower ven two calexercilss that are identical in every respect price, the one with the price wilthel have at least stock as muchcanvalue as the oneatwia tlohwerthe price. higher exercise price. This issebecause underlying be purchased Professor's Note: The derivation of this result is included here although it is not explicitly required by the LOS.

The method here,intofora portfoli both putso andandexamine calls, istheto combine twopayoffs options with different exercise prices portfolio at expiration for the three possible stock prichave e ranges. We usevaltheue tofactestablish that a portfoli o withrelnoatiopossibility of a negati v e payoff cannot a negative the pricing ns for options with differing times to expiration. For X1 X2, consider a portfolio at time that holds the following positions: ct(X1) = a long call with an exercise price ofX1 ct(Xz) = a short call with an exercise price ofXz three expiration date 6.(t = T) conditions and payoffs that need to be considered here areThesummari zed in Figure <

t

Figure 6: Exercise Price vs. Call Price Expiration Date Condition

Option Value

Portfolio Payoff

ST ::; X1

�(X1) = �(X2) = 0

0

X , < ST < Xz

Xz ::; ST

�(X,) = ST �(Xz) = 0

- x,

�(X I ) = ST - XI �(Xz) = ST - Xz

ST - XI > 0

(ST - XI) - (ST - Xz) = Xz - XI > 0

Wi t h no negati v e payoffs at expiration, the current portfoli o of c (X ) c ( X ) must 0 0 2 1 have a value greater than or equal to zero, and we have proven that c0 (X1) � c0 (Xz). Page 242

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts

Simi larlse yprice , consider a portfolio short a put wiration th exerci sepayoffs price X1thatandweloneed ng a toputconsider with exerci X , where . The expi date are summarized2in Figure 7. 2 Figure 7: Exercise Price vs. Put Price X1

Expiration Date Condition

<

Option Value

ST � �

pT (X ,)

� > ST > X1

PT(X ,) PT(X2)

X1 � ST

X

PT(X ,) PT(X2)

=

PT(�)

Portfolio Payoff =

X2 - sT > o

=

0

=

X2 - ST

= =

0

0

x, - ST X2 - ST

(X2 - ST) - (X, - ST) X2 - X1 > 0 =

Here again, withmust no negati vaevalue payoffsgreater at expiration, the current portfoli oproves of that have than or equal to zero, whi c h � In summary, we have shown that, all else being equal: Callprices pricesarearedirectl inversely relatedtotoexercise exerciseprice. prices. Put y related Inmoney general,options, a longer time totimexpiration willno increase anweoption' ssayvalue. For far out-of-the­ the extra e may have effect, but can the longer-term option will be no less valuable that the shorter-term option. The case that doesn' t fi t this pattern is the European put. Recal l that the minimum value T r - Sr. ofWhianleinlo-the-money European put at any ti m e t pri o r to expi r ati o n i s (1 RFR nger time to valexpiration inoption creasespayoff optionatvalue throughForincreased volatility, it decreases the present u e of any expiration. this reason, we cannot state positivelyput.that the value of a longer European put will be greater than the value of a shorter-term If volatility is high and the put discount ratemorelow,valuable. the extraLowtimevolatil valueitywiand ll behitheghdominant factor and the longer-term wi l l be rates have the opposite effect and the value of a longer-term in-the-money putinterest option can be less than the value of a shorter-term put option. p 0 (�) - p0 (X) Po (�) Po (X l).

• •

XI

+

)

LOS 63.m: Explain put-call parity for European options, and explain how put-call parity is related to arbitrage and the construction of synthetic options. CFA® Program Curriculum, Volume 6, page 98

derivation of put-call aOurfiduciary call and a protectiparity ve put.is based on the payoffs of two portfolio combinations, ©20 12 Kaplan, Inc.

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #63

-

Option Markets and Contracts

is a combination of apayoff pure-discount, risklaryesscalbond thatratipayson Xis Xat when maturity and a call with exerci s e price The for a fi d uci l at expi the call is out of the money, and (S = S when the call is in the money. is a share of stock together with a put option on the stock. The expi payofftheforputa protecti is S) S = when the put is in the money,rationanddate5 when is out ofvetheputmoney.

A fiduciary

call

X.

A protective put

X+

- X)

(X -

+

X

Professor's Note: When working with put-call parity, it is important to note that the exercise prices on the put and the call and the face value of the riskless bond are all equal to X.

When the put is in the money, the call is out of the money, and both portfolios pay X at expiration. Simi5larlatyexpiration. , when the put is out of the money and the call is in the money, both portfolios pay Put-call arbi paritytrage.holdsWethatcanportfolios identical fs must sellas:for the same price to prevent express thewithput-call paritypayof relationship c RFR)T = S p valenciesas:for each of the individual securities in the put-call parity relationship can beEquiexpressed TT Sp == c-c-pS RFR) T c = S pRFR) - T = S RFR) RFR) p- c The si n gl e securiti e s on the left-hand side of the equations all have exactly the same payoffs as the portfoli os eonntstheofright-hand side.onThe portfolios on thetheright-hand side arebe European-styl the synthetic equival the securi t ies the left. Note that options must relations to hold.e and the puts and calls must have the same exercise price for these For to synthetically use theexample, following relationship:produce the payoff for a long position in a share of stock, S = c-p RFR)T This on a inlonga ristock be synthetically a shortmeans put, that and athelongpayoff position sk-freecandiscount bond. created with a long call, The other securities in the put-call parity relationship can be constructed in a similar manner. +

+ X I (1 +

+ X I (1 +

+ X I (1 + + X I (1 + X I (1 +

+

+ X I (1 +

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts

Professor's Note: After expressing the put-call parity relationship in terms ofthe security you want to synthetically create, the sign on the individual securities will indicate whether you need a long position (+ sign) or a short position (- sign) in the respective securities.

Example: option valuation using put-call parity Suppose thata 3-month the currentputstock pricewitihs $52 and these price risk-free rateTheis 5%.putYoupricehaveis $1.50, found abutquote for option an exerci of $50. due to$50lightcall.tradiEstimate ng in thethecallpriceoptions, was notcallaoption. listed quote for the 3-month, of thethere 3-month Answer: Rearranging put-call parity, we find that the call price is: call = put+ stock-present value (X) call= $1.50 +$52- 1.0$505 . = $4.11 This means that if a 3-month, $50 call is available, it should be priced at $4.11 per share. Call

0 25

LOS 63 .n: Explain how cash flows on the underlying asset affect put-call parity and the lower bounds of option prices. CFA® Program Curriculum, Volume 6, page I 04

positivevalcash fltheowscash overfltheows.period of thethinoption, the costa stock of theforasset isIfsimultaneously ltheess asset by thehaspresent u e of You can k of buying Sand borrowing theloan(s), present and valuetheofloan(s) the cashwifllloreduce ws, PVthe. netThecostcashoffltheow(s)asset will provide the payoff of the . Therefore, for assets with positive cash flows over the term of the option, to Scan- PVsubstitute weand thi s (lower) net cost, - PV , for S in the lower bound conditions in all the parity relations. The lower bounds for European options at time t = 0 can be expressed as: T], and cPo0 �� max[O, X (1 + RFR) S PV 0 T max[O, X (1 + RFR) - (S0 -PV The put-call parity relations can be adjusted to account for asset cash flows in the same manner. (S0 - PV = C-TP =+ (SX -(1PV+ RFR)+ PT, and C + X (1 + RFR) 0 CF

CF

S

I

I

CF)

CF -

I

I

CF

cp) ]

cF)

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts

LOS 63.o: Determine the directional effect of an interest rate change or volatility change on an option's price. CPAÂŽ Program Curriculum, Volume 6, page I 05

When i n terest rates increase, t h e value of a cal l option i n creases and the val u e of a put option decreases (holding the pricerateofoptions the underlying security constant). This general resul t may not appl y to interest or to bond or T-hill options, where a change in the risk-free rate may affect the value of the underlying asset. The no-arbitrage relations for puts and calls make these statements obvious: TT =S RFR) P= S RFR) T. This will have the Here we can see that an i n crease in RFR decreases RFR) effect of increasing value ofthethevaluecall,ofanda calldecreasing value ofthethevalue put. Aofdecrease ioption. n interest rates willthedecrease option andthe increase a put C

+ P - X I (1 + C - + X I (1 +

X I (1 +

Professor's Note: Admittedly, this is a partial analysis of these equations, but it does give the right directions for the effects of interest rate changes and will help you remember them ifthis relation is tested on the exam.

Greater vol a ti l i t y in the val u e of an asset or i n terest rate underlying an option contract ioptions ncreasesaretheone-sided. values of both puts and cals lvalue s (andfalcapsls noandlowerfloors). Thezeroreason isit that Since an option' than when expifrom res out of the money, the increased upside potential (wi t h no greater downsi d e ri s k) increased volatility, increases the option's value.

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts

KEY CONCEPTS

LOS 63.a

Athecallobligation, option ontoabuy financial or ephysical asset githevesasset the option' s owner thewriright, butthenot a specifi d quanti t y of from the option t er at exerci s e price specifi e d in the option for a gi v en time period. The wri t er of a cal l option it.is obligated to sell the asset at the exercise price if the option's owner chooses to exercise Anotputtheoption on a financial or physical asset gives theasset option'to thes owner thewriter right,atbutthe obligation, to sell a specifi e d quantity of the option exerci ed inthetheassetoptionat theforexerci a givense price time period. The wris owner ter ofchooses a put option iexercise s oblisgeatedit.pricetospecifi purchase if the option' to owneris(buyer) is said to be long the option, and the writer (seller) of anTheoption said to ofbeanshortoption the option. LOS 63.b

American options can be exercised at any time up to the option's expiration date. European options can be exercised only at the option's expiration date. Moneyness for puts s is determined and the market priceandof thecallunderlying stockby the difference between the strike price (X) LOS 63.c

(5):

Moneyness

Galt Option

Put Option

In the money At the money Out of the money

LOS 63.d

Exchange-traded options arearestandardized, regulated,custom and options backed bythata have clearinghouse. Over-the-counter options largely unregulated counterparty risk. Options are avai l abl e on fi n ancial securities, futures contracts, interest rates, and commodities.

LOS 63.e

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts

63.frate option payoffs are the difference between the market and strike rates, Interest adjusted for the loan period, multiplied by the principal amount. Atstrikexpiration, an i n terest rate call receives a payment when the reference rate is above the the strie rate, ke rate.and an interest rate put receives a payment when the reference rate is below An FRA can be replicated with two interest rate options: a long call and a short put. 63.grate caps put a maximum (upper limit) on the payments on a floating-rate loan Interest and are equi v alent ( f rom the borrower' s perspective) to a series of long interest rate call s at the cap rate. Interest ratevflalent oors put a minimum (lower limit) on theto apayments on a flinoterest ating-rate loan and are equi ( f rom the borrower' s perspective) series of short rate puts at the floor rate. Anfloatiinterest combinesa capa cap ng-raterateloancollbyarbuying andandsellinga floaor.floor.A borrower can create a collar on a 63. h The payoffoccurs to theatholder of a call put option on a stock is the option's intrinsic value. Payment expiration of theor option. Payoffs on interest are paid after expiration, at the end of the interest rate (loan) period specifrateied ioptions n the contract. 63.i value of an option is the payoff from immediate exercise if the option is in The intrinsic the money, and zero otherwise. The time (speculative) value of an option i s the difference between its premium (market price) and its intrinsic value. At expiration, time value is zero. 63.j,kand maximum option values: Minimum LOS

LOS

LOS

LOS

LOS

Option

sr

RFR) T-1 t RFR)T- - St]

st

American call

Cr 2: max[O, St- X I ( 1

European put

Pr 2: max[O, X I ( 1

+

Maximum Value RFR)T-1

ct 2: max[O, St - X I (1

American put

Page 248

Minimum Value

European call

+

+

P 2: max[O, X - S ]

Š2012 Kaplan, Inc.

X I (1

+

t RFR) T-

X


Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts

LOS 63.1 Cal l s with loexercise wer exercise worthly more). at least as much as otherwise identical calls with higher pricesprices (and aretypical Puts wi t h hi g her exerci s e prices are worth at l e ast as much as otherwise identical puts with lower exercise prices (and typically more). Otherwise identical options are worth more when there is more time to expiration, with two exceptions: out-of-the-money options withe todiexpiration fferent expiration dates anmayoptibeoequal in value. WiFar t h European puts, l o nger ti m may decrease n' s value when they are deep in the money. 63.m call (a call option and a risk-free zero-coupon bond that pays the strike price ALOSfiatduciary expiration) and a protective put (a share of stock and a put at have the same payoffs trages establishes will force these equal options. prices: c at expiration, RFR? = Sso arbip. Thi put-callpositions parity forto have European Based on theby put-call paritylongrelation, a synthetic security (stock,threebond,securities. call, or put) can be created combining and short positions in the other cp == Sc - Sp - RFR) RFR)TT T S = c -pRFR)T = S RFR) p-c LOS 63.n When the underl y ing asset has positive cash fl o ws, the minima, maxima, and put-call parity relations are adjusted bythesubtracting the present valuebe replaced of the expected cash flows from the assets over the l i f e of option. That is, S can by (S PV of expected cash flows). 63.o in the risk-free rate will increase call values and decrease put values (for AnLOS increase options that do not explicitly depend on interest rates or bond values). Increased call values.volatility of the underlying asset or interest rate increases both put values and •

X

X)

+ X I (1 +

+

• • • •

X I (1

+

+

X I (1 + + X I (1 + + X I (1 +

+

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #63

-

Option Markets and Contracts

CONCEPT CHECKERS 1.

of theis following statements aboutmoney. moneyness is When: A.Which S 0, a call option i s i n the B. SS =a 0,puta calloptionoptionis inistheat themoney. money. Which of the following statements about American and European options is wibecause ll alwaysofbeexchange-rate some price dirisk. fference between American and European A. There options B. European options allanowAmerican for exercioption se on ormaybefore thea higher optionvalexpiration date. Priequiorvaltoentexpiration, have u e than an European option. ofprithece follof theowioption ng statements about putthanandthecalprice l options isunderlying stock. A.Which The is less vol a ti l e of the B. Option prices are general l y higher the longer the time until the option expues. For the strike price relative to the stock's underlying price,puttheoptions, more thetheputhigher is worth. Which of the foll o wi n g statements about options i s A. The wriputteroption. of a put option has the obligation to sell the asset to the holder of the B. The holders price of a callrisesoption hasthe thestrikeobligati on to sell to the option writer if theThestock' above price. holder of a put option has the right to sell to the writer of the option. the and risk-free rate of interest will: A.AB. idecrease ncreaseinput call prices. put prices and i n crease call prices. increase put prices and decrease call prices. A $40 call on a stock trading at $43 is priced at $5. The time value of the option A.B. $2.$5. $8. expiration, an- AmericanRFR) putToption on a stock: A.B.Priowiirstobounded by S . lcanl never never sellsell forfor more less thanthanitsitsintrinsic value. intrinsic value. ownerexerciofsae callthe option onandoiltakefutures withofa thestrikoil.e price of $68.70: A.The can option del i very can exercineverse theexercise optiontheandoption takewhen a longtheposition i n oil futures. B. would spot price of oil is less than the strike price. C.

2.

-X -X > X,

Least accurate?

>

most accurate?

C.

3.

least accurate?

C.

4.

most accurate?

C.

5.

decrease

C.

6.

IS:

c.

7.

X I (1

+

C.

8.

C.

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts

lower bound for a European put option is: 9. A.Themax(O, S -X). T-S]. max[O, XS -X I (1 I+(1RFR) B.C. max[O, + RFR?J. 10. A.Themax(O, lower bound for an American call option is: S -X). T- S].T B.C. max[O, max[O, XS -X 1(1 +I (1RFR)+ RFR) ]. 11. Totheaccount forparitypositive cashby:flows from the underlying asset, we need to adjust put-call formula A.B. adding adding the the future future valvaluuee ofof thethe cash cash flfloowsws toto C. subtracting the present value of the cash flows from 12. AA.forward rate agreement is equivalent to the following interest rate options: long a call and a put. a call and long a put. B.C. short long a call and short a put. payoffonly on anatiexerci nterestse.rate option: 13. A.Thecomes greatersometheperiod higherafter the "strike" rate. B.C. iscomes option expiration. 14. Anequiivnalent teresttoratea serifloores onof: a floating-rate note (from the issuer's perspective) is interest rate puts. A.B. long interest rate C. short short interest rate puts. calls. relati oTns. is accurate? 15. A.WhichP =ofC-theS fol+ Xlowing I (1 + RFR) T. B.C. XC =I (1S -+ PRFR) + XTI -(1P+=RFR) S - C. isselling sellingforat $40, a 3-month put atrate$50is is6%.selling formuch, $11,ifa anything, 3-month callcan 16. Aat stock $50 i s $1, and the ri s k-free How an arbitrage? A.beB. made $0$0.2(no8.onarbitrage). $0.72. the follinowivolati ng wility.ll the value of a put option? 17. A.WhichAn ofincrease the exerci se price. C.B. AA decrease decrease iinn time to expiration. S.

X.

S.

least likely

c.

increase

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Page 25 1


Study Session 17 Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts

ANSWERS - CONCEPT CHECKERS

Page 252

>

<

1.

C

A put option is out of the money when S statements are true.

2.

C

American and European options both give the holder the right to exercise the option at expiration. An American option also gives the holder the right of early exercise, so American options will be worth more than European options when the right to early exercise is valuable, and they will have equal value when it is not, C � c and Pr � P · r r r

3.

A

Option prices are more volatile than the price of the underlying stock. The other statements are true. Options have time value, which means prices are higher the longer the time until the option expires, and a higher strike price increases the value of a put option.

4.

C

The holder of a put option has the right to sell to the writer of the option. The writer of the put option has the obligation to buy, and the holder of the call option has the right, but not the obligation to buy.

5.

C

Interest rates are inversely related to put prices and directly related to call prices.

6.

A

The intrinsic value is S - X = $43 - $40 = $3. So, the time value is $5 - $3 = $2.

7.

B

At any time t, an American put will never sell below intrinsic value, but may sell for more than that. The lower bound is max[O, X - SJ.

8.

B

A call on a futures contract gives the holder the right to buy (go long) a futures contract at the exercise price of the call. It is not the current spot price of the asset underlying the futures contract that determines whether a futures option is in the money, it is the futures contract price {which may be higher).

9.

B

The lower bound for a European put ranges from zero to the present value of the exercise price less the prevailing stock price, where the exercise price is discounted at the risk-free rate.

10. C

The lower bound for an American call ranges from zero to the prevailing stock price less the present value of the exercise price discounted at the risk-free rate.

11. C

If the underlying asset used to establish the put-call parity relationship generates a cash flow prior to expiration, the asset's value must be reduced by the present value of the cash flow discounted at the risk-free rate.

12. C

The payoff to a FRA is equivalent to that of a long interest rate call option and a short interest rate put option.

13. C

The payment on a long put increases as the strike rate increases, but not for calls. There is only one payment and it comes after option expiration by the term of the underlying rate.

14. B

Short interest rate puts require a payment when the market rate at expiration is below the strike rate, j ust as lower rates can require a payment from a floor.

15. B

The put-call parity relationship is S + P = C + X I ( 1 + RFR) T. All individual securities can be expressed as rearrangements of this basic relationship.

X and in the money when S

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts

16. C

A synthetic stock is: S C - P + X I ( 1 + RFR) T $ 1 - $ 1 1 + 50 I ( 1 .06) 0 路 25 $39.28. Since the stock is selling for $40, you can short a share of stock for $40 and buy the synthetic for an immediate arbitrage profit o f $0.72.

17. A

Increased volatility of the underlying asset increases both put values and call values.

=

=

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The following is a review of the Derivatives principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in:

SWAP MARKETS AND CONTRACTS Study Session 17 EXAM Focus

This topic revi e w introduces swaps. The fi r st thing you must learn is the mechanics of swaps so that youbecanablcalculate the payments oncashanyflofowstheoftypes of can swapsbecovered. Beyond that, you should e to recognize that the a swap duplicated with capital markets transactions (make a loan, issue a bond) or wi t h other deri v ati v es (a series of forward rate agreementsfloating or inrate terestdetermi rate options). Common mistakes include forgetti ng that the current-period n es the next payment, forgetti n g to adj u st the interestfiedrates forswap, the payment period, forgetti ng toswaps add anyinvolmargin above theofflocurrencies ating rate speci i n the and forgetti n g that currency v e an exchange at the initiation and termination of the swap. Don't do these things. SwAP CHARACTERISTics

Before wethegetdifferent into thetypes detailofs ofswaps. swaps,Youa simple introduction mayswapshelpasastheyouexchange go of through can vi e w interest rate one loan for another. If you lend me $10, 0 00 at a fl o ating rate, and I lend you $10, 0 00 atchange a fixedhands. rate, The we have created a swap.makeTherethisispointless. no reasonAtforeachthepayment $10,000date, to actual llyl two equal loans I wi make a payment to you based on the fl o ati n g rate, and you wi l l make one to me based onthethelargerfixedpayment rate. Again, it makes no sense to exchange thedifference full amounts; the oneThiwisth liability wi l l make a payment of the to the other. describes the payments of a fixed-for-floating or "plain vanilla" swap. Aratecurrency swapandcanyoube vilendewedmethethesame way. Ifiamount lend youof yen1,000,at 0today' 00 euros at the euro of interest, equivalent s exchange rate atsame the yenamounts rate ofofincurrency terest, weathave done a currency swap.twoWeloans. will "swap" back I these the maturity date of the In the interim, borrowed yen, so Iinmake interest payments euros.yen interest payments, and you borrowed euros and must make For other types of swaps, we just need to describe how the payments are calculated on Fortoantheequity swap, Istock couldindex, promiseandtoyoumakecouldquarterly payments onfixed-rate your loan tothe(ormeflloans. equal return on a promise to make ovating-rate) payments toed-rate me. Ifpayment the stocktoindex goesa down, myequal payments todecline you are negati e (i. e . , you make a fi x me payment to the in the indexbasedoveronthethequarter). If theincrease indexiwent upindex.overAgain, the quarter, I would coul maked bea payment percentage n the the payments "netted" so that only the difference changes hands. This intui t i v e expl a nation of swaps should make the fol l owing a bit easier to understand. Now let's dive into the mechanics and terminology of swaps. We have to specify exactly and

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts

howloaned, the interest payments wiloans l be calareculfor.ated,Swapshowareoftencustom they instruments, are made, howandmuch is to bespecify and how l o ng the we can any terms both of us can agree on. LOS 64.a: Describe the characteristics of swap contracts and explain how swaps are terminated. CPA® Program Curriculum, Volume 6, page 120

Swaps are agreements to exchange a series of cash flows on periodic over aswap, certainonetime period (e.g., quarterly payments overontwotheyears). In theprincipal simplestspecif typeiedof in party makes interest payments notional the swapthe two in return for are sopayments from the other party.isAtmade. eachThe settlement date, payments that only one (net) payment party witermed th thethegreater liability makesanda payment to theendsother party.termination The lengthdate.of theA swap swapcanis of the swap the contract on the bedates.decomposed into a series of forward contracts (FRAs) that expire on the settlement In many respects, swaps are similar to forwards: Swaps typical ly require no payment by either party at initiation. Swaps are custom instruments. Swaps areare largely not traded in anyated.organized secondary market. Swaps unregul Default risk i s an important aspect of the contracts. Most particiarepantsrarelinytheswapsswapsmarket marketparticipants. are large institutions. Individuals There areThere swaps arefacilitators who large bringbanks togetherandparties withfirms, needswho for theact opposite sides ofin swaps. also dealers, brokerage as principals trades just as theycontracts do in forward contracts. rge business; the total notional principal of swaps is estimated at overIt is$50a latrillion. settlement dates

fixed-rate floating-rate netted

tenor

• • •

How Swaps are Terminated

There are ways terminate a swap prior to its original termination date. Aforwards, cash payment cancan beaccumulate made by one party that isprices acceptable to theratesother party. Li k e swaps value as market or interest change. If the party that has been disadvantaged by the market movements is wicounterparty lling to makeis will a payment of theit,swap'theys value to the ycounterparty, ing to accept can mutuall terminate theandswap.the 2. offers for early termination Just as wiareth forwards, if thethetermsalternati oftheveoriginal counterparty unacceptable, is to enter an offsetting swap. Ifprice our 5-year quarterly-pay flveoating swapswap has two years to go, weourcanfloseek a current on a pay-fi x ed (recei fl o ating) that will provide ating payments and leave us with a fixed-rate liability. four

to

1 . Mutual termination.

Offsetting contract.

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts

Just aswewitrecei h forwards, exixedtinong aourswaporiginal may in5-year volve pay takinflgoatia loss. Consider the casepay where v e 3o/o fi n g swap, but must 4o/o fi x ed on the offsetting swap. We have locked in a loss because we must pay 1 o/o higher ratesquarterly on the offsetti ng swapfor thethannextwe recei vyears, e on theandswap wee nothing are offsetting. We must make payments two recei v i n return. Exiting a swap through an off s etting swap with other than the original counterparty will also expose the investor to default risk, just as with forwards. 3. counterparty It is possible to sell the swap to another party, with the permission of the to the swap.market. This would be unusual, however, as there is not a functioning secondary 4. offsetting Aswap providesis anan option toto enter into aanswap. The optionConsider to enterthat, into iann the option terminate existi n g swap. case ofpaythe fiprevious 5-year pay. Exercising floating swap, we purchased a 3-year call optionswap on ato 2-year x ed swap at 3o/o this swap would give us the offsetting exit our original swap. The cost for such protection is the swaption premium. Resale.

Swaption.

swaption

LOS 64.b: Describe, calculate, and interpret the payments of currency swaps, plain vanilla interest rate swaps, and equity swaps. CPA® Program Curriculum, Volume 6, page 123

Inpayments a from the other one party makes payments denominated in one currency, whi l e the party are made in currencies a second currency. Typically, the notional amounts of the contract, expressed i n both at the current exchange rate, are exchanged at contract initiation and returned at the contract termination date in the same amounts. Aninitiation examplein ofreturn a currency swapmillion. is as follows: Party 1 pays Party 2dates, $10 million athavicontract for On each of the settlement Party 1, ngto received euros, makes payments at a 6o/ o annualized rate in euros on the million Party 2. Party 2 makes payments at an annualized rate of 5o/ o on the $10 million to Party These settlement single 1.currency interest ratepayments swap. are both made. They are not netted as they are in a Aswishes an exampl e ofishwhat motivatesin Australia a currencyandswap,wantsconsider that thea U.costs S. firm,in Australian Party A, to establ operations to finance dollars (AUD). The firmUSD-denominated finds, however, thatdebt,issuing debttheyin AUD is relativelyunknown more in expensive than issuing because are relatively Austral i a n financial markets. An al t ernative to issuing ADD-denominated debt is to issue USD debtfindsandanenter into a USD/AUD currency swap.theThrough a swapsinfacilitator, the U. S . firm Australian firm, Party B, that faces same situation reverse. They wish to issue AUD debt and swap into a USD exposure. There are four available. 1. Party A pays a fi x ed rate on AUD received, and Party B pays a fi x ed rate on USD received. currency swap,

€9.8

€9.8

possible types of currency swaps

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts

2. Parry received.A pays a floating rate on AUD received, and Parry B pays a fixed rate on USD A pays a fi x ed rate on AUD received, and Parry B pays a fl o ati n g rate on USD 3. Parry received. 4. Parry received.A pays a floating rate on AUD received, and Parry B pays a floating rate on USD Following are the steps in a fixed-for-fixed currency swap: The notional principal actualBlyandchanges handsback. at theWhy? beginning ofthethemotivation swap. Party A gi v es USD to Party gets AUD Because of Parry A was to get AUD and the motivation of Parry B was to get USD. Interestianpayments areratemade without netting. Parryof AUD A, whotogotParryAUD, pays B,the Austral interest on the notional amount B. Parry who got toUSD,ParrypaysA. Since the U.theS. inpayments terest rateareonmade the notional amount ofUSDnetting received in di f ferent currencies, is not a typical practice. Ateachtheother termination the swap notional agreementamounts. (maturity), the counterparties give back theofexchanged currency swap are illustrated in Figure 1. The cash flows associated with this Step 1 :

Notional principal is swapped at initiation.

Step 2:

Full interest payments are exchanged at each settlement date, each in a different currency.

Step 3:

Notional principal is swapped

again at the termination ofthe agreement.

Figure 1: Fixed-for-Fixed Curren cy Swap SWAP INITIATION The Australian firm wanes USD.

Swaps AUD for USD

Has or can borrow AUD. Swaps USD for AUD

The U.S. firm wants AUD. Has or can borrow USD.

SWAP INTEREST PAYMENTS TI1e Australian firm

Australian pays USD interest

has use of the USD.

The U.S . firm has use of the AUD.

U.S. firm pays AUD interest SWAP TERM INATION The Australian firm returns

--------+ďż˝

USD returned

the USD borrowed. AUD returned

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The U.S. firm returns the AUD borrowed.

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts

Calculating the Payments on a Currency Swap

swap BBUnited can borrow in the United States for 9o/o, whil e AA has to pay 1 Oo/ o to borrow in the States. AAl becandoing borrowbusiness in Australia for 7o/oa and, whilneeds e BBAUD, has towhipayle8o/AAo towiborrow in Australia. BB wil i n Australi l l be doinneeds g business i1.n0themillion UnitedandStates and needs USD. The exchange rate itos 2AUD/USD. AA USD BB needs AUD2. 0 million. They decide borrow the funds lhave ocallypaidandhadswaptheytheborrowed borrowedinfunds, charging each other the rateperiodthe isother party would the forei g n market. The swap for fi ve years. Calculate the cash flows for this swap. Example: Fixed-for-fixed currency

Answer: AA and BB each go to

their own domestic bank:

AA borrows AUD2.0 million, agreeing to pay the bank 7o/o, or AUD 140,000 annual l y . BBannuall borrows USD 1.0 million, agreeing to pay the bank 9o/o , or USD90, 0 00 y. AA and BB swap currencies: AA gets AUD2. USDI.O0 million, interestininAUD USDannuall annualyly. . BB gets million, agreeing agreeing toto pay pay BBAA 10o/o 8o/o interest •

• •

They pay each other the annual interest: •

AA owes AA BB AUD USD 100, BB owes 160,000000 inin interest interesttoto bebe paid paid onon each each settlement settlement date. date.

They each owe their own bank the annual interest payment: • • •

AA pays the000Australian bankAUD140,000 (but getsAUD160,000 from BB, an AUD20, gain). BBUSD10, pays 0the00U.gain). S. bank USD90,000 (but gets USD100,000 from AA, a They both gain by swapping (AA is ahead AUD20, 0 00 and BB is ahead USD 10,000).

In jive years, they reverse the swap. They return the notionalprincipal. • •

AA gets AUD2. million from fromAABB and and then then pays pays back backthethe Australian BB gets USDI.O0 million U.S. bank. bank.

Interest Rate Swaps

flThe ng-rate) payments. (A foroatianother.

ininvolves volves traditrading ng fixoneed interest for set of florateatingpayments rate payments

plain vanilla interest rate swap basis swap

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts

Thetheparty who wants flotheatinswap. g-rateTheinterest payments who agreesreceives to paythefixed-rate interest andand has si d e of counterparty, fi x ed payments agrees to pay variable-rate interest, has the side of the swap and is called the flat orTheplusfloating a spread.rate quoted is generally the Let's look at the cash flows that occur in a notional principal is thetosame for both counterparties and is iBecause n the samethe currency units, thereswapped iins sinonglneed actually exchange the cash. eatcurrency swaps. of the settlement The determi n ati o n of the variabl e rate is the beginning period, and the cash interest payment is made at the end of the settlement period. Because the interest payments are ithen thecash.sameThecurrency, therebetween is no need forxed-rate both counterparties to actual l y transfer di f ference the fi payment and the variable-rate payment is calculated and paid to the appropriate counterparty. Atno thetransfer conclusion of funds.of the swap, since the notional principal was not swapped, there is You loses.should note that swaps are a zero-sum game. What one party gains, the other party The net is:formula for the based on a 360-day year and a floating rate of ( ) (=( 360 If this Ifnumber is positive, the fixed-rate payer apayer net payment toa nettheflow floating-rate party. this number is negative, then the fixed-rate from the floating-rate payer. pay-fixed

pay-floating

floating-rate payer.

London Interbank Offered Rate (LIBOR),

plain vanilla interest rate swap.

Notional

principal is generally not swapped

Net interest is paid by the one who owes it.

fixed-rate payer,

LIBOR

(net fixed-rate payment)

swap fixed rate - LIBOR c-l )

number of days

(notional principal)

owes

receives

Professor's Note: For the exam, remember that with plain vanilla swaps, one party pays fixed and the other pays a floating rate. Sometimes swap payments are based on a 365-day year. For example, the swap will specify whether 90/360 or 90/365 should be used to calculate a quarterly swap payment. Remember, these are custom instruments. Example: Interest rate risk

Consi d er a bank. Its deposi t s represent liabilities and are most li k el y short term in Inloans. other words, deposits represent floofating-rate liabilities. The bank assets are prinature. m arily Most loans carry fi x ed rates interest. The bank assets are fi x ed-rate and bank liabilities are fl o ating. Explai n the nature of the interest rate ri s k that the bank faces, and describe how an interest rate swap may be used to hedge this risk. ©20 12

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts

Answer: The risk the bank faces i s that short-term interest rates will rise, causing cash payment depositsrates to increase. This would not beloana major problem ifwilcashl not.inflows albank so increase asonremains interest ri s e, but with a fi x ed-rate portfoli o they If the unhedged as interest rates rise, cash outflows rise and bank profits fall. The bank can hedge thi s ri s k by entering into a fi x ed-for-fl o ating swap as the fi x ed-rate payer. Theonflodeposits. ating-rateNote payments received would offsets costs any idoncrease in thestillfloating-rate payments that if rates fall, the bank' not. They pay fitoxed fortheirthelower termcosts of theonswap and recei v e (l o wer) fl o ati n g-rate payments that correspond deposits. Calculating the Payments on an Interest Rate Swap

Example: Calculating the payments on an interest rate swap Bank A enters intoat aafi$1,xed000,rate0of006%quarterly-pay plai n vanilla interest rate swap aspayer the fiagrees xed-rate payer based on a 360-day year. The fl o ating-rate to pay 90-day LIBOR plus a 1 o/o margin; 90-day LIBOR is currently 4%. now 90-day LIBOR rates are: 5.0% 4.5% 90180daysdaysfrom from now 360 days days from from now now 6.5.5% 0% 270 Calculate the amounts Bank A pays or receives 90, 270, and 360 days from now. Answer: The payment 90 days from now depends on current LIBOR and the fixed rate (don' t forget the 1 o/o margin). Fixed-rate payer pays: [o.o6 (;;o)-(o.o4 o.o1)(;6°0 )jx 1,ooo,ooo = $2,500 +

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts

270 days from now, the payment i s based on LIBOR 180 days from now, whi c h is 5%. Addi makes payment. the floating-rate 6%, which is equal to the fixed rate, so therenigs nothenet1%thimargin rd quarterly The bank's "payment" 360 days from now is: [o.o6(;6°0 )-(0.055 o.o 1)(;6°0 )] 1,ooo,ooo -$1,250 Because ating-rate payment $1,250 atthetheflofourth payment date.exceeds the fixed-rate payment, Bank A will +

x

=

receive

Equity Swaps

Inby anoneequity swap, the return on a stock, a portfolio, or a stock index is paid each period party in returnorfortheatotal fixed-rate orincluding floating-rate payment. Thestock, returnportfolio, can be theor capital appreciation return dividends on the index. Inpayorder to reduce equity risk, a portfolio manager might enter into a 1-year quarterly­ S&Peach500quarter indexisswap andagainst agree tothereceive a fixedto determine rate. The percentage increase in the index netted fixed rate the payment to be made. Ifinthethe index return is negative,manager. the fixed-rate payeramong mustswaps, also payequity the percentage decline index to the portfolio Uniquely swap payments can be floating on bothratesidesswaps, and thebothpayments areandnotfloating knownpayments until the areendknown of the at the quarter. With interest the fixed beginning of period for which they will be paid. Aoverswaptheonperiod a singleof thestockswap.canTobe protect motivateda large by acapital desire gain to protect the value of a position in ana single stock, and to avoid aequity-returns sale for tax orpayer controlandreasons, an investor could enter into equity swap as the receive a fixed rate i n return. Any decline i n the stock price would be paid to thetheinvestor the settlement dates, pluslessthethefixed-rate payment. If the stock appreciates, investoratmust pay the appreciation fixed payment.

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts

Calculating the Payments on an Equity Swap

Example: Equity swap payments Ms. Smi t h enters into a 2-year $10 million quarterly swap as the fi x ed payer and will receive they atindex return on theof theS&Pnext500.three Thequarters, fixed ratetheis 8%, andleveltheis:in1030, dex is 968, currentl 986. At the end i n dex and 989. Cal c ul a te the net payment for each of the next three quarters and identify the direction of the payment. Answer: The percentage change in the index each quarter, Q, is: Q1 = 4.46%, Q2 = -6.02%, and Q3 = 2.17%. The index return payer will receive 0. 0 8 I 4 = 2% each quarter and pay the index return, therefore: Q1: Index Index return return payer payer pays 4.46% - 2.02.0%00%= 2.=46% or $246, 000.000. Q2: receives 6. 0 2% 8. 0 2% or $802, Q3: Index return payer pays 2.17% - 2.00% = 0.17% or $17,000. +

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts

KEY CONCEPTS

LOS 64.aare based on a notional amount of principal. Each party is obligated to pay a Swaps percentage return onPercentage the notionalpayments amountareat periodic settlement datesfiover the liorfe the (tenor) of the swap. based on a fl o ating rate, x ed rate, return on an equity index or portfolio. Except in periodic the case ofpayments a currencyare swap, no(themoney changes hands atargerthe amount inceptionpaysof thethe swap and netted party that owes the l difference to the other). Swaps instruments, are largely(defaul unregulated, markets,areandcustom are subject to counterparty t) risk. do not trade in secondary SwapsEntering can be into terminated prior toswap,theirsometimes stated termination datesa by:swaption (most an offsetting by exercising common).with the counterparty to terminate (likely involves making or receiving Agreeing compensation). Selling the swap to a third party with the consent of the original counterparty (uncommon). 64.b vanilla (fixed-for-floating) interest-rate swap, one party agrees to pay a floating InLOS a plain rate of interest on the notional amount and the counterparty agrees to pay a fi x ed rate of interest. The formula for the net payment by the fi x ed-rate payer, based on a 360-day year and the number of days in the settlement period is: (net fixed rate payment )r = (swap fixed rate-LIBORr-I ) ( number360of days ) (notional principal) In an equityor swap, thein exchange returns payer makes payments basedpayments. on the return onstock, a stock, portfolio, index, for fi x edor fl o ating-rate If the portfolio, or index,anddeclines in value the returns interest payment a payment basedoveron thethe period, percentage decline payer in value.receives the In thea currency swap,of thetheswap, notional principal (in two differentin twocurrencies) iscurrencies exchangedare atexchanged inception periodic i n terest payments different on settlement dates, and the same notional amounts are exchanged (repaid) on the termination date of the swap. •

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts

CONCEPT CHECKERS

1. A.WhichIn anof ithenterest following statements about principal swaps is is swapped.correct? rate swap, the notional B.C. The defaulvanill t problem is theratemostswap,important In a plain a interest fixed rateslimitation are tradedto thefor swap variablemarket. rates. following statements about swaps is correct? 2. A.WhichTheoftimethe frame of a swap i s cal l e d i t s tenor. currency swap, swap, only net interest payments are made. B.C. InIn aa currency the notional principal is actually twice, once at the beginning of the swap and again at the terminationswapped of the swap. oflithettlefollowing statements is an advantage of swaps? Swaps: 3. Which A.B. have or no regulation. minimize defaultcontracts. risk. C. have customized 4. A.In ansettlequity swap: e ment i s made only at swap termination. notionalforprincipal. B.C. shares returnsareonexchanged an index canforbetheswapped fixed-rate payments. vanillaprincipal interest rateis swapped. swap: 5. A.In atheplainnotional the net iprincipal nterest payments B.C. only the notional is returnedareatmade. the end of the swap. the follorate wingswap statements about swap markets is correct? 6. A.WhichIn anofinterest only the net interest i s exchanged. notional principal is swapped at inception and at termination of a B. The currency swap. C. exchanged Only the netin dia fcurrency ference between swap. the dollar interest and the foreign interest is least likely

least likely

least likely

least likely

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts

Use the following data to answer Questions 7 through Consider a 3-year units annualandcurrency swap(USF) that takes place betweenunits. a foreign firmthe(FF) wirate thpayer FC currency a U. S . firm with $ currency USF is fixed­ andandFF8o/ois theat thefloating-rate payer. The fixed interest rate5%atcurrently; the initiation ofthethe swap i s 7%, end of the swap. The variable rate i s 6o/o at endswap, of year$1.1;08o/omillion at theisendexchanged of year 2;at and 7% at therateendofofFC2. year03.= At$1.the0 . Atbeginning of the an exchange the end of the swap period, the exchange rate is FC 1.5 = $1.0. Note: Wiinterest th thisrates. currency swap, end-of-period payments are based on beginning-of­ period the initiation of the swap, which of the following statements is 7. Atcorrect? FF gigivesvesUSFFF $1.0 million. A.B. USF $1.0 million. C. USF gives FF FC2.0 million. 8. AtA. theUSFendpaysof year 2: FC140, 000;00;FFFFpayspays$70,$60,0000.00. B.C. USF USF pays FC60, 0 pays USD70,000; FF pays FC60,000. 9. Atamounts? the termination of the swap, FF gives USF which of the following notional A.B. $1FC2,million. 000,0000.00. C. FC1,500, of year 3, FF wi l l pay whi c h of the followi n g total amounts? 10. A.At the$1,end B.C. FC2, $1,0070,80,160,0000.00.000 10.

most likely

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Study Session 17 Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts

13. Lambda Corp.quarterly-pay has a floating-rate liability and wants a fixed-rate exposure. Theypayer. enter into a 2-year $4,000, 0 00 fixed-for-floating swap as the fixed-rate The Gamma Corp. The is 6o/o year. and theRealizations floating rateofLIBOR is 90-dayare: LIBORcounterparty 1 o/o, withisboth calculated basedfixedon arate360-day Annualized LIBOR 5.0% Current InIn 21 quarter 5.5% quarters 5.4% InIn 34 quarters 5.8% quarters 6.0% first swap payment is: 11. A.Thefrom Gamma to Lambda.of the swap. B. known at the initiation $5,000. second from net swap payment is: 12. A.The$5,000 Lambda to Lambda. Gamma. 000 from Gamma to B.C. $4,$5,000 from Gamma to Lambda. fi f th net quarterly payment on the swap is: 13. The A.B. 0.$10,000. $40,000. Use the following information to answer Questions 11 through

+

c.

c.

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Study Session 1 7 Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts

ANSWERS - CONCEPT CHECKERS 1.

A

In an interest rate swap, the notional principal is only used to calculate the interest payments and does not change hands. The notional principal is only exchanged in a currency swap.

2.

B

In a currency swap, payments are not netted because they are made in different currencies. Full interest payments are made, and the notional principal is also exchanged.

3.

B

Swaps do not minimize default risk. Swaps are agreements between two or more parties, and there are no guarantees that one of the parties will not default. Note that swaps do give traders privacy and, being private transactions, have little to no regulation and offer the ability to customize contracts to specific needs.

4.

C

Equity swaps involve one party paying the return or total return on a stock or index periodically in exchange for a fixed return.

5.

B

In a plain vanilla interest rate swap, interest payments are netted. Note that notional principal is not exchanged and is only used as a basis for calculating interest payments.

6.

C

In a currency swap, full interest payments are made, and the notional principal is exchanged.

7.

B

Because this is a currency swap, we know that the notional principal is exchanged. Because USF holds dollars, it will be handing over dollars to FF.

8.

A

Remember, the currency swap is pay floating on dollars and pay fixed on foreign. Floating at the end of year 1 is 6o/o of $ 1 .0 million. Since payments are made in arrears, FF pays $60,000 and USF pays FC140,000 at the end of year 2.

9.

A

The notional principal is exchanged at termination. FF gives back what it borrowed, $ 1 .0 million, and the terminal exchange rate is not used.

10. A

FF is the floating-rate dollar payer. FF will pay the return of $ 1 . 0 million in principal at the termination of the swap, plus the floating rate payment (in arrears) of 8% x $ 1 .0 million $80,000. The total payment will be $ 1 ,080,000. =

11. B

The first payment is based on the fixed rate and current LIBOR + 1 o/o, which are both 6o/o. There is no net payment made at the first quarterly payment date and this is known at the initiation of the swap.

12. C

The second quarter payment is based on the realization of LIBOR at the end of the first 90 4, 000,000 = $65,000. The fixed quarter, 5.5%. The floating rate is: (5.5% + 1 o/o) 360

( )

rate payment is $60,000, making the net payment $5,000 from Gamma to Lambda. 13. B

The fifth quarterly floating-rate payment is based on the realization of LIBOR at the end of the fourth quarter, which is 6o/o. With the 1 o/o margin, the floating rate is 7o/o compared to 6o/o fixed, so the net payment is $ 1 0,000.

Š20 12 Kaplan, Inc.

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The following is a review of the Derivatives principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in:

RISK MANAGEMENT APPLICATIONS OF OPTION STRATEGIES Study Session 17 EXAM Focus

The mostdiaigrams mportantfor aspect ofputthiors topi c erevicalelwpositions is the interpretation ofoption profi t diarevi grams.ew. Payoff singl e si n gl were covered in our options Inththioptions. s review,Inwea protective introduce put profiposition, t diagramsweandcombine two option strategi es andthatacombine stock wistrategy, a share of stock put. With this we essenti a l y purchase downsi d e protection for the stock (li k e insurance). A covered positing othen consists of buyingona share of stockin return and selliforntheg a caladded l on income it. This from strategytheequates tothecallsellicall. upside potential the stock salebutof On the Level CFA® Exam, you wi l not be required to draw payoff di a grams, you are expected to know how to interpret them and fi n d the breakeven price, maxi m um gains and losses, and the gains and losses for any stock price at option expiration. I

LOS 65.a: Determine the value at expiration, the profit, maximum profit, maximum loss, breakeven underlying price at expiration, and payoff graph of the strategies of buying and selling calls and puts and determine the potential outcomes for investors using these strategies. CPA® Program Curriculum, Volume 6, page 144

C