TEST BANK for Derivatives Markets 3rd Edition by Robert L. McDonald. ISBN 9780133468786. All Chapter

Derivatives Markets, 3e (McDonald) Chapter 1 Introduction to Derivatives 1.1 Multiple Choice 1) Which of the following is not a derivative instrument?

A) Contract to sell corn B) Option agreement to buy land C) Installment sales agreement D) Mortgage backed security Answer: C 2) Who from the following list would be considered a speculator by entering into a futures or options contract on commodities?

A) Farmer B) Corn delivery truck driver C) Food manufacturer D) None of the above Answer: B 3) A mutual fund is engaged in the short term and temporary purchase of index futures, for purposes of minimizing its cash exposures. Which "use" most closely explains their actions?

A) Risk management B) Speculation C) Reduced transaction costs D) Regulatory arbitrage Answer: C 4) During the growing season, a corn farmer sells short corn futures contracts in an amount equal to her crop. If upon harvesting and selling her crop she maintains the contracts, she is then considered a(n): A) Hedger B) Speculator C) Arbitrager D) None of the above Answer: B 5) All of the following are financially engineered products, except: A) Mortgage B) Mortgage backed security C) Interest only D) Principal only Answer: A

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6) Select the family member who is offering the most diversification to the rest of the family.

A) Dad works for General Motors B) Mom works for Goodyear C) Daughter works for Jiffy Lube D) Son works for Eli Lilly & Company Answer: D 7) What is the cost of 100 shares of Jiffy, Inc. stock given that the bid-ask prices are $31.25 - $32.00 and a $15.00 commission per transaction exists?

A) $3215 B) $3140 C) $3125 D) $3200 Answer: A 8) Assume that you purchase 100 shares of Jiffy, Inc. common stock at the bid-ask prices of $32.00 - $32.50. When you sell, the bid-ask prices are $32.50 - $33.00. If you pay a commission rate of 0.5%, what is your profit or loss?

A) $0 B) $16.25 loss C) $32.50 gain D) $32.50 loss Answer: D 9) Assume that you open a 100-share short position in Jiffy, Inc. common stock at the bid-ask price of $32.00 - $32.50. When you close your position, the bid-ask prices are $32.50 - $33.00. If you pay a commission rate of 0.5%, what is your profit or loss on the short investment?

A) $32.50 gain B) $16.25 loss C) $132.50 loss D) $100.00 gain Answer: C 10) Assume that you open a 100-share short position in Jiffy, Inc. common stock at the bid-ask prices of $32.00 - $32.50. When you close your position, the bid-ask prices are $32.50 - $33.00.

You pay a commission rate of 0.5%. The market interest rate is 5.0% and the short rebate rate is 3.0%. What is your additional gain or loss due to leasing the asset?

A) $64.00 loss B) $160.00 loss C) $96.00 gain D) $0 Answer: A

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11) Assume that an investor lends 100 shares of Jiffy, Inc. common stock to a short seller. The bid-ask prices are $32.00 - $32.50. When the position is closed, the bid-ask prices are $32.50 - $33.00. The commission rate is 0.5%. The market interest rate is 5.0% and the short rebate rate is 3.0%. Calculate the gain or loss to the lender. Assume the lender is not subject to a bid-ask loss or commissions.

A) $164.00 gain B) $164.00 loss C) $100.00 gain D) $100.00 loss Answer: A 12) According to trading volume data tabulated by the Wall Street Journal for April 15, 2010, which index futures contact experienced the highest total open interest?

A) DJ Industrial Average B) S&P 500 Index C) Mini S&P 500 D) Mini Nasdaq 100 Answer: C 13) A firm provides a service that benefits from decreasing employment. This firm has a risk exposure to macro event. All other variables being equal, which of the following derivative securities is the firm most likely use to hedge its exposure?

A) Short position in an economic futures B) Long position in an economic futures C) Short position in an interest rate futures D) Long position in an interest rate futures Answer: B 1.2 Short Answer Essay Questions 1) Why might a variable rate mortgage be considered a "derivative" and a fixed rate mortgage not?

Answer: The pure definition of a derivative is one in which its value is determined by the price of another item. ARMs often use LIBOR to determine their value, thus have their values "derived" from another security. This answer may, of course, be splitting hairs.

2) Why would a corn farmer, who maintains a short futures contract after harvesting and selling her crop, be considered a speculator?

Answer: The farmer was a hedger until she sold her crop. Her perspective then changed since she no longer had an asset to hedge. Her naked contract is now a speculation.

3) For families employed and living in "company towns" (i.e., where the major employer owns all homes, retail stores, etc.), explain the lack of diversification.

Answer: Since the large local employer owns all retail establishments, the demise of the company will cause the demise of the entire town. Distribution of ownership would reduce the impact of a company failure.

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4) Describe the concept of a bid-ask spread and how that impacts the cash flows of an investor.

Answer: In some markets, especially OTC, dealers complete transactions. Buyers of stock pay the higher of the spread and sellers receive the lower price in the spread. The difference is the dealer's profit.

5) What would cause the spread between the market rate of interest and the repo rate to be small?

Answer: If there is a low demand to short sell a security or a large supply of the security repo rates will be higher due to lack of demand for short instruments.

1.3 Class Discussion Question 1) Discuss the origins of derivatives in terms of risk reduction using the concept of evolution to integrate the additional uses of derivatives into the discussion. Conclude by asking students to list methods by which third parties could make fees by interjecting themselves into the process.

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Derivatives Markets, 3e (McDonald) Chapter 2 An Introduction to Forwards and Options 2.1 Multiple Choice 1) The spot price of the market index is $900. A 3-month forward contract on this index is priced at $930. What is the profit or loss to a short position if the spot price of the market index rises to $920 by the expiration date?

A) $20 gain B) $20 loss C) $10 gain D) $10 loss Answer: C 2) The spot price of the market index is $900. A 3-month forward contract on this index is priced at $930. The market index rises to $920 by the expiration date. The annual rate of interest on treasuries is 2.4% (0.2% per month). What is the difference in the payoffs between a long index investment and a long forward contract investment? (Assume monthly compounding.)

A) $10.84 B) $24.59 C) $26.40 D) $43.20 Answer: B 3) The spot price of the market index is $900. A 3-month forward contract on this index is priced at $930. The annual rate of interest on treasuries is 2.4% (0.2% per month). What annualized rate of interest makes the net payoff zero? (Assume monthly compounding.)

A) 4.8% B) 8.5% C) 11.2% D) 13.2% Answer: D 4) The spot price of the market index is $900. After 3 months, the market index is priced at $920.

An investor has a long call option on the index at a strike price of $930. After 3 months, what is the investor's profit or loss?

A) $10 loss B) $0 C) $10 gain D) $20 gain Answer: B

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5) The spot price of the market index is $900. After 3 months the market index is priced at $920.

The annual rate of interest on treasuries is 2.4% (0.2% per month). The premium on the long put, with an exercise price of $930, is $8.00. What is the profit or loss at expiration for the long put?

A) $2.00 gain B) $2.00 loss C) $1.95 gain D) $1.95 loss Answer: C 6) The spot price of the market index is $900. After 3 months the market index is priced at $920.

The annual rate of interest on treasuries is 2.4% (0.2% per month). The premium on the long put, with an exercise price of $930, is $8.00. At what index price does a long put investor have the same payoff as a short index investor? Assume the short position has a breakeven price of $930.

A) $921.90 B) $930.00 C) $938.05 D) $940.00 Answer: C 7) All of the positions listed will benefit from a price decline, except: A) Short put B) Long put C) Short call D) Short stock Answer: A 8) The spot price of the market index is $900. The annual rate of interest on treasuries is 2.4% (0.2% per month). After 3 months the market index is priced at $920. An investor has a long call option on the index at a strike price of $930. What profit or loss will the writer of the call option earn if the option premium is $2.00?

A) $2.00 gain B) $2.00 loss C) $2.01 gain D) $2.01 loss Answer: C 9) The spot price of the market index is $900. After 3 months the market index is priced at $915.

The annual rate of interest on treasuries is 2.4% (0.2% per month). The premium on the long put, with an exercise price of $930, is $8.00. Calculate the profit or loss to the short put position if the final index price is $915.

A) $15.00 gain B) $15.00 loss C) $6.95 gain D) $6.95 loss Answer: D

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10) If your homeowner's insurance premium is $1,000 and your deductible is $2000, what could be considered the strike price of the policy if the home has a value of $120,000?

A) $118,000 B) $120,000 C) $117,000 D) $122,000 Answer: A 11) A put option is purchased and held for 1 year. The Exercise price on the underlying asset is $40. If the current price of the asset is $36.45 and the future value of the original option premium is (-$1.62), what is the put profit, if any, at the end of the year?

A) $1.62 B) $1.93 C) $3.55 D) $5.17 Answer: B 12) The premium on a long term call option on the market index with an exercise price of 950 is $12.00 when originally purchased. After 6 months the position is closed, and the index spot price is 965. If interest rates are 0.5% per month, what is the Call Payoff?

A) $2.64 B) $12.00 C) $12.36 D) $15.00 Answer: D 13) The premium on a call option on the market index with an exercise price of 1050 is $9.30 when originally purchased. After 2 months the position is closed, and the index spot price is 1072. If interest rates are 0.5% per month, what is the Call Profit?

A) $9.30 B) $9.39 C) $12.61 D) $22.00 Answer: C 2.2 Short Answer Essay Questions 1) The spot price of the market index is $900. A 3-month forward contract on this index is priced at $930. Draw the payoff graph for the short position in the forward contract.

Answer:

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2) An investor has a long call option on the market index at a strike price of $930. At expiration the index price is $920. Explain the profit and loss.

Answer: The long call investor has the right, not the obligation, to exercise. Thus, she will elect to let the option expire unexercised and realize no profit or loss.

3) The spot price of the market index is $900. After 3 months the market index is priced at $920.

The annual rate of interest on treasuries is 4.8% (0.4% per month). The premium on the long put, with an exercise price of $930, is $8.00. Draw the payoff graph for the long put position at expiration. Include strike price, breakeven price, and max loss.

Answer:

4) Develop the payoff table for the previous question, using at least five different possible index prices, in addition to the strike price and breakeven price.

Answer:

5) As with Chrysler Corp. many years ago, the government occasionally guarantees loans. What option is the government granting and to whom in a loan guarantee?

Answer: The government is giving the banks (or lenders) a put option. If the borrower defaults (thus the price of the loan drops) the banks may exercise their put options and sell the loans to the government.

2.3 Class Discussion Question 1) Engage the class in a conversation about auto insurance. Why do people feel their premium is wasted if they do not file a claim? Steer the class towards an understanding of put options and potential gain should a loss occur. It may also be beneficial to ask students to relate insurers' pooling of losses with the concept of risk management.

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Derivatives Markets, 3e (McDonald) Chapter 3 Insurance, Collars, and Other Strategies 3.1 Multiple Choice 1) A strategy consists of buying a market index product at $830 and longing a put on the index with a strike of $830. If the put premium is $18.00 and interest rates are 0.5% per month, what is the profit or loss at expiration (in 6 months) if the market index is $810?

A) $20.00 gain B) $18.65 gain C) $36.29 loss D) $43.76 loss Answer: D 2) A strategy consists of buying a market index product at $830 and longing a put on the index with a strike of $830. If the put premium is $18.00 and interest rates are 0.5% per month, compute the profit or loss from the long index position by itself expiration (in 6 months) if the market index is $810.

A) $45.21 loss B) $21.22 loss C) $18.00 gain D) $24.25 gain Answer: A 3) A strategy consists of buying a market index product at $830 and longing a put on the index with a strike of $830. If the put premium is $18.00 and interest rates are 0.5% per month, compute the profit or loss from the long put position by itself (in 6 months) if the market index is $810.

A) $3.45 gain B) $1.45 gain C) $2.80 loss D) $1.36 loss Answer: B 4) A strategy consists of buying a market index product at $830 and longing a put on the index with a strike of $830. If the put premium is $18.00 and interest rates are 0.5% per month, what is the estimated price of a call option with an exercise price of $830?

A) $42.47 B) $45.26 C) $47.67 D) $49.55 Answer: A

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5) A strategy consists of longing a put on the market index with a strike of 830 and shorting a call option on the market index with a strike price of 830. The put premium is $18.00 and the call premium is $44.00. Interest rates are 0.5% per month. Determine the net profit or loss if the index price at expiration is $830 (in 6 months).

A) $0 B) $23.67 loss C) $26.79 gain D) $28.50 gain Answer: C 6) A strategy consists of longing a put on the market index with a strike of 830 and shorting a call option on the market index with a strike price of 830. The put premium is $18.00 and the call premium is $44.00. Interest rates are 0.5% per month. What is the breakeven price of the market index for this strategy at expiration (in 6 months)?

A) $802.12 B) $830.00 C) $855.21 D) $866.32 Answer: C 7) At the 6-month point, what is the breakeven index price for a strategy of longing the market index at a price of 830? Interest rates are 0.5% per month.

A) $802.12 B) $830.00 C) $855.21 D) $866.32 Answer: C 8) The $850 strike put premium is $25.45 and the $850 strike call is selling for $30.51. Calculate the breakeven index price for a strategy employing a short call and long put that expires in 6 months. Interest rates are 0.5% per month.

A) $822.67 B) $824.79 C) $830.76 D) $875.82 Answer: B 9) What is the maximum profit that an investor can obtain from a strategy employing a long 830 call and a short 850 call over 6 months? Interest rates are 0.5% per month.

A) $6.80 B) $7.68 C) $9.24 D) $12.32 Answer: B

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10) What is the maximum loss that an investor can obtain over 6 months from a strategy employing a long 830 call and a short 850 call? Interest rates are 0.5% per month.

A) $6.80 B) $7.68 C) $9.24 D) $12.32 Answer: D 11) What is the breakeven point that an investor can obtain from a 6-month strategy employing a long 830 call and a short 850 call? Interest rates are 0.5% per month.

A) $832.82 B) $842.32 C) $852.22 D) $862.92 Answer: B 12) The owner of a house worth $180,000 purchases an insurance policy at the beginning of the year for a price of $1,000. The deductible on the policy is $5,000. If after 6 months the homeowner experiences a casualty loss valued at $45,000, what is the homeowner's net gain/loss? Assume an opportunity cost of capital of 4.0% annually.

A) $0 B) $1,000 C) $5,000 D) $6,020 Answer: D 13) Using option strategy concepts, what is the value of an insured home, if the value of the uninsured home is $220,000, the house was purchased for $180,000 and the house has a casualty policy costing $500 with a $2,000 deductible? Ignore interest costs.

A) $180,000 B) $217,500 C) $220,000 D) $222,500 Answer: B 14) An investor purchases a call option with an exercise price of $55 for $2.60. The same investor sells a call on the same security with an exercise price of $60 for $1.40. At expiration, 3 months later, the stock price is $56.75. All other things being equal and given an annual interest rate of 4.0%, what is the net profit or loss to the investor?

A) $1.21 loss B) $1.50 loss C) $0.54 gain D) $1.65 gain Answer: C

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3.2 Short Answer Essay Questions 1) Explain how a long stock and long put strategy equals the cash flow from a long call strategy.

Answer: The net effect of the long put and long stock creates a cash flow identical to the long call, provided you include the cost of funds.

2) Why might the manager of a portfolio employ a protective put strategy?

Answer: If the manager desires to protect against a price decline, but is restricted from selling assets, a long put creates a floor below which losses cannot occur.

3) What is the difference between naked and covered call writing?

Answer: A covered position is one in which the individual also owns the underlying asset in addition to the short call. A naked position involves writing the call alone.

4) What are the similarities and differences between bear and bull spreads?

Answer: Both have floors and ceilings. The bear position has a ceiling where prices are falling and a floor where prices rise. A bull spread has the opposite floor and ceiling.

5) Why is a straddle position considered a speculation on the asset's volatility?

Answer: The strategy loses money if prices stay constant, but benefits from large changes in prices, either up or down.

3.3 Class Discussion Question 1) Compare the butterfly spread, bear spread, bull spread, covered call, straddle, and other strategies. Is any one strategy better than another? Are there trade-offs between each that is almost perfect or do significant advantages exist from one strategy to another?

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Derivatives Markets, 3e (McDonald) Chapter 4 Introduction to Risk Management 4.1 Multiple Choice 1) To plant and harvest 20,000 bushels of corn, Farmer Jayne incurs fixed and variable costs totaling $33,000. The current spot price of corn is $1.80 per bushel. What is the profit or loss if the spot price is $1.90 per bushel when she harvests and sells her corn?

A) $3,000 gain B) $3,000 loss C) $5,000 gain D) $5,000 loss Answer: C 2) Farmer Jayne decides to hedge 10,000 bushels of corn by purchasing put options with a strike price of $1.80. Six-month interest rates are 4.0% and the total premium on all puts is $1,200. If her total costs are $1.65 per bushel, what is her marginal change in profits if the spot price of corn drops from $1.80 to $1.75 by the time she sells her crop in 6 months?

A) $248 loss B) $0 C) $252 gain D) $1,500 loss Answer: B 3) A 6-month forward contract for corn exists with a price of $1.70 per bushel. If Farmer Jayne decides to hedge her 20,000 bushels of corn with the forward contract, what is her profit or loss if spot prices are $1.65 or $1.80 when she sells her crop in 6 months? Her total costs are $33,000.

A) $1,000 gain or $1,000 loss B) $0 gain or $3,000 gain C) $0 loss or $3,000 loss D) $1,000 gain or $1,000 gain Answer: D 4) Corn call options with a $1.75 strike price are trading for a $0.14 premium. Farmer Jayne decides to hedge her 20,000 bushels of corn by selling short call options. Six-month interest rates are 4.0% and she plans to close her position in 6 months. What is the total premium she will earn on her short position?

A) $2,800 B) $2,912 C) $800 D) $1,600 Answer: B

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5) Two 6-month corn put options are available. The strike prices are $1.80 and $1.75 with premiums of $0.14 and $0.12, respectively. Total costs are $1.65 per bushel and 6-month interest rates are 4.0%. Farmer Jayne wishes to hedge 20,000 bushels for 6 months. What is the highest profit or minimum loss between the two options if the spot price in 6 months is $1.70 per bushel?

A) $88 loss B) $88 gain C) $496 loss D) $496 gain Answer: B 6) Corn call options with a $1.70 strike price are trading for a $0.15 premium. Farmer Jayne decides to hedge her 20,000 bushels of corn by selling short call options. Six-month interest rates are 4.0% and she plans to close her position and sell her corn in 6 months. What is her profit or loss if spot prices are $1.60 per bushel when she closes her position?

A) $1,000 loss B) $2,000 gain C) $2,120 loss D) $2,120 gain Answer: D 7) When selecting among various put options with different strike prices, in order to hedge a long asset position, which of the following statements is true?

A) Higher strike puts cost more and provide higher floors B) Higher strike puts cost less and provide higher floors C) Lower strike puts cost more and provide higher floors D) Lower strike puts cost less and provide higher floors Answer: A 8) Which of the following situations does NOT describe someone who should implement a hedge strategy?

A) Mary is very nervous about losing profits if selling prices drop B) Melanie's creditors will not lend her money if her crops might lose money C) Katherine's board of directors will not tolerate losses, even if it means profits are smaller D) Dawn wants to reduce price fluctuations, but will need to conduct many transactions to achieve her goals Answer: D 9) KidCo Cereal Company sells "Sugar Corns" for $2.50 per box. The company will need to buy 20,000 bushels of corn in 6 months to produce 40,000 boxes of cereal. Non-corn costs total $60,000. What is the company's profit if they purchase call options at $0.12 per bushel with a strike price of $1.60? Assume the 6-month interest rate is 4.0% and the spot price in 6 months is $1.65 per bushel.

A) $6,504 profit B) $8,005 loss C) $12,064 profit D) $11,293 loss Answer: A 2 Copyright © 2013 Pearson Education, Inc.

10) KidCo bought forward contracts on 20,000 bushels of corn at $1.65 per bushel. Corporate tax rates are 35.00%. Revenue is $100,000 and other costs are $60,000. Spot prices on corn are $1.75 per bushel. Calculate the after-tax net income.

A) $7,000 loss B) $7,000 gain C) $4,550 loss D) $4,550 gain Answer: D 11) Farmer Jayne bought a $1.70 strike put option for $0.11 and sold a $1.75 strike call option for a premium of $0.14. Her total costs are $1.65 per bushel and interest rates are 4.0% over this period. What is the floor in her strategy assuming a 20,000-bushel crop?

A) $624 B) $1,624 C) $2,624 D) $3,624 Answer: B 12) A $1.75 strike call option has a $0.14 premium. The $1.75 strike put option premium is $0.12. What is the net cost for Farmer Jayne to create a synthetic short forward contract?

(Assume 4.0% interest.)

A) $0.0208 B) -$0.0208 C) $0.000 D) -$0.0424 Answer: A 13) A farmer expects to harvest 800,000 bushels of corn. To eliminate price risk, the farmer elects to short corn futures. What would cause the farmer to short only 720,000 bushels of corn?

A) Basis risk B) Illiquid futures markets C) Margin requirements D) Quantity uncertain Answer: D 14) Given a 25% chance of a 600,000 bushel yield and a 75% chance of a 500,000 bushel yield, what quantity should the farmer hedge in order to protect against an uncertain harvest? Assume the farmer is willing to take reasonable risk.

A) 0 B) 500,000 C) 525,000 D) 600,000 Answer: C

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15) A farmer sells 4 million bushels of corn at a spot price of $2.10 per bushel. The total cost of production was $9.2 million. The farmer has an effective tax rate of 25%. If the farmer entered into a futures contract at a price of $2.40 per bushel on 4 million bushels, what is the farmer's net loss or gain?

A) $100,000 loss B) $800,000 loss C) $300,000 gain D) $400,000 gain Answer: C 4.2 Short Answer Essay Questions 1) From a strictly conceptual perspective, why would any manufacturer consider hedging their variable costs? Answer as if you own the company.

Answer: I manufacture a product. Profits come from selling at the market-determined price, which is above my production costs. Without hedging, my profit is influenced by commodity price fluctuations, which are outside the expertise of running my business. Thus, I hedge that risk.

2) Why would a manufacturer elect to use a long call strategy instead of a forward contract to hedge the risk associated with variable costs?

Answer: The long call strategy allows the manufacturer to benefit from price declines, while still maintaining a hedge against price increases.

3) Explain the relationship between options costs and profits under a put option insurance strategy.

Answer: The higher strike puts have higher premiums since they are deeper in the money. Deep in-the-money puts have higher profit potential as prices decline. Lower strike puts cost less, but have reduced profit potential.

4) Why are managerial controls over option and forward trading departments vital to proper risk control?

Answer: Hedging requires matching derivative trading activities with the operations of the company. Trading that is not matched to the firm's business is speculation and increases the firm's risk.

5) Why are synthetics created and/or calculated when the actual derivative is available?

Answer: The pricing of a synthetic may reveal an arbitrage opportunity, or at least a cheaper method, by which to employ the desired strategy.

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4.3 Class Discussion Question 1) Engage the class in a discussion of why firms hedge risks. Steer them towards an understanding that firms manufacture products, they do not speculate in commodity markets.

Now, turn the tables and ask why manufacturers do not employ pure hedge strategies with forward contracts. Try to get the class to arrive at the conclusion that since firms are experts in their respective industries, their knowledge may benefit them by implementing creative strategies, while still hedging losses.

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Derivatives Markets, 3e (McDonald) Chapter 5 Financial Forwards and Futures 5.1 Multiple Choice 1) KMW, Inc. plans to pay a dividend of $0.50 per share both 3 and 6 months from today.

KMW's share price today is $36.00 and the continuously compounded quarterly interest rate is 1.5%. What is the price of a 6-month prepaid forward contract, which expires immediately after the second dividend?

A) $35.00 B) $35.02 C) $36.98 D) $37.00 Answer: B 2) The S&P 500 Index is priced at $950.46. The annualized dividend yield on the index is 1.40%. What is the price of a 6-month prepaid forward contract on the S&P 500 Index?

A) $943.83 B) $950.00 C) $964.26 D) $984.21 Answer: A 3) HAW, Inc. plans to pay a $1.10 dividend per share in 3 months and a $1.15 dividend in 6 months. HAW's share price today is $45.60 and the continuously compounded quarterly interest rate is 2.1%. What is the price of a forward contract, which expires immediately after the second dividend?

A) $45.28 B) $45.96 C) $45.60 D) $46.24 Answer: A 4) The S&P 500 Index is priced at $950.46. The annualized dividend yield on the index is 1.40%. The continuously compounded annual interest rate is 8.40%. What is the price of a forward contract that expires 9 months from today?

A) $937.48 B) $942.66 C) $984.36 D) $1001.69 Answer: D

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5) Which of the following statements does NOT accurately reflect the relationship between securities and synthetic forward contracts?

A) Forward = stock - zero coupon bond B) Zero coupon bond = stock - forward C) Prepaid forward = forward - zero coupon bond D) Stock = forward + zero coupon bond Answer: C 6) The annualized dividend yield on the S&P 500 Index is 1.40%. The continuously compounded interest rate is 6.4%. If the 9-month forward price is $925.28 and the index is priced at $950.46, what is the profit/loss from a cash-and-carry strategy?

A) $25.18 loss B) $25.18 gain C) $61.50 loss D) $61.50 gain Answer: C 7) The price of an S&P 500 Index futures contract is $988.26 when you decide to enter a long position. When the position is closed the futures price is $930.32. If there are no settlement requirements, what is your dollar gain or loss? (Ignore opportunity costs.)

A) $14,485 loss B) $14,485 gain C) $57.94 loss D) $57.94 gain Answer: A 8) The price of an S&P 500 Index futures contract is $988.26 when you decide to enter a long position. When the position is closed the futures price is $930.32. If there are no settlement requirements, what is your percentage gain or loss under a 15.0% margin requirement? (Ignore opportunity costs.)

A) 39% gain B) 39% loss C) 43% gain D) 43% loss Answer: B 9) Consider an investment in five S&P 500 Index futures contracts at a price of $924.80. The initial margin requirement is 15.0% and the maintenance margin is 10.0%. If the continuously compounded interest rate is 5.0% what will the futures price need to be for a margin call to occur 10 days from now? Assume no settlement within the 10 days.

A) $852.64 B) $872.79 C) $898.63 D) $905.25 Answer: B

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10) The S&P 500 Index price is $925.28 and its annualized dividend yield is 1.40%. LIBOR is 4.2%. How many futures contracts will you need to hedge a $25 million portfolio with a beta of 0.9 for one year?

A) 105 B) 120 C) 80 D) 95 Answer: D 11) Interest rates on the U.S. dollar are 5.4% and euro rates are 4.6%. Given a dollar per euro spot rate of 0.918, what is the 6-month forward rate ($/E)?

A) 0.912 B) 0.917 C) 0.922 D) 0.934 Answer: C 12) Interest rates on the U.S. dollar are 6.5% and euro rates are 5.5%. The dollar per euro spot rate is 0.950. What is the arbitrage profit on a required 1 million euro payment if the forward rate is 0.980 dollars per euro and the exchange occurs in one year?

A) $10,000 B) $21,000 C) $28,000 D) $34,000 Answer: B 13) An investor wants to hold 200 euro two years from today. The spot exchange rate is $1.31 per euro. If the euro denominated annual interest rate is 3.0% what is the price of a currency prepaid forward?

A) $200 B) $206 C) $231 D) $247 Answer: D 14) The manager of a blue chip growth stock mutual fund is trying to fully hedge the $650 million portfolio position during the last two months of the calendar year. The current price of the S&P 500 Index futures contract is 1200. If the mutual fund has a beta of 1.24, how many contracts will be needed to hedge the fund?

A) 1,083 B) 3,033 C) 242,963 D) 541,666 Answer: B

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15) The current currency spot rate is $1.31 per euro. If dollar denominated interest rates are 3.0% and euro denominated interest rates are 4.0%, what is the likely dollar per euro exchange rate for a 2-year forward contract?

A) $1.28 B) $1.30 C) $1.31 D) $1.33 Answer: A 5.2 Short Answer Essay Questions 1) Explain the impact transaction costs have on the ability to make arbitrage profits in forward and futures markets.

Answer: The existence of bid-ask spreads, commissions, and taxes take away from profits. The existence of security mispricing and implementation of arbitrage strategies, therefore, may not produce profits if these costs exceed the potential profit.

2) Name some advantages that futures contracts have over forward contracts.

Answer: Futures are more liquid and positions are easily closed. Futures eliminate counter party credit risk. Since futures are standardized, opening a position is easier and less expensive.

3) What is the process involved in creating a cash-and-carry strategy?

Answer: Buy a tailed position in a security and sell it at time T. Borrow the amount necessary to enter the tailed position and repay the loan at time T. Short a forward contract and close the transaction at time T. 4) What are some uses for index futures contracts?

Answer: In no particular order, the most common uses are index arbitrage, asset allocation, cross-hedging, risk management, and controlling transaction costs. Futures can also speed up the investment process as well as provide quick short-term vehicles.

5) Explain the steps necessary to take advantage of an arbitrage opportunity, which may exist between the dollar and yen, when a future yen payment is required.

Answer: Rather than lock in the cost of a future yen payment with a forward or futures contract, calculate the PV of the yen payment using yen rates. Convert this figure to dollars at the spot rate. Borrow at the dollar rate, thus locking in your dollar cost. Exchange those funds and place in a yen time deposit account until needed.

5.3 Class Discussion Question 1) Throughout the chapter the topic of arbitrage is mentioned. Ask the class to explain arbitrage.

Follow-up the answers by asking what role arbitrage plays in futures and forward markets. Finish up the Q & A with a group discussion of why arbitrage exists, given the limited opportunity for arbitrage profits. Guide students towards an understanding of the necessity of the arbitrage function, despite the limited opportunity for profit.

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Derivatives Markets, 3e (McDonald) Chapter 6 Commodity Forwards and Futures 6.1 Multiple Choice When answering the questions below, refer to the following table of commodity forward and spot prices. The annual risk free interest rate is 4.0%.

Table 6.1

1) Refer to the table 6.1. What is the approximate annualized lease rate on the 12-month corn forward contract?

A) 0.00% B) 2.25% C) 3.92% D) 7.84% Answer: D 2) Refer to the table 6.1. What is the approximate annualized lease rate on the 18-month soybean forward contract?

A) 0.69% B) 1.52% C) 2.69% D) 3.31% Answer: C 3) Refer to the table 6.1. If wheat farmers expect a return of 8.0% on their investment in wheat, what is the approximate implied increase in wheat commodity prices over the next 6 months?

A) 3.75% B) 4.59% C) 5.26% D) 6.37% Answer: B 4) Refer to the table 6.1. Which of the following terms most accurately describes the forward curve for soybeans over the next two years?

A) Contango B) Backwardation C) Contango and backwardation D) None of the above Answer: C 1 Copyright © 2013 Pearson Education, Inc.

5) Refer to the table 6.1. Given a lease rate of 7.0% on the 24-month corn forward contract, what is the approximate potential arbitrage profit per contract?

A) 3.68 cents B) 4.48 cents C) 5.84 cents D) 6.90 cents Answer: B 6) Refer to the table 6.1. The lease rate on the 6-month soybean contract is 0.35%. What is the implied annual storage cost if the cost is continuously paid and proportional?

A) 0.84% B) 1.62% C) 2.30% D) 4.0% Answer: A 7) The spot price of gasoline is 258 cents per gallon and the annualized risk free interest rate is 4.0%. Given a lease rate of 1.0%, a continuously paid storage rate of 0.5%, and a convenience yield of 0.75%, what is the no-arbitrage price range of a 1-year forward contract (in cents)?

A) 265.19 to 267.19 B) 258 to 265.19 C) 258 to 267.19 D) 247.16 to 265.19 Answer: A 8) Nine-month gold futures are trading for $1565 per ounce. The spot price is $1509 per ounce.

LIBOR during each of the upcoming 4 quarters is listed as 1.04%, 1.22%, 1.30%, and 1.35%, respectively. Calculate the 9-month lease rate on the futures contract.

A) 2.4% B) 2.1% C) 1.3% D) 0.0% Answer: D 9) Forward prices for gold, in dollars per ounce, for the next five years are 1350, 1400, 1560, 1675, and 1756, respectively. A mine can be opened for 3 years at a cost of $2,000. Annual mining costs are a constant $500 and interest rates are 5.0%. When should the mine be opened to maximize NPV? A) Year 1 B) Year 2 C) Year 3 D) Never Answer: C

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10) The 6-month futures price for oil is $96.60 per barrel (or 2.30 cents per gallon). The 6-month futures prices for gasoline and heating oil are 2.50 cents and 2.15 cents, respectively. What is the gross margin on a simple 3-2-1 crack spread?

A) $0.25 B) $0.35 C) $0.54 D) $0.68 Answer: A 11) The spot price of corn is $5.85 per bushel. The opportunity cost of capital for an investor is 0.5% per month. If storage costs of $0.04 per bushel per month are factored in, all else being equal, what is the likely price of a 4-month forward contract?

A) $5.808 B) $5.736 C) $5.968 D) $6.006 Answer: A 12) The spot price of corn is $5.82 per bushel. The opportunity cost of capital for an investor is 0.6% per month. If storage costs of $0.03 per bushel per month are factored in, all else being equal, what is the future value of storage costs over a 6-month period?

A) $0.1534 B) $0.1684 C) $0.1772 D) $0.1827 Answer: D 13) Oil is selling at a spot price of $42.00 per barrel. Oil can be stored at a cost of $0.42 per barrel per month. The opportunity cost of capital is 7.2% per year (or 0.6% per month). What is the gain or loss realized by an oil refinery that floats its exposure and purchases oil on the spot market in 2 months at a price of $43.00 per barrel, instead of hedging with a forward contract?

A) $0.35 gain B) $0.35 loss C) $1.00 gain D) $1.00 loss Answer: A 6.2 Short Answer Essay Questions 1) Explain how a negative correlation between agricultural production and commodity prices creates a natural hedge.

Answer: The goal of hedging is to level the volatility in cash flows. The increased revenue, which accompanies higher output, will be offset by lower prices. Lower output and revenue, in turn, is offset by higher prices, thus, a natural hedge.

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2) Give one example of how price discovery functions in the commodity futures market.

Answer: Lease rates, which are readily available in financial futures markets, are not given in commodity markets. Lease rates are implied and, therefore, calculable from listed futures prices.

3) Why is the cash-and-carry strategy employed in the financial futures market not readily available in the commodity futures market?

Answer: Since the holder of a commodity has a financial investment in the commodity, he will require compensation for lending it to another investor. This adds a cost to the short seller's cash flow calculation.

4) What function does the convenience yield serve in setting forward prices and how does this influence arbitrage opportunities?

Answer: In contrast to a speculator, a manufacturer earns the convenience yield. This yield should be factored in to forward prices for manufacturers, but not for speculators. The result is a range of possible forward prices, which could be considered an arbitrage-free zone.

5) When is it possible for the lease rate to fall below zero?

Answer: In high growth segments of the economy the lease rate formula can become negative.

When growth exceeds the opportunity cost of capital, negative values result.

6.3 Class Discussion Question 1) A review of seasonality forward curves may lead students to adopt a technical analysis mentality. Ask students to explain why such ideas may pop into their heads. Proceed to inquire as to why the curves have the appearances they do. An actual numerical example may be in order. If any still hold fast to their technical roots, insist that they show the profit numerically after considering all storage and other costs.

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Derivatives Markets, 3e (McDonald) Chapter 7 Interest Rate Forwards and Futures 7.1 Multiple Choice 1) The price of a 3-year zero coupon government bond is 85.16. The price of a similar 4-year bond is 79.81. What is the yield to maturity (effective annual yield) on the 4-year bond?

A) 4.6% B) 5.5% C) 5.8% D) 6.7% Answer: C 2) The price of a 3-year zero coupon government bond is 85.16. The price of a similar 4-year bond is 78.81. What is the yield to maturity (effective annual yield) on the 3-year bond?

A) 4.6% B) 5.5% C) 5.8% D) 6.7% Answer: B 3) The price of a 3-year zero coupon government bond is 85.16. The price of a similar 4-year bond is 78.81. What is the 1-year implied forward rate from year 3 to year 4?

A) 4.6% B) 5.5% C) 5.8% D) 6.7% Answer: D 4) The prices of 1, 2, 3, and 4-year zero coupon government bonds are 95.42, 90.36, 85.16, and 78.81, respectively. What is the implied 2-year forward rate between years 2 and 4?

A) 4.8% B) 5.2% C) 5.5% D) 6.4% Answer: D 5) The prices of 1, 2, 3, and 4-year zero coupon government bonds are 95.42, 90.36, 85.16, and 78.81, respectively. What is the par coupon on a 4-year coupon bond selling at par?

A) 5.02% B) 5.43% C) 5.81% D) 6.06% Answer: D

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6) The prices of 1, 2, 3, and 4-year zero coupon government bonds are 95.42, 90.36, 85.16, and 78.81, respectively. What is the continuously compounded 3-year zero yield?

A) 5.35% B) 5.85% C) 6.12% D) 6.40% Answer: A 7) The annual coupon rate on a 1-year treasury bond is 5.5%. The coupon on a 2-year treasury bond is 5.8%. What is the implied YTM on a hypothetical 2-year zero coupon treasury bond?

A) 5.45% B) 5.50% C) 5.75% D) 5.81% Answer: D 8) The annual coupon rate on a 1-year treasury bond is 5.5%. The coupon on a 2-year treasury bond is 5.8%. What is the continuously compounded yield on a 2-year zero coupon bond?

A) 5.55% B) 5.65% C) 5.75% D) 5.85% Answer: B 9) A Forward Rate Agreement contains an agreed interest rate of 3.1% on a 6-month loan. If settled at the time of borrowing, what amount would the borrower pay or receive on a $500,000 loan if the prevailing 6-month interest rate is 2.9%?

A) $1,000 payment B) $1,000 receipt C) $972 payment D) $972 receipt Answer: C 10) A Forward Rate Agreement contains an agreed interest rate of 3.1% on a 6-month loan. If settled in arrears, what amount would the borrower pay or receive on an $800,000 loan if the prevailing 6-month interest rate is 3.6%?

A) $4,000 payment B) $4,000 receipt C) $1,729 payment D) $1,729 receipt Answer: B

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11) Two months from today you plan to borrow $3 million for 6 months at LIBOR. You hedge your interest rate risk with a euro dollar futures contract priced at 93.6. If settled in arrears, what is your payment if the 6-month LIBOR is 2.5% in two months?

A) $8,500 B) $10,500 C) $13,500 D) $15,500 Answer: B 12) Given a 3-year, 8.0% annual coupon bond with a par value of $1,000, what is the bond's Macaulay duration if the yield to maturity is 9.5%?

A) 2.779 B) 2.634 C) 2.535 D) 2.442 Answer: A 13) A 4-year bond with a price of 100.696 exists. The duration on the bond is 3.674. If the yield rises from 5.8% to 6.2%, what is the new bond price as estimated by the duration?

A) $98.40 B) $99.30 C) $100.60 D) $101.40 Answer: B 14) Compute the conversion factor on a semi-annual 6.8% coupon bond, which matures in 1 exactly 5 years.

2 A) 1.037 B) 1.046 C) 1.052 D) 1.068 Answer: A 15) The conversion factor on a deliverable bond is 1.03 and the bond price is 100.50. The observed futures price is 97.5 and the YTM is 5.8%. What is invoice less market price on the security?

A) +0.08 B) -0.08 C) -0.02 D) +0.02 Answer: B

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16) You wish to create a synthetic forward rate agreement in which you would lock in a return between 150 and 310 days. The price of a 150-day zero coupon bond is 0.9823 and the price of 310-day zero coupon bond is 0.9634. What is the approximate yield on the synthetic FRA? A) 1.8% B) 2.0% C) 2.9% D) 3.8% Answer: B 17) You wish to create a synthetic forward rate agreement in which you would lock in a return between 150 and 310 days. The price of a 150-day zero coupon bond is 0.9823 and the price of 310-day zero coupon bond is 0.9634. What are the transactions used to create this instrument?

A) Borrow one 150-day bond and invest in 1.02 of the 310-day bonds B) Borrow two 150-day bonds and invest in 0.98 of the 310-day bonds C) Lend one of the 150-day bonds and borrow 1.02 of the 310-day bonds D) Lend two of the 150-day bonds and borrow 0.98 of the 310-day bonds Answer: A 18) The price of a 6-month T-bill is 96.73. You wish to enter into a repurchase agreement that provides for your purchase of a $100,000 bond in 10 days at a price of 97.02. What is the implied 10 day repo rate in this transaction?

A) 0.10% B) 0.20% C) 0.30% D) 0.40% Answer: C 7.2 Short Answer Essay Questions 1) What is the pure yield curve and why is it common to present coupon-based yield curves in practice?

Answer: The pure yield curve is a graph of annualized zero coupon yields for existing or hypothetical zero coupon treasury securities. Coupon bonds are often used to present the yield curve since they are easier to find than zeros.

2) Explain the expectations hypothesis and its ability to accurately forecast interest rates.

Answer: The expectations hypothesis is a generally held belief that the implied forward rate equals the spot rate of interest that will occur in the future. Since risk premiums exist, this forecast is biased and usually does not accurately predict interest rates.

3) Explain the process of creating a synthetic Forward Rate Agreement.

Answer: This is accomplished by trading a series of zero coupon bonds so as to simulate FRA cash flows at time 0, time t, and time t + s. Short at time 0 the present value of a zero coupon bond, maturing at time t. At time 0 buy the exact same dollar value of zeros, which mature at time t + s.

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4) What is the rationale behind cheapest-to-deliver calculations and why do we perform such calculations?

Answer: Unlike other futures, treasury rate and treasury bond futures are actually delivered. The futures is on a hypothetical bond, therefore, multiple bonds are deliverable. The short position gets to choose which bond to deliver, within certain guidelines. The short investor will, obviously, calculate the least cost bond and deliver said bond.

5) Why can repos be used to simulate borrowing?

Answer: Since a repo is the sale of a security with an agreement to buy it back, the seller is getting a synthetic loan, which can be used in other transactions.

7.3 Class Discussion Question 1) How is duration calculated? What is the nature and use of duration? How does duration compare to the linear concept of the bond price and interest rate relationship? Is duration better than convexity or worse? Duration is considered common knowledge in the fixed income world and should be discussed at length.

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Derivatives Markets, 3e (McDonald) Chapter 8 Swaps 8.1 Multiple Choice 1) Given zero-coupon bond yields are 2.0%, 2.5%, and 2.8% in years 1, 2, and 3, respectively, calculate the prepaid swap price for corn. Assume corn forward prices for the proceeding 3 years are $5.00, $5.20, and $5.35, respectively.

A) $14.87 B) $15.04 C) $16.12 D) $16.20 Answer: A 2) What is the 3-year swap price on corn? Assume interest rates over the next 3 years are 2.0%, 2.5%, and 2.8%. The prepaid swap price is given as $15.50.

A) $5.10 B) $5.30 C) $5.43 D) $5.64 Answer: C 3) Assume oat spot prices over the next 3 years are $2.20, $2.35, and $2.28, respectively. The original swap price was $2.30 per bushel. If cash settlement occurs, what transaction will the counter-party make in year 2 on a 5,000-bushel swap agreement?

A) $250 payment B) $250 receipt C) $100 payment D) $100 receipt Answer: A 4) Assume oat forward prices over the next 3 years are $2.25, $2.35, and $2.28, respectively.

Effective annual interest rates over the same period are 5.2%, 5.5%, and 5.8%. What is the 2-year swap price on a hypothetical "forward swap" that begins at the end of year 1?

A) $2.14 B) $2.32 C) $2.41 D) $2.53 Answer: B

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5) The 3-year swap price on a new oat swap agreement is $5.94. Interest rates immediately rise on 1, 2, and 3-year zero coupon bonds from 5.1%, 5.4%, and 5.7% to 5.2%, 5.6%, and 6.0%, respectively. What is net swap payment per year if the reverse transaction occurs? Assume year 1, 2, and 3 forward prices are $2.05, $2.15, and $2.30, respectively and do not change.

A) $0.35 B) $0.49 C) $0.64 D) $0.75 Answer: B 6) Assume the net swap payment is $.50 on a reverse transaction involving a 3-year oat swap.

What is the market value of the swap given interest rates on zero coupon treasury bonds are 5.2%, 5.6%, and 6.0% for 1, 2, and 3 years, respectively?

A) $0.96 B) $1.10 C) $1.25 D) $1.34 Answer: D 7) IBM and AT&T decide to swap $1 million loans. IBM currently pays 9.0% fixed and AT&T pays 8.5% on a LIBOR + 0.5% loan. What is the net cash flow for IBM if they swap their fixed loan for a LIBOR + 0.5% loan and LIBOR rises to 8.5%?

A) -$50,000 B) $50,000 C) -$90,000 D) 0 Answer: D 8) Euro dollar futures prices with maturities of 3, 6, and 9 months are 89.04, 88.75, and 88.55, respectively. What is the annualized swap rate on 9-month securities?

A) 8.55% B) 9.68% C) 11.34% D) 13.24% Answer: C 9) Your company can get yen loans for 2.0%. Dollar rates on the same loans are 4.5%. The spot yen per dollar exchange rate is 104. The forward rates for years 1 thru 4 are, 101.51, 99.08, 96.71, and 94.40, respectively. What is the dollar value of a 4-year 1 million yen loan?

A) $9,615.33 B) $10,422.46 C) $11,618.04 D) $13,527.89 Answer: A

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10) Your company can get yen loans for 2.0%. Dollar rates on the same loans are 4.5%. The spot yen per dollar exchange rate is 104. The forward rates for years 1 thru 4 are, 101.51, 99.08, 96.71, and 94.40, respectively. What is the present value of the market-maker's net cash flow if spot rates are 102 instead?

A) $188.59 B) $206.43 C) $219.96 D) $242.06 Answer: A 11) A portfolio manager enters into a total return swap. She swaps 50% of her $50 million index based portfolio for 4.5% yield bonds. If the annualized total return on the index is 2.5%, what net cash flow will the manager experience under the swap agreement?

A) + $250,000 B) -$250,000 C) + $500,000 D) -$500,000 Answer: C 12) An investor enters into a 2-year swap agreement to purchase crude oil at $105.65 per barrel.

Soon after the swap is created forward prices rise and the new swap price on a similar swap is $108.32. If interest rates are 3.0% per year, what is the gain to be made from unwrapping the original swap agreement?

A) $2.67 B) $5.11 C) $5.34 D) $5.67 Answer: B 13) The forward prices on a barrel of crude oil are $112 and $118 in years one and two, respectively. The interest rates on zero coupon government bonds are 3.0% and 3.5% in years one and two, respectively. What is the likely 2-year swap price on a barrel of crude oil?

A) $112.00 B) $116.60 C) $118.00 D) $120.50 Answer: B 14) An investor enters into a 2-year swap agreement to euros at $1.32 per euro. Soon after the swap is created forward prices rise and the new swap price on a similar swap is $1.45. If dollar denominated interest rates are 4.0% and 4.5% on 1- and 2-year zero coupon government bonds, respectively, what is the gain to be made from unwrapping the original swap agreement?

A) $0.24 B) $0.45 C) $0.65 D) $0.82 Answer: A 3 Copyright © 2013 Pearson Education, Inc.

8.2 Short Answer Essay Questions 1) Describe briefly the nature of a swap and its primary component.

Answer: A swap is an agreement between two parties. The main part is the contractual obligation to exchange some specified cash flows.

2) Under what circumstances would a multinational company elect to enter into a currency swap agreement?

Answer: A firm with exposure to currency risk, via foreign currency denominated debt, may wish to remove this risk. Currency swaps accomplish this goal.

3) Explain a "diff swap" as it relates to currency swaps.

Answer: In a diff swap the settlement payments are based on the difference in floating interest rates in two different countries, with the notational amount being a constant in a single currency.

4) How would a market-maker hedge a swap involving variable price and quantity?

Answer: The market-maker will enter into varying quantities of forward contracts in different months to match the variable quantity called for in the swap.

5) Why do arbitrage profits rarely exist in interest rate swap pricing?

Answer: Interest rate swaps can be equated to borrowing at a variable interest rate in order to purchase a fixed rate bond. The pricing of these instruments are set in high volume markets and correspond with bond yield curves.

8.3 Class Discussion Question 1) How does the existence of swaptions add to the possibilities in risk management techniques?

While option strategies have not yet been discussed, students should be able to draw conclusions from prior chapters. Lead the class in a discussion of how options lead to an infinite range of possible strategies for swap investors.

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Derivatives Markets, 3e (McDonald) Chapter 9 Parity and Other Option Relationships 9.1 Multiple Choice 1) Jafee Corp. common stock is priced at $36.50 per share. The company just paid its $0.50 quarterly dividend. Interest rates are 6.0%. A $35.00 strike European call, maturing in 6 months, sells for $3.20. What is the price of a 6-month, $35.00 strike put option?

A) $1.20 B) $1.64 C) $2.04 D) $2.38 Answer: B 2) Rankin Corp. common stock is priced at $74.20 per share. The company just paid its $1.10 quarterly dividend. Interest rates are 6.0%. A $70.00 strike European call, maturing in 6 months, sells for $6.50. How much arbitrage profit/loss is made by shorting the European call, which is priced at $2.50?

A) $0.12 loss B) $0.12 gain C) $0.36 loss D) $0.36 gain Answer: B 3) A company is forecasted to pay dividends of $0.90, $1.20, and $1.45 in 3, 6, and 9 months, respectively. Given interest rates of 5.5%, how much dollar impact will dividends have on option prices? (Assume a 9-month option.)

A) $3.45 B) $3.90 C) $4.22 D) $4.50 Answer: A 4) The price of a stock is $52.00. Lacking additional information, what is your forecasted difference between a put option and a call option on this stock? Assume 38 days to expiration and 6.0% interest.

A) $0.16 B) $0.32 C) $0.48 D) $0.64 Answer: B

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5) Jillo, Inc. stock is selling for $54.70 per share. Calls and puts with a $55 strike and 40 days until expiration are selling for $1.65 and $1.23, respectively. What potential arbitrage profit exists?

A) $0.12 B) $0.24 C) $0.36 D) $0.48 Answer: A 6) The spot exchange rate of dollars per euro is 0.95. Dollar and euro interest rates are 7.0% and 6.0%, respectively. The price of a $0.93 strike 6-month call option is $0.08. What is the price of the put?

A) $0.016 B) $0.032 C) $0.056 D) $0.078 Answer: C 7) The 6-month call and put premiums are $0.114 and $0.098, respectively, with a $0.94 strike.

Dollar and euro interest rates are 7.0% and 6.0%, respectively. What spot exchange rate is implied by this data?

A) $0.98 dollars per euro B) $1.02 dollars per euro C) $1.05 dollars per euro D) $1.09 dollars per euro Answer: B 8) Which of the following options will NOT be exercised early?

A) Put on a dividend paying stock B) Call on a dividend paying stock C) Put on a non-dividend paying stock D) Call on a non-dividend paying stock Answer: D 9) Call options with strikes of $30, $35, and $40 have option premiums of $1.50, $1.70, and $2.00, respectively. Using strike price convexity, which option premium, if any, is not possible?

A) C (30) B) C (35) C) C (40) D) All are possible Answer: D

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10) Put options with strikes of $70, $75, and $85 have option premiums of $6.00, $8.50, and $11.00, respectively. Using strike price convexity, which option premium, if any, is not possible?

A) P (70) B) P (75) C) P (85) D) All are possible Answer: B 11) Consider the case of an exchange option in which the underlying stock is Eli Lilly and Company with a current price of $56.00 per share. The strike asset is Merck, with a per share price of $52.00. Interest rates are 5% and the 3-month call option is trading for $7.00. What is the price of the put?

A) $3.00 B) $4.00 C) $7.00 D) $11.00 Answer: D 12) The spot exchange rate in dollars per euro is $1.31. Dollar denominated interest rates are 4.0% and euro denominated interest rates are 3.0%. What is the difference in call and put option prices given a 2-year option and a $1.34 strike price?

A) -$0.1041 B) -$0.0652 C) $0.1233 D) $0.1546 Answer: A 13) The price of a non-dividend paying stock is $55 per share. A 6-month, at the money call option is trading for $1.89. If the interest rate is 6.5%, what is the likely price of a European put at the same strike and expiration?

A) $0.05 B) $0.13 C) $0.56 D) $0.88 Answer: B 9.2 Short Answer Essay Questions 1) Using the synthetic long stock strategy, explain the difference in call and put prices.

Answer: The synthetic stock strategy (long call and short put) defers the cash purchase of the stock. The interest on the current stock price for the remaining life of the options equals the difference between calls and puts with identical strikes and maturities.

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2) Jillo, Inc. stock is selling for $54.70 per share. Calls and puts with a $55.00 strike and 40 days until expiration are selling for $1.65 and $1.23, respectively. Draw a profit and loss graph illustrating the arbitrage.

Answer:

3) Explain in simple terms why a call option on a non-dividend paying stock should never be exercised early.

Answer: The price of the American option will always exceed the intrinsic value, thus we would lose money exercising on American call prior to expiration, as opposed to selling the option.

4) The necessary condition for early exercise is that we prefer to receive something sooner rather than later. With a dividend paying call and a non-dividend paying put, what do we receive?

Answer: With the call and the put we receive the dividend on the stock and the interest on the strike, respectively.

5) All else being equal, explain why American options are at least as valuable as European options.

Answer: The rare instances in which early exercise might occur, due to the desire to get dividends or interest on the strike, adds value since European options can never take advantage of such opportunities.

9.3 Class Discussion Question 1) Put-call parity allows a discussion of option pricing relationships without actually pricing an option. Have the class list all the possible pricing relationships they can recall. Add to the list until reasonably complete. Follow up this exercise by listing puts and calls, while asking students to state if certain premiums are possible.

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Derivatives Markets, 3e (McDonald) Chapter 10 Binomial Option Pricing: Basic Concepts 10.1 Multiple Choice 1) A stock is currently selling for $22.00 per share. Ignoring interest, determine the intrinsic value of a call option should there exist equally probable stock prices of $25.00 and $23.00.

A) $0.00 B) $1.00 C) $2.00 D) $3.00 Answer: C 2) Compute Δ for the following call option. The stock is selling for $23.50. The strike price is $25. The possible stock prices at the end of 6 months are $27.25 and $21.75.

A) 0.4091 B) 0.6822 C) 0.8433 D) 0.9216 Answer: A 3) The stock price in KMW, Inc. is $50, $54, $56, and $48 on four consecutive days of trading.

What is the continuously compounded return on the stock over this time frame?

A) -3.85 % B) -4.00 % C) -4.08 % D) -4.16 % Answer: C 4) A stock is selling for $32.70. The strike price on a call, maturing in 6 months, is $35. The possible stock prices at the end of 6 months are $39.50 and $28.40. If interest rates are 6.0%, what is the option price?

A) $1.90 B) $2.80 C) $3.40 D) $4.20 Answer: C 5) The monthly standard deviation for a stock is 4.2%. What is the 6 month standard deviation for the security?

A) 4.2 % B) 10.3 % C) 25.2 % D) 50.4 % Answer: B

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6) A stock is selling for $18.50. The strike price on a call, maturing in 6 months, is $20. The possible stock prices at the end of 6 months are $22.50 and $15.00. Interest rates are 6.0%. How much money would you borrow to create an arbitrage on a call trading for $2.00?

A) $2.54 B) $4.85 C) $6.60 D) $8.85 Answer: B 7) A stock is selling for $41.60. The strike price on a call, maturing in 6 months, is $45. The possible stock prices at the end of 6 months are $35.00 and $49.00. Interest rates are 5.0%. Given an under-priced option, what are the short sale proceeds in an arbitrage strategy?

A) $6.36 B) $8.22 C) $10.43 D) $11.89 Answer: D 8) A stock is selling for $53.20. Interest rates are 6.0% and the returns on the stock have a standard deviation of 24.0%. What is the forecasted up movement in the stock over a 6-month interval?

A) $64.96 B) $69.69 C) $73.48 D) $76.96 Answer: A 9) A stock is selling for $53.20. Interest rates are 6.0% and the returns on the stock have a standard deviation of 24.0%. What is the forecasted up movement in the stock over 6 months, assuming two periods of 3 months each?

A) $64.96 B) $69.69 C) $73.48 D) $76.96 Answer: B 10) A stock is selling for $68.50. Interest rates are 6.0% and the returns on the stock have a standard deviation of 32.0%. What is the forecasted price of the stock using 3-month periods at Suudu?

A) $74.08 B) $94.24 C) $100.17 D) $111.12 Answer: C

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11) Using a binomial tree, what is the price of a $40 strike 6-month call option, using 3-month intervals as the time period? Assume the following data: S = $37.90, r = 5.0%, σ = 0.35 A) $2.50 B) $2.76 C) $2.92 D) $3.08 Answer: D 12) Using a binomial tree, what is the price of a $40 strike 6-month put option, using 3-month intervals as the time period? Assume the following data: S = $37.90, r = 5.0%, σ = 0.35 A) $3.52 B) $3.66 C) $3.84 D) $3.91 Answer: D 13) A call option has an exercise price of $30. The stock price at a point on the binomial tree is $36.24. The calculated present value of the option at that same point is $5.86. What figure should be used to calculate option prices at points moving toward the final price?

A) $5.86 B) $6.24 C) $6.62 D) $7.01 Answer: B 14) In the case of a 1-year option, the current stock price is $52 per share. If the stock price has an equal chance of ending the year at either $58 or $45, what is the △ given an interest rate of 6.0% and an exercise price of $50?

A) 0.2145 B) 0.3254 C) 0.5411 D) 0.6154 Answer: D 15) For an option trading in the money, what is the likely impact on the binomial option price as the number of binomial steps is increased?

A) The price will fall B) The price will increase C) The price will remain constant D) The impact cannot be determined Answer: A

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10.2 Short Answer Essay Questions 1) Draw the binomial tree listing only the option prices at each node. Assume the following data on a 6-month call option, using 3-month intervals as the time period. K = $40, S = $37.90, r = 5.0%, σ = 0.35 Answer:

2) Draw the binomial tree listing only the stock prices at each node. Assume the following data on a 6-month call option, using 3-month intervals as the time period. K = $70, S = $68.50, r = 6.0%, σ = 0.32 Answer:

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3) Draw the binomial tree listing only the option prices at each node. Assume the following data on a 6-month put option, using 3-month intervals as the time period. K = $40.00, S = $37.90, r = 5.0%, σ = 0.35 Answer:

4) Using a binomial tree explanation, explain the situation in which an American option would alter the pricing of an option.

Answer: The value of an American option at a node is the maximum of its intrinsic value or the discounted value of the subsequent nodes. Early exercise permits the realization of the intrinsic value, should it be the higher number. European options may not consider this potential gain.

5) Explain the impact a constant dividend yield would have on the price of a call option.

Answer: The impact of a dividend will be to reduce the price of the option. Stocks which are exdividend tend to decline in price, thus reducing the intrinsic value of call options and the resulting option prices.

10.3 Class Discussion Question 1) Discuss options on other assets. Ask students to define currency options, futures options, index options, and commodity options. Require that the students state which variables in the securities listed above correspond with the binomial pricing inputs used for stock options.

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Derivatives Markets, 3e (McDonald) Chapter 11 Binomial Option Pricing: Selected Topics 11.1 Multiple Choice 1) Consider a two-period binomial model, where each period is 6 months. Assume the stock price is $46.00, σ = 0.28, r = 0.06 and the dividend yield is 2.0%. What is the maximum approximate strike price where early exercise would occur with an American call option?

A) $29 B) $33 C) $42 D) $46 Answer: A 2) Consider a two-period binomial model, where each period is 6 months. Assume the stock price is $75.00, σ = 0.35, and r = 0.05. An American call option with a strike price of $80 would be exercised early at what dividend yield?

A) 5.0% B) 7.0% C) 9.0% D) Never exercise early Answer: D 3) Consider a two-period binomial model, where each period is 6 months. Assume the stock price is $50.00, σ = 0.20, r = 0.06 and the dividend yield = 3.5%. What is the lowest strike price where early exercise would occur with an American put option?

A) $50 B) $55 C) $60 D) $65 Answer: C 4) Consider a two-period binomial model, where each period is 6 months. Assume the stock price is $60.00, σ = 0.30, r = 0.05. An American put option with a strike price of $65 would be exercised early at what dividend yield?

A) 5.0% B) 6.0% C) 11.0% D) Never exercised early Answer: D

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5) Consider a one-period binomial model of 6 months. Assume the stock price is $45.00, σ = 0.20, r = 0.06 and the stock's expected return is 12.0%. What is the discount rate for a $45.00 strike European call option (Y)?

A) 38.2% B) 39.1% C) 42.5% D) 45.6% Answer: B 6) Consider a one-period binomial model of 6 months. Assume the stock price is $63.00, σ = 0.28, r = 0.05 and the stock's expected return is 14.0%. What is the true probability of the stock going up?

A) 56.6% B) 52.4% C) 48.2% D) 46.4% Answer: A 7) Consider a one-period binomial model of 12 months. Assume the stock price is $54.00, σ = 0.25, r = 0.04 and the exercise price of a call option is $55. What is the forecasted price of the stock given an upward movement during the year?

A) $56.16 B) $61.01 C) $65.12 D) $72.16 Answer: D 8) Consider a one-period binomial model of 12 months. Assume the stock price is $54.00, σ = 0.25, r = 0.04 and the exercise price of a call option is $55. What is the forecasted price of the stock given a downward movement during the year?

A) $43.77 B) $ 45.28 C) $48.98 D) $51.84 Answer: A 9) Consider a three-period binomial model of 12 months. Assume the stock price is $37.50, σ = 0.20, r = 0.05 and the exercise price of a call option is $35. What is the forecasted price of the stock at the node after two consecutive upward movements of the stock price?

A) $38.68 B) $42.80 C) $48.84 D) $50.06 Answer: C

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10) A stock price is $85.00. Assume r = 0.07 and there is no dividend. What is the 6-month forward price?

A) $88.03 B) $89.16 C) $90.26 D) $92.33 Answer: A 11) Using a binomial pricing model, what is the impact on the price of a call option if the company increases the dividend paid to shareholders? The call option price: A) Will drop B) Will increase C) Will remain constant D) Impact cannot be determined Answer: A 12) What economic concept is central to proving that risk neutral pricing functions in the establishing of option prices?

A) Consumption possibilities B) Factor analysis C) Marginal average cost D) Declining marginal utility Answer: D 13) Why is an American call option rarely exercised early, and thus priced similar to European options?

A) Early exercise requires purchasing the stock B) Most option sellers cannot deliver the stock C) Option prices usually exceed intrinsic values D) Short sellers disrupt delivery Answer: C 11.2 Short Answer Essay Questions 1) Under what circumstances should an option be exercised early?

Answer: Whenever the dividend gain exceeds both the interest savings on the dividend plus the implicit insurance value of the option.

2) What is the relationship between dividends and the forecasted stock price in a binomial model?

Answer: The dividend acts to reduce the forecasted stock price at each node in the binomial model.

3) In a binomial pricing model, what is the lowest price of an option at any node and why?

Answer: Zero, because the price of the option can never fall below its intrinsic value, which has a floor of zero.

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4) What is the primary potential for error when using the Cox-Ross-Rubenstein binomial tree?

Answer: When either the time period or standard deviation is large, it is possible for erh > e h , which is not possible for a valid binomial tree.

5) When developing a binomial tree model where stocks pay discrete dividends, what problem may occur?

Answer: Trees created with stocks paying discrete dividends do not completely recombine after the dividend.

11.3 Class Discussion Question 1) Ask the class to prove that option pricing is consistent with standard discounted cash flow calculations. Propose that students form groups and develop two binomial trees for the same set of data. One tree should use real probabilities as defined in chapter 11 and the other as defined in chapter 10.

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Derivatives Markets, 3e (McDonald) Chapter 12 The Black-Scholes Formula 12.1 Multiple Choice 1) What is the price of a $35 strike call? Assume S = $38.50, σ = 0.25, r = 0.06, the stock pays no dividend and the option expires in 45 days.

A) $3.50 B) $3.65 C) $3.80 D) $3.95 Answer: D 2) What is the price of a $60 strike put? Assume S = $63.75, σ = 0.20, r = 0.055, the stock pays no dividend and the option expires in 50 days?

A) $0.66 B) $0.55 C) $0.44 D) $0.33 Answer: C 3) What is the price of a $25 strike call? Assume S = $23.50, σ = 0.24, r = 0.055, the stock pays a 2.5% continuous dividend and the option expires in 45 days?

A) $0.60 B) $0.50 C) $0.40 D) $0.30 Answer: D 4) What is the price of a $30 strike put? Assume S = $28.50, σ = 0.32, r = 0.04, the stock pays a 1.0% continuous dividend and the option expires in 110 days?

A) $2.70 B) $2.10 C) $1.80 D) $1.20 Answer: A 5) What is the delta on a $20 strike call? Assume S = $22.00, σ = 0.30, r = 0.05, the stock pays a 1.0% continuous dividend and the option expires in 80 days?

A) 0.790 B) 0.820 C) 0.850 D) 0.880 Answer: A

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6) What is the delta on a $25 strike put? Assume S = $24.00, σ = 0.35, r = 0.06, the stock pays a 2.0% continuous dividend and the option expires in 40 days?

A) 0.582 B) 0.602 C) 0.662 D) 0.702 Answer: B 7) Assume that a $50 strike call has a 3.0% continuous dividend, σ = 0.27, r = 0.06 and 60 days from expiration. What is the gamma for a stock price movement from $48.00 to $49.00?

A) 0.046 B) 0.074 C) 0.089 D) 0.099 Answer: B 8) Assume that a $55 strike call has a 1.5% continuous dividend, r = 0.05 and the stock price is $50.00. If the option has 45 days until expiration, what is the vega, given a shift in volatility from 33.0% to 34.0%?

A) 0.20 B) 0.15 C) 0.10 D) 0.05 Answer: D 9) Suppose the spot exchange rate is $1.43 per British pound and the strike on a dollar denominated pound call is $1.30. Assume r = 0.045, rf = 0.06, σ = 0.15 and the option expires in 180 days. What is the call option price?

A) $0.133 B) $0.143 C) $0.153 D) $0.163 Answer: A 10) Suppose the spot exchange rate is $1.22 per British pound and the strike on a dollar denominated pound put is $1.20. Assume r = 0.04, rf = 0.05, σ = 0.20 and the option expires in 270 days. What is the put option price?

A) $0.075 B) $0.085 C) $0.095 D) $0.105 Answer: A

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11) Suppose the 180-day futures price on crude oil is $110.00 per barrel and the volatility is 20.0%. Assume interest rates are 3.5%. What is the price of a $120 strike call futures option that expires in 180 days?

A) $1.89 B) $2.19 C) $2.59 D) $3.09 Answer: C 12) Suppose the 120-day futures price on crude oil is $115.00 per barrel and the volatility is 20.0%. Assume interest rates are 3.5%. What is the price of a $110 strike call futures option that expires in 120 days?

A) $3.09 B) $2.99 C) $2.89 D) $2.79 Answer: B 13) Assume that a $60 strike call has a 2.0% continuous dividend, r = 0.05, and the stock price is $61.00. What is the theta of the option as the expiration time declines from 60 to 50 days?

A) -0.52 B) -0.42 C) -0.32 D) -0.22 Answer: C 14) Assume that a $75 strike call has a 1.0% continuous dividend, 90 days until expiration and stock price of $72.00. What is the rho of the option as the interest rate changes from 6.0% to 5.0%?

A) 0.07 B) 0.12 C) 0.16 D) 0.20 Answer: A 15) Suppose a $60 strike call has 45 days until expiration and pays a 1.5% continuous dividend.

Assume S = $58.50, σ = 0.25, and r = 0.06. What is the option elasticity given an immediate price increase of $1.50?

A) 24.61 B) 18.61 C) 14.61 D) 9.61 Answer: B

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16) Assume that an investor is currently holding a reverse straddle position (i.e. a short put and short call), which is currently a profitable investment. All else being equal, what would this investor like to happen to vega?

A) Decrease B) Increase C) Stay constant D) Indifferent Answer: A 17) If an investor is speculating with a long call position, what is the most likely preference of the investor, relative to a change in rho?

A) Decrease B) Increase C) Stay constant D) Indifferent Answer: A 18) As the date of expiration approaches, what change in theta might counteract or slow down the drop in the option price?

A) Decrease B) Increase C) Stay constant D) Indifferent Answer: A 12.2 Short Answer Essay Questions 1) Which Greek is also called time decay and why?

Answer: Theta is called time decay because it measures the change in the option price relative to a change in the time to expiration.

2) Draw a payoff diagram for a long put position, depicting options that expire at 0, 30 and 60 days.

Answer:

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3) What is the difference between a standard bull spread and a calendar bull spread?

Answer: A standard spread involves two options with different strike prices. A calendar spread has all the same all characteristics, but with different expiration dates.

4) What is the difference between implied volatility and historical volatility?

Answer: The historical figure is calculated using past returns. Implied is an observable figure derived from actual option prices and the Black-Scholes formula.

5) What unique feature about perpetual options makes it possible to derive a valuation formula?

Answer: The time to expiration is constant: infinity. Given that time to expiration is constant, the price for early exercise is also a constant.

12.3 Class Discussion Question 1) Why do we care about Greeks? Use this as an opportunity to introduce students to option strategies. Ask students to create simple strategies such as covered calls. Introduce Greeks and show how "not all covered calls are created equal." Encourage the class to explain how the Greeks tell us which options are better to use than others.

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Derivatives Markets, 3e (McDonald) Chapter 13 Market-Making and Delta-Hedging 13.1 Multiple Choice 1) Assume that a $50 strike call pays a 2.0% continuous dividend, r = 0.07, σ = 0.25, and the stock price is $48.00. What is the profit or loss, per share, for a short call position if the option expires in 60 days and the price rises to $50.00 after 5 days?

A) $0.84 gain B) $0.84 loss C) $0.95 gain D) $0.95 loss Answer: B 2) Assume that a $60 strike call pays a 1.0% continuous dividend, r = 0.05, σ = 0.28, and the stock price is $62.00. What is the profit or loss per share if on a long call position, with 73 days until expiration, the price immediately rises to $63.00?

A) $0.68 gain B) $0.68 loss C) $0.88 gain D) $0.88 loss Answer: A 3) What is the total dollar cost to create a delta hedge position against a 200 short call position?

Assume calls are priced at $4.16, the delta is 0.7644, and stock price is $73.00.

A) $9,880 B) $10,328 C) $11,168 D) $12,660 Answer: B 4) Assume S = $33.00, σ = 0.32, r = 0.06, div = 0.01. You short 100 $35 strike calls at 68 days until expiration. Under a delta hedge position, what is your overnight profit/loss if the stock rises to $34.50?

A) $9.23 loss B) $9.23 gain C) $7.62 loss D) $7.62 gain Answer: C

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5) Assume that a $50 strike put pays a 2.0% continuous dividend, r = 0.07, σ = 0.25, and the stock price is $48.00. What is the profit or loss, per share, for a short put position if the option expires in 60 days and the price rises to $50.00 after 5 days?

A) $1.05 loss B) $1.05 gain C) $1.12 gain D) $1.12 loss Answer: C 6) Assume S = $33.00, σ = 0.32, r = 0.06, div = 0.01. You short 100 $35 strike puts at 68 days until expiration. Under a delta hedge position, what is your overnight profit/loss if the stock rises to $34.50? Assume no cost to short stock.

A) $8.30 gain B) $8.30 loss C) $9.56 gain D) $9.56 loss Answer: D 7) What is net dollar gain or cost required to create a short put delta hedge against a 100 short put position? Assume puts are priced at $1.98, the delta is 0.489, the stock price is $34.50, and no cost to short stock.

A) $1,540.50 gain B) $1,540.50 cost C) $2,319.58 gain D) $2,319.58 cost Answer: C 8) Assume S = $33.00, σ = 0.32, r = 0.06, div = 0.01, on a $35 strike call. Given delta = 0.3854 and gamma = 0.0847, what is the delta-gamma approximation for the call price on a $0.50 stock price increase? Assume 68 days until expiration.

A) $1.34 B) $1.36 C) $1.38 D) $1.40 Answer: A 9) Assume S = $45, σ = 0.25, r = 0.05, div = 0.0, on a 45 strike call and 55 days until expiration.

Given delta = 0.5502 and gamma = 0.0876, what is the delta-gamma approximation for the call price on a $0.90 stock price decline?

A) $1.35 B) $1.45 C) $1.55 D) $1.65 Answer: B

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10) Assume S = $56.00, σ = 0.45, r = 0.05, div = 0.0, on a $55 strike call and 45 days until expiration. Given delta = 0.6253, gamma = 0.0735, and theta = -0.0253, what is the approximate change in call price over 1 day, all else being the same?

A) $0.00 B) $0.01 C) $0.02 D) $0.03 Answer: A 11) Since delta of an option changes over the same time period that a stock price is changing, what is the delta used to calculate the approximate change in the option price?

A) Delta at the start of the time period B) Delta at the end of the time period C) The average delta over the time period D) The median delta over the time period Answer: C 12) Which of the following is NOT a source of cash while maintaining a delta neutral hedge?

A) Borrowing B) Purchase or sale of shares C) Interest D) Self financing Answer: D 13) Assume S = $62.50, σ = 0.20, r = 0.03, div = 0.0, on a $60 strike call and 81 days until expiration. Given a delta = 0.7092, gamma = 0.0582, and theta = -0.0158, what is the PREDICTED call price, using the delta, gamma, theta approach, after 1 day, assuming a $0.50 rise in the stock price?

A) $4.364 B) $4.376 C) $4.390 D) $4.392 Answer: B 13.2 Short Answer Essay Questions 1) Describe the true relationship between option prices and delta. Use calls as an example.

Answer: Delta as a measurement of option price sensitivity will understate actual option price changes when stock prices rise and overstate actual option price changes when stock prices decline.

2) The equation used by Black and Scholes to characterize the behavior of an option, expressed with Greeks, holds true for American options as well as European options with one exception.

What is the exception?

Answer: It does not hold true when it is optimal to exercise an option early.

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3) What prevents a market-maker from readjusting her delta hedge on a continual basis?

Answer: Transaction costs as well as the lack of price movement make constant readjustment impractical.

4) What actions are required to both delta-hedge and gamma-hedge a written option position?

Answer: We must long a different option so as to offset the short call gamma.

5) What are the two methods by which insurance companies hedge their risk of extreme losses?

Answer: Insurance companies can either hold large amounts of capital or purchase reinsurance, thus shifting the risk to another firm.

13.3 Class Discussion Question 1) Discuss the three methods used to reduce the risk of extreme price moves. Ask the class to also elaborate on why simple delta hedging is inadequate to the task.

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Derivatives Markets, 3e (McDonald) Chapter 14 Exotic Options: I 14.1 Multiple Choice 1) What is the payoff on a 75 strike Asian option given it is a geometric average price call? The recent prices are 72, 76, 74, 78, and 78.

A) 0.46 B) 0.56 C) 0.66 D) 0.76 Answer: B 2) What is the payoff on a 90 strike Asian option given it is a geometric average price put? The recent prices are 89, 90, 91, 87, 87, and 88.

A) 1.25 B) 1.35 C) 1.45 D) 1.55 Answer: B 3) The value of an Asian call option is computed using the geometric average strike. What is the expected payoff if the observed prices to date are 69, 70, 72, 71, 75, and 73, respectively?

A) 1.26 B) 1.36 C) 1.46 D) 1.56 Answer: B 4) The value of an Asian put option is computed using the geometric average strike. What is the expected payoff if the observed prices to date are 71, 72, 70, 68, 69, and 68, respectively?

A) 1.35 B) 1.45 C) 1.55 D) 1.65 Answer: D 5) Assume S = $55, K = $55, r = 0.07, σ = 0.27, div = 0.0, and 180 days until expiration. What is the premium on an Asian average price call, where N = 5?

A) $2.89 B) $2.99 C) $3.09 D) $3.19 Answer: D

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6) Assume S = $60, K = $60, r = 0.07, σ = 0.24, div = 0.02, and 90 days until expiration. What is the premium on an Asian average price put where N = 4?

A) $1.74 B) $1.84 C) $1.94 D) $2.04 Answer: A 7) Assume S = $36, K = 35, div = 0.0, r = 0.08, σ = 0.40, and 270 days until expiration. What is the premium on an Asian average strike call where N = 2?

A) $1.91 B) $2.01 C) $2.11 D) $2.21 Answer: A 8) Assume S = $43, K = 45, div = 0.0, r = 0.09, σ = 0.36, and 90 days until expiration. What is the premium on an Asian average strike put where N = 3?

A) $0.26 B) $0.36 C) $0.46 D) $0.56 Answer: C 9) Assume S = $52, K = 50, div = 0.01, r = 0.06, σ = 0.22, and 45 days until expiration. What is the premium on an Asian average strike call where N = 1?

A) $0.00 B) $0.10 C) $0.20 D) $0.30 Answer: A 10) Assume S = $51, K = $50, div = 0.0, r = 0.05, σ = 0.20, and 55 days until expiration. What is the premium on a knock-in call option with a down-and-in barrier of $48?

A) $0.175 B) $0.185 C) $0.195 D) $0.205 Answer: B 11) Assume S = $63, K = 60, div = 0, r = 0.04, σ = 0.35, and 90 days until expiration. What is the premium on a knock-in call option with an up-and-in barrier of $65?

A) $1.96 B) $2.06 C) $2.16 D) $2.26 Answer: B 2 Copyright © 2013 Pearson Education, Inc.

12) Assume S = $53, K = 50, div = 0, r = 0.03, σ = 0.30, and 100 days until expiration. What is the premium on a knock-in put option with an up-and-in barrier of $55?

A) $0.63 B) $0.73 C) $0.83 D) $0.93 Answer: C 13) Assume S = $66, K = 65, div = 0, r = 0.04, σ = 0.25, and 60 days until expiration. What is the premium on a knock-out call option with a down-and-out barrier of $60?

A) $2.40 B) $2.70 C) $3.00 D) $3.30 Answer: D 14) Assume S = $46, K = 45, div = 0, r = 0.03, σ = 0.20, and 50 days until expiration. What is the premium on a knock-out put option with an up-and-out barrier of $50?

A) $0.83 B) $0.93 C) $1.13 D) $1.33 Answer: A 15) Assume S = $42, K = 45, div = 0, r = 0.04, σ = 0.48, and 80 days until expiration. What is the premium on a knock-out put option with a down-and-out barrier of $44?

A) $2.13 B) $3.13 C) $3.47 D) $4.07 Answer: C 16) Assume S = $31.75, div = 0, r = 0.03, and σ = 0.20, and 90 days until the expiration of a standard call option. A call on call compound option with an exercise price of $2.00 has 180 days until expiration. What is the premium of the call on call option?

A) $1.46 B) $2.46 C) $3.04 D) $3.53 Answer: A

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17) Assume S = $31.75, div = 0, r = 0.03, and σ = 0.20, and 90 days until the expiration of a standard call option. A put on call compound option with an exercise price of $2.00 has 180 days until expiration. What is the premium of the put on call option?

A) $0.42 B) $0.48 C) $0.85 D) $1.11 Answer: A 18) The underlying stock for a European exchange option has S = $27.15, div = 2.0%, and σ = 0.18. The strike stock has S = $30.00, div = 0.0%, and σ = 0.22. The two stocks have a correlation coefficient of 0.73. If the exchange option expires in 2 years, what is the price of the call using a Black-Scholes approach?

A) $0.88 B) $0.98 C) $1.09 D) $1.19 Answer: C 14.2 Short Answer Essay Questions 1) Why might a down-and-in put option be more attractive than a standard option when hedging a foreign currency position?

Answer: At a given exercise price, the down-and-in put will cost less yet still provide protection against a drop in exchange rate.

2) When hedging a foreign currency position, what makes a down-and-out put unattractive?

Answer: Since you need protection against a rate decline, the termination of the put under a down-and-out barrier defeats the purpose of the hedge.

3) Why is the premium on a standard option and down-and-in call the same when the barrier price exceeds the stock price?

Answer: When the barrier price exceeds the stock price the option is "knocked-in" and thus will be priced as a standard option.

4) For a long put position, what benefit is provided by a gap option should prices rise?

Answer: If prices rise, the gap option has no cost since it acts like a "pay later" situation.

5) What is the primary difference between a standard option and an exchange option?

Answer: When exercised, payment is made with cash under a standard option and it is made via an asset under an exchange option.

14.3 Class Discussion Question 1) Why are exotic options not so exotic? Ask the class to explain why an option described as exotic is merely a standard option with different terms. Ask students to create exotic options that are different than the text examples.

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Derivatives Markets, 3e (McDonald) Chapter 15 Financial Engineering and Security Design 15.1 Multiple Choice 1) Mel, Inc. stock is $135.00 per share. The company's semi-annual dividend is forecasted as $2.10 per share, indefinitely. What is the price of a zero-coupon equity-linked bond, promising to pay one share in 3 years, given annual interest rates of 5.0%?

A) $101.35 B) $110.26 C) $123.45 D) $155.22 Answer: C 2) Albert, Inc. stock is $42.00 per share. The company's quarterly dividend is forecasted as $0.50 per share, increasing 10.0% at the start of every year. What is the price of a zero-coupon equitylinked bond, promising to pay one share in 3 years, given annual interest rates of 8.0%?

A) $32.60 B) $36.20 C) $42.60 D) $62.40 Answer: B 3) Dawn, Inc. stock is $37.00 per share. The company's semi-annual dividend is forecasted as $0.25 per share, increasing every 6 months by 20.0%. What is the price of a zero-coupon equitylinked bond, promising to pay one share in 4 years, given annual interest rates of 6.0%?

A) $32.29 B) $33.49 C) $34.39 D) $35.69 Answer: B 4) Wayne, Inc. stock is $40.00 per share. The company's quarterly dividend is forecasted as $0.45 per share, indefinitely. A coupon equity-linked bond, promising to pay one share of Wayne, Inc. in 3 years pays a quarterly coupon of $0.50. If annual interest rates are 4.0%, what is the price of the bond?

A) $40.56 B) $42.60 C) $44.56 D) $46.60 Answer: A

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5) Will, Inc. stock is $63.35 per share. The company's quarterly dividend is forecasted as $0.10 per share, increasing 5.0% every quarter. A coupon equity-linked bond, promising to pay one 1 share of Will, Inc. in 2 years pays a semi-annual coupon of $0.20. If annualized interest rates 2 are 8.0%, what is the price of the bond?

A) $59.55 B) $61.14 C) $63.12 D) $65.22 Answer: C 6) Assume the spot price of gold is $750 per ounce, the 1-year forward price is $770, and the annual interest rate is 4.5%. What is the price of a zero-coupon note paying 1 ounce of gold in one year?

A) $770 B) $750 C) $725 D) $736 Answer: D 7) Assume the spot price of gold is $745 per ounce and the 2-year forward price is $773.

Annualized 1-year and 2-year forward interest rates are 5.0% and 5.2%, respectively. For a commodity-linked note to sell at par, what is the annual coupon?

A) $23.09 B) $24.09 C) $25.09 D) $26.09 Answer: D 8) Assume oil prices rise dramatically and the spot price of oil is $230 per barrel and the 3-year forward price is $245. Annualized 1-year, 2-year, and 3 year interest rates are 4.2%, 4.4%, and 4.6%, respectively. For a commodity-linked note to sell at par, what is the annual coupon?

A) $6.00 B) $16.00 C) $26.00 D) $36.00 Answer: A 9) Assume the price of Mary, Inc. stock is $56.00, interest rates are 4.8%, div yield = 0, and σ = 0.35. What is the price of a $1,000 par value 2-year price-participation note paying a 5.0% annual coupon and receiving 50.0% of all price appreciation above $65.00?

A) $896.44 B) $996.44 C) $1006.44 D) $1106.44 Answer: C 2 Copyright © 2013 Pearson Education, Inc.

10) What is the price of a 2-year equity-linked CD under the following terms? No coupon is paid. At maturity the CD pays 80.0% of the S&P 500 index appreciation. The S&P 500 price = 900, div = 0.02, σ = 0.20, and interest rates are 5.0%.

A) $890.22 B) $990.23 C) $1064.20 D) $1110.55 Answer: A 11) We wish to cap participation in a 3-year equity-linked option at 50.0% return. Our profit alpha is 3.0%. The S&P 500 price = 950, div = 0.015, σ = 0.22, and interest rates are 4.8%. What is the implied participation rate?

A) 0.66 B) 0.76 C) 0.96 D) 1.16 Answer: B 12) A commodity linked bond is issued with an embedded call option. The current commodity price is $110, as is the exercise price on the call option. The call option is priced at $3.41. If the promised payment on the bond is the same as the issue price of $100, what is the implied coupon if effective interest rates are 3.0% and the bond has a 1-year maturity?

A) $0.66 B) $0.77 C) $0.88 D) $0.99 Answer: D 13) A commodity linked bond is issued with an embedded call option. The current commodity price is $52, as is the exercise price on the call option. The call option is priced at $5.56. If the promised payment on the bond is the same as the issue price of $40, what is the yield on the bond if effective interest rates are 4.0% and the bond has a 1-year maturity?

A) 2.24% B) 2.80% C) 3.50% D) 4.0% Answer: A 14) Which of the following financially engineered products is NOT used to defer the payment of capital gains taxes on securities that have appreciated?

A) Commodity Linked Options B) DECS C) Equity Linked Notes D) PEPS Answer: A

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15.2 Short Answer Essay Questions 1) For whom would the issue of an oil-linked debt instrument not be considered a risky issue?

Answer: Any firm engaged in oil production would be perfectly hedged by the issuance of oillinked debt.

2) Instead of issuing a pure commodity-linked debt, why would the commodity producing firm consider a combining interest plus participation in the commodity price appreciation?

Answer: With the coupon interest, the bondholder assumes price risk in the commodity. The combination implies a coupon plus a call option.

3) What possible tax advantage exists in equity-linked notes?

Answer: Equity-linked notes can be used to defer income, thus delay taxes. Such schemes delay taxes and act like interest free loans.

4) How does a coupon bond differ from an equity-linked bond?

Answer: Instead of paying cash at maturity the equity-linked bond pays the bondholder equity shares.

5) What is the primary difference between an equity-linked bond and a currency-linked bond?

Answer: Instead of the dividend yield on stock, the currency-linked bond considers the foreign interest rate.

15.3 Class Discussion Question 1) The chapter discusses the merging of debt and options. Ask the class why firms would consider such instruments. Highlight the use of a PERC by a company that has difficulty issuing debt, yet can offer the carrot of price appreciation.

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Derivatives Markets, 3e (McDonald) Chapter 16 Corporate Applications 16.1 Multiple Choice 1) We will assume that Nathans, Inc. has 3-year zero-coupon debt outstanding, which will pay $200 at maturity. The assets are valued at $175, σ = 0.20, r = 0.04, and the company does not pay a dividend. Using a Black-Scholes model, what is the value of the equity?

A) $23.05 B) $43.05 C) $63.05 D) $83.05 Answer: A 2) Jessie, Inc. has 4-year zero-coupon bonds outstanding, which will pay $1,000 at maturity. The assets are valued at $900, σ = 0.25, r = 0.045, and the company does not pay a dividend. Using a Black-Scholes model, what is the yield on debt?

A) 4.68% B) 6.48% C) 8.46% D) 8.64% Answer: B 3) Compute the yield on debt given a 10-year zero-coupon bond paying $500 at maturity.

Assume the asset value is $450, σ = 0.35, r = 0.06, and no dividend is paid.

A) 6.62% B) 7.26% C) 8.26% D) 9.62% Answer: C 4) What is the expected return on equity using the Black-Scholes formula, given a zero-coupon bond that pays $250 at maturity in 4 years? Assume assets are worth $200, r = 0.05, σ = 0.30, and no dividend is paid. The return on assets is 11.5%.

A) 10.27% B) 14.27% C) 18.27% D) 22.27% Answer: D

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5) What is the difference in the expected returns on equity when using a Black-Scholes formula versus a traditional weighted average formula? Assume rA = 0.12, rf = 0.06, asset value = $170, equity value = $45, debt to value ratio = 0.55, and delta = 0.6500.

A) 1.00% B) 1.20% C) 1.40% D) 1.60% Answer: C 6) James, Inc. has zero-coupon outstanding debt maturing in 8 years. In rank of seniority, each pays at maturity $20 million, $15 million, and $40 million. Assume asset value = $60 million, r = 0.05, σ = 0.28, and no dividend is paid. What is the yield on the $15 million subordinate debt?

A) 5.72% B) 6.72% C) 7.72% D) 8.72% Answer: B 7) Daniels, Inc. has assets valued at $2 million and 50,000 outstanding shares. A 5-year zerocoupon bond exists, which pays $400,000 at maturity. The bond is convertible into 10,000 shares. Assume σ = 0.30, r = 0.055, and no dividend is paid. What is the value of the bond?

A) $402,672 B) $452,172 C) $415,022 D) $385,172 Answer: A 8) Willco, Inc. issues compensation options with the following terms. Strike = $45, price = $42.00, σ = 0.48, r = 0.05, div = 0.02. What is the value of the option if it will be repriced at $30? Assume 10 years to expiration.

A) $22.78 B) $24.65 C) $26.22 D) $30.46 Answer: A 9) Lechno, Inc. issues compensation options with the following terms. Strike = $65, price = $63.50, σ = 0.22, r = 0.045, div = 0.015. What is the value of the option if it will be repriced at $40? Assume 10 years to expiration.

A) $18.64 B) $22.22 C) $24.32 D) $26.84 Answer: D

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10) A company issues an option grant with an outperformance feature, against the S&P 500.

Assume S&P 500 = 950, S = 22, k = 25, σ = 0.25, r = 0.06, and 5 years until expiration. The S&P 500 has a dividend yield of 2%, standard deviation of 18.0% and a 0.30 correlation coefficient with the stock. What is the value of the outperformance feature?

A) $0.99 B) $1.31 C) $1.59 D) $1.72 Answer: C 11) A company issues an option grant with an outperformance feature, against the S&P 500.

Assume S&P 500 = 1100, S = 46, k = 45, σ = 0.30, r = 0.04, and 10 years until expiration. The S&P 500 has a dividend yield of 2.5%, standard deviation of 20.0% and a 0.45 correlation coefficient with the stock. What is the value of the outperformance option?

A) $11.92 B) $15.99 C) $19.75 D) $21.05 Answer: C 12) A company issues an option grant with an outperformance feature, against the S&P 500.

Assume S&P 500 = 1100, S = 46, k = 45, σ = 0.30, r = 0.04, and 10 years until expiration. The S&P 500 has a dividend yield of 2.5%, standard deviation of 20.0% and a 0.45 correlation coefficient with the stock. What is the value of the outperformance feature?

A) $2.25 B) $3.29 C) $4.11 D) $4.78 Answer: B 13) A company issues an option grant with an outperformance feature, against the S&P 500.

Assume S&P 500 = 1100, S = 46, k = 45, σ = 0.30, r = 0.04, and 10 years until expiration. The S&P 500 has a dividend yield of 2.5%, standard deviation of 20.0% and a 0.45 correlation coefficient with the stock. What is the value of the outperformance option?

A) $11.92 B) $15.99 C) $19.75 D) $21.05 Answer: C 14) In the case of an acquisition, with which of the following offer structures does the acquired firm bear the most risk between the time the offer is accepted and the time it is consummated?

A) Fixed stock offer B) Floating stock offer C) Fixed collar offer D) Floating collar offer Answer: A 3 Copyright © 2013 Pearson Education, Inc.

16.2 Short Answer Essay Questions 1) How does a reload option provide additional compensation compared to regular compensation options?

Answer: The reload option gives the option-holder new options when existing options are exercised.

2) Why does a company sell a put when issuing compensation options?

Answer: The short put acts like a hedge against the repurchasing of shares.

3) What feature of reload options prevents the use of a Black-Scholes valuation?

Answer: The options may be exercised early.

4) What three components exist in the value of an "outperform stock option"?

Answer: The standard option price, the outperformance feature, and the multiplier.

5) The use of collars in acquisitions serves the purpose of addressing what two issues in an offer?

Answer: Which company will bear the risk of a change in the stock price and the magnitude of this exposure.

16.3 Class Discussion Question 1) Why should or should not a company expense compensation options? Divide the class into two groups and assign each a different opinion. Have each prepare arguments to support their case. After brief group meetings, have each group present their conclusions.

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Derivatives Markets, 3e (McDonald) Chapter 17 Real Options 17.1 Multiple Choice 1) Mead, Inc. may invest $20 million in a new fiber optic project. Due to market conditions, annual production costs and revenues are forecasted at $10 million and $8 million, respectively, starting next year. Revenues are expected to grow at 4.0% and interest rates are 6.0%. What is the change in value if the project is commenced in 5 years instead of today? (Use static analysis.)

A) $8.84 million B) $10.84 million C) $12.84 million D) $14.84 million Answer: B 2) Techie, Inc. may invest $5 million in a new Star Communicator project. Annual production costs and revenues are projected to be $2 million and $1.5 million, with each growing at 2.0% and 4.0%, respectively. At an interest rate of 5.5%, what is the approximate investment year that will maximize value? (Use static analysis.)

A) Year 20 B) Year 15 C) Year 10 D) Year 5 Answer: A 3) Geek Is Us, Inc. may invest $8 million in an Alien Spectograph project. Annual costs and revenues, starting next year, are forecasted to be $3 million and $2 million growing at 0.0% and 4.0%, respectively. If the opportunity cost of capital is 6.0% and σ = 0.0, what is the investment trigger price?

A) $20.95 million B) $30.95 million C) $40.95 million D) $50.95 million Answer: D 4) Walla, Inc. may invest $6 million in a Buffalo harvesting project. Annual costs and revenues, starting next year, are forecasted to be $1 million and $0.7 million, growing at 0.0% and 3.0%, respectively. If the opportunity cost of capital is 4.5%, what is the investment trigger price?

A) $19.25 million B) $21.25 million C) $23.25 million D) $25.25 million Answer: C

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5) Use Cox-Ross-Rubenstein to construct a 2-year binomial tree for the evolution of cash flows with a binomial period of 1. Assume the initial cash flow (CF1) is $20 million, σ = 0.45, r = 0.13, g = 0.02, and the project lasts 2 years. What is the value of the project on the up node in year 1?

A) $85 million B) $185 million C) $285 million D) $385 million Answer: C 6) Use a binomial tree to value the following option. Assume rf = 0.04, rp =0.12, σ = 0.35, E(CF1) = $30, and cost = $300. What is the value of this project option?

A) $40.74 B) $50.60 C) $55.32 D) $62.12 Answer: A 7) Use Cox-Ross-Rubenstein to construct a 2-year binomial tree for the evolution of cash flows with a binomial period of 1. Assume the initial cash flow is (CF1) = $62 million, σ = 0.20, rp = 0.14, and g = 0.03. What is the highest possible value of the project?

A) $222 million B) $314 million C) $622 million D) $841 million Answer: D 8) Use a binomial tree to value to following option. Assume rf = 0.045, rp = 0.14, σ = 0.20, E(CF1) = $62 million, g = 0.03, time horizon = 2 years, binomial period = 1 year, and cost = $500 million. What is the value of this project option?

A) $47 million B) $57 million C) $67 million D) $77 million Answer: C 9) The current price per cord of lumber is $26.00. The effective annual lease rate is 2.0% and the risk free rate is 4.0%. The cost to harvest one cord is $20.00 and constant. What is the trigger price at which we will harvest the lumber?

A) $27.61 B) $31.61 C) $35.61 D) $39.61 Answer: D

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10) The current price per ton of iron ore is $145.00. The effective lease rate is 3.0% and the risk free rate is 4.5%. The cost to mine one ton of iron ore is $110.00 and constant. What is the trigger price at which we will mine the iron ore?

A) $163.80 B) $180.40 C) $210.50 D) $205.70 Answer: A 11) The current price of silver is $ 31.00 per ounce. The effective lease rate and risk free rate are 1.0% and 3.5%, respectively. If the cost to mine one ounce of silver is a constant $25.00, what is the value of an option to wait and mine the silver later?

A) $13.50 B) $14.50 C) $15.50 D) $16.50 Answer: B 12) The current price of silver is $32.00 per ounce. The effective lease rate and risk free rate are 3.0% and 4.0%, respectively. If the cost to mine one ounce of silver is a constant $25.00, what is the trigger price per ounce at which the silver will be mined?

A) $33.17 B) $35.17 C) $37.17 D) $39.17 Answer: A 13) The price of oil is $120 per barrel. The effective lease rate and risk free rate are 5.0% and 6.0%, respectively. The constant cost of extraction is $105 per barrel and the volatility of prices is 18.0%. What is the value of an option to defer extraction?

A) $30.68 B) $32.08 C) $34.56 D) $38.34 Answer: B 14) The price of oil is $115 per barrel. The effective lease rate and risk free rate are 3.0% and 4.0%, respectively. The constant cost of extraction is $85 per barrel and the volatility of prices is 15.0%. If an untapped well costs $2,100 to open and can produce indefinitely, what is the value of the unopened well?

A) $724 B) $854 C) $913 D) $1,025 Answer: C

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15) The price of oil is $115 per barrel. The effective lease rate and risk free rate are 3.0% and 4.0%, respectively. The constant cost of extraction is $85 per barrel and the volatility of prices is 15.0%. If an untapped well costs $2,100 to open and can produce indefinitely, at what price per barrel should the well be opened?

A) $349 B) $423 C) $454 D) $484 Answer: A 16) An existing well is operating and the price of oil is $115 per barrel. The effective lease rate and risk free rate are 3.0% and 4.0%, respectively. The constant cost of extraction is $85 per barrel and the volatility of prices is 15.0%. If it costs nothing to shut down the well, at what price would we close the well?

A) $41 B) $48 C) $52 D) $59 Answer: A 17.2 Short Answer Essay Questions 1) What is the relationship, in general, between volatility and trigger prices, assuming constant costs?

Answer: Higher volatility increases the optimal trigger price.

2) Why is the perpetual call formula used to price commodity extraction options?

Answer: First, the option is a call since we have the right to invest. Second, the option, in theory, never expires and can be exercised early, thus, the perpetual call.

3) What is the main difference in pricing R & D options versus most other real options?

Answer: R & D options require continual expenditures, while most other real options are exercised with a one-time expenditure.

4) In the context of peak-load energy generation and a European exchange option, what is the spark spread?

Answer: The difference between the price of electricity and the cost of generation.

5) What two components go into valuing an infinite commodity reserve?

Answer: First, we compute the value of ongoing production, and then we value the option to pick the time to make the investment.

17.3 Class Discussion Question 1) How are call and put options used to value starting, stopping, and restarting commodity extraction projects? Ask students to identify the calls and puts in each situation.

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Derivatives Markets, 3e (McDonald) Chapter 18 The Lognormal Distribution 18.1 Multiple Choice 1) What is the area under the standard normal distribution curve and is less than 0.654?

A) 0.5115 B) 0.6215 C) 0.7434 D) 0.8283 Answer: C 2) What is the probability that a number drawn from the standard normal distribution will be between -0.60 and 0.45?

A) 0.40 B) 0.50 C) 0.60 D) 0.70 Answer: A 3) What is the probability that a number drawn from the standard normal distribution will NOT be between -1 and 1?

A) 0.22 B) 0.32 C) 0.42 D) 0.52 Answer: B 4) Given a mean of 4.5 and a standard deviation of 12 from a sample of variables, what is the equivalent draw from a standard normal distribution for 6.0?

A) 0.065 B) 0.075 C) 0.095 D) 0.125 Answer: D 5) Given a mean of -4.3 and a standard deviation of 26, what is the equivalent draw from a normal distribution for a standard normal sample variable of 0.67?

A) -13.12 B) 03.12 C) 13.12 D) 23.12 Answer: C

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6) Given a mean of -7.8 and a standard deviation of 16 from a normally distributed sample, what is the probability of an observation being below 12.0?

A) 0.51 B) 0.61 C) 0.71 D) 0.81 Answer: D 7) Given a mean of 45 and a standard deviation of 32 from a normally distributed sample, what is the probability of an observation being between 35 and 75?

A) 0.35 B) 0.45 C) 0.55 D) 0.65 Answer: B 8) For a stock price that was initially $55.00, what is the price after 4 years if the continuously compounded returns for these 4 years are 4.5%, 6.2%, 8.9%, -3.2%?

A) $64.80 B) $74.80 C) $84.80 D) $94.80 Answer: A 9) A stock is valued at $55.00. The annual expected return is 12.0% and the standard deviation of annualized returns is 22.0%. If the stock is lognormally distributed, what is the expected price after 3 years?

A) $78.83 B) $88.83 C) $98.83 D) $108.83 Answer: A 10) A stock is valued at $55.00. The annual expected return is 12.0% and the standard deviation of annualized returns is 22.0%. If the stock is lognormally distributed, what is the expected median stock price after 3 years?

A) $57.67 B) $67.67 C) $77.67 D) $87.67 Answer: A

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11) A stock is valued at $55.00. The annual expected return is 12.0% and the standard deviation of annualized returns is 22.0%. If the stock is lognormally distributed, what is the price of the stock given a one standard deviation move up after 3 years?

A) $64.41 B) $74.41 C) $84.41 D) $94.41 Answer: C 12) A stock is valued at $28.00. The annual expected return is 9.0% and the standard deviation of annualized returns is 19.0%. If the stock is lognormally distributed, what is the expected price after 4 years?

A) $28.00 B) $32.33 C) $40.13 D) $54.60 Answer: C 13) A stock is valued at $28.00. The annual expected return is 9.0% and the standard deviation of annualized returns is 19.0%. If the stock is lognormally distributed, what is the expected median stock price after 4 years?

A) $28.00 B) $32.33 C) $40.13 D) $54.60 Answer: B 14) A stock is valued at $28.00. The annual expected return is 9.0% and the standard deviation of annualized returns is 19.0%. If the stock is lognormally distributed, what is the price of the stock given a one standard deviation move up after 4 years?

A) $28.00 B) $32.33 C) $40.13 D) $54.60 Answer: D 18.2 Short Answer Essay Questions 1) Give a very brief definition of conditional expected stock price.

Answer: It is the expected stock price given that an option expires in the money.

2) In a lognormal model of stock price movement, describe the mean and variance of the continuously compounded returns.

Answer: The return is normally distributed while both the return and variance grow proportionally with time.

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3) What assumption is made in the Black-Scholes model concerning volatility?

Answer: The assumption made is that volatility is constant over time.

4) Why might normally distributed returns appear non-normal?

Answer: The variance may change even though the distribution is still normal. A histogram may appear non-normal when it is a mixture of normals.

5) How are partial expectation prices converted to conditional expectation prices?

Answer: By dividing the partial expectation by the probability of the conditioning event, we determine the conditional expectation.

18.3 Class Discussion Question 1) Why do we assume a lognormal distribution in option pricing? Ask the class to explain the pluses and minuses to this assumption. Once the downfalls are established, probe students to find out if a better alternative exists.

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Derivatives Markets, 3e (McDonald) Chapter 19 Monte Carlo Valuation 19.1 Multiple Choice 1) Given X1 = N (0, 1) and X2 = N (0.5, 8), what is the mean of ex2?

A) 69.97 B) 79.97 C) 89.97 D) 99.97 Answer: B 2) Monte Carlo simulation assumes all assets earn: A) Risk-free rate B) Market Index return C) YTM on AAA Bonds D) Brokers call Answer: A 3) A critical assumption in Monte Carlo simulations is that valuation is based on: A) Random variables B) True probabilities C) Risk-neutral probabilities D) None of the above Answer: C 4) When valuing options using true probabilities, the discount rate is computed as follows: A) Once using the risk-free rate B) At the final period C) For each node D) For each path Answer: D 5) What type of random variable is necessary for a Monte Carlo valuation?

A) Standard normal distribution B) Normal distribution C) Lognormal distribution D) All of the above Answer: D 6) In what option does it benefit to simulate the path of potential asset prices?

A) Barrier B) European C) Asian D) A and C Answer: D 1 Copyright © 2013 Pearson Education, Inc.

7) What statistic is used to determine the accuracy of a Monte Carlo simulation?

A) Mean B) Standard deviation C) Covariance D) Correlation coefficient Answer: B 8) Which of the following options would not benefit from using a Monte Carlo simulation?

A) American B) Asian C) European D) Barrier Answer: C 9) What method uses the insight that for each simulated realization there is an opposite and equally likely realization?

A) Stratified sampling B) Control variate C) Antithetic variate D) Efficient variate Answer: C 10) Which distribution is a discrete probability distribution that counts the number of events, such as large stock price moves, that occur over a period of time?

A) Latin hypercube B) Normal C) Lognormal D) Poisson Answer: D 11) When a stock price movement occurs and is more than we would expect from a lognormal distribution, we refer to this as: A) Pull B) Jump C) Squat D) Push Answer: B 12) A stock owned by a portfolio has a bankruptcy probability of 1% per year. Using a Poisson distribution, what is the probability that this firm will not declare bankruptcy over the upcoming 10 years?

A) 60% B) 70% C) 80% D) 90% Answer: D 2 Copyright © 2013 Pearson Education, Inc.

13) What technique might be used to improve the accuracy of a Monte Carlo simulated output?

A) Arithmetic Asian option B) Control variate method C) Poisson Distribution with jumps D) Risk neutral probabilities Answer: C 14) If using Monte Carlo simulation, what is a typical number of iterations employed in the model?

A) 1 B) 10 C) 1,000 D) 1,000,000 Answer: C 19.2 Short Answer Essay Questions 1) How does the number of draws impact the validity of a Monte Carlo simulation?

Answer: The larger the number of draws, the better the results.

2) Why does an Asian option benefit from a larger number of draws in a Monte Carlo simulation?

Answer: Since an Asian option uses the average price and not the actual price, the larger sample size reduces the variance of individual outcomes.

3) How does a control variate method make a naive Monte Carlo more efficient?

Answer: An estimate of the error in each trial relative to a related option issued to improve the accuracy of each successive trial.

4) Why are covariances and correlations relevant to simulation development?

Answer: Stocks often move together to varying degrees. Covariances and correlation coefficients allow us to model these behaviors.

5) What advantage does a variance reduction technique offer?

Answer: When repeated Monte Carlo simulations are performed, techniques exist to increase the efficiency of the simulations and identify better fitting distributions.

19.3 Class Discussion Question 1) Ask the class to state how simulations could be used to improve pricing models. Highlight situations where historical results violated pricing assumptions and how simulations may have provided better results.

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Derivatives Markets, 3e (McDonald) Chapter 20 Brownian Motion and Ito's Lemma 20.1 Multiple Choice 1) Assume a stock price of S(0) = $62.00, r = 0.05, σ = 0.30, and dividend = 0. What is the price of a claim that pays S ? Use formula 20.29.

A) $7.59 B) $8.59 C) $9.59 D) $10.59 Answer: A 2) Assume a stock price of S(0) = $83.00, r = 0.045, σ = 0.25, and dividend = 0.02. What is the price of a claim that pays S3? Use formula 20.29.

A) $423,323 B) $710,695 C) $624,165 D) $818,123 Answer: B 3) Assume a stock price of S(0) = $45.00, r = 0.03, σ = 0.40, and dividend = 0.015. What is the price of a claim that pays 3 S ? Use formula 20.29.

A) $6.41 B) $5.41 C) $4.41 D) $3.41 Answer: D 4) Assume a stock price of S(0) = $80.00, r = 0.05, σ = 0.35, and dividend = 0.01. What is the price of a claim that pays S-2/3? Use formula 20.29.

A) $0.25 B) $0.35 C) $0.05 D) $0.15 Answer: C 5) Assume the following: LN(S) and LN(Q) have a correlation coefficient of 0.40, S(0) = 60, Q(0) = 60, r = 0.05, σs = 0.30 σQ = 0.25, and dividend = 0. Using formula 20.39, what is the price of a claim that pays S Q ?

A) $243.96 B) $322.96 C) $479.96 D) $532.96 Answer: C 1 Copyright © 2013 Pearson Education, Inc.

6) Assume the following: LN(S) and LN(Q) have a correlation coefficient of -0.65, S(0) = 55, Q(0) = 60, r = 0.04, σs = 0.22 σQ = 0.15, and dividends = 0. Using formula 20.39, what is the price of a claim that pays Q/ S ?

A) $8.16 B) $9.16 C) $10.16 D) $11.16 Answer: A 7) Assume the following: LN(S) and LN(Q) have a correlation coefficient of -0.20, S(0) = 45, S(Q) = 55, r = 0.03, σs = 0.18 σQ = 0.28, and no dividends. Using formula 20.39, what is the price of a claim that pays 1/ QS ?

A) $3.02 B) $2.02 C) $1.02 D) $0.02 Answer: D 8) The value of Z(t) at any point in time can be described as a process in which there is a cumulative effect of infinitely small movements. This process is called: A) Ornstein-Uhlenbeck B) Diffusion C) Ito D) Geometric Answer: B 9) A modification to the Brownian process that permits mean reversion is called: A) Ornstein-Uhlenbeck B) Diffusion C) Ito D) Geometric Answer: A 10) A modification to the Brownian process in which the drift and volatility depend on the stock price is called: A) Ornstein-Uhlenbeck B) Diffusion C) Ito D) Geometric Answer: C

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11) For purposes of option pricing, when the movement of a stock price follows a geometric Brownian motion, the stock price is said to follow which type of distribution?

A) Bimodal B) Latin hypercube C) Lognormal D) Normal Answer: C 12) A Brownian motion is a stochastic process that can be described as a: A) Pattern of movements with continuous movements B) Pattern of movements with discrete movements C) Random walk with continuous movements D) Random walk with discrete movements Answer: C 13) The deterministic drift of a pure Brownian motion that is virtually undetectable is sometimes referred to as the: A) Distribution B) Expected return C) Random walk D) Standard deviation Answer: B 20.2 Short Answer Essay Questions 1) What are two important implications of assuming that prices follow a geometric Brownian motion?

Answer: The distribution dictated is lognormal and we are able to describe the path taken by stock prices.

2) Provide a definition of Brownian motion.

Answer: A random walk occurring in continuous time with movements that are continuous rather than discrete.

3) Define the term drift.

Answer: The expected change per unit time in an asset price.

4) When considering drift and noise, how would you explain price movements over smaller and smaller time intervals?

Answer: As time decreases drift becomes undetectable and returns tend to reflect a random Brownian motion.

5) What is the relationship of the Sharpe ratios and risk premiums between stocks and options?

Answer: Since volatility of options is higher than stocks, they do not have the same risk premiums, however, they will have the same Sharpe measures.

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20.3 Class Discussion Question 1) Why is Brownian motion the foundation for modern derivatives pricing models? Attempt to elicit responses that understand the shortcomings of using this motion for just asset pricing and the advantages in risk measurement.

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Derivatives Markets, 3e (McDonald) Chapter 21 The Black-Scholes-Merton Equation 21.1 Multiple Choice 1) What term is sometimes used to describe the price at a particular point in time, say maturity, that is necessary to calculate today's price?

A) Face value B) Par value C) Boundary condition D) All of the above Answer: D 2) What is the boundary condition for a European call option?

A) Max [0,S(T)-K] B) Max [0,K-S(T)] C) Min [0,S(T)-K] D) Min [0,K-S(T)] Answer: A 3) What is the boundary condition for a European put option?

A) Max [0,S(T)-K] B) Max [0,K-S(T)] C) Min [0,S(T)-K] D) Min [0,K-S(T)] Answer: B 4) What do we call an option in which the holder has a claim that pays one share of stock if S(T) > K, and nothing otherwise?

A) Cash-or-nothing option B) Asset-or-nothing option C) Exotic option D) Digital cash Answer: B 5) Which of the following equations represents a call power option?

A) Min (Ka-Sa,0) B) Max (Ka-Sa,0) C) Min (Sa-Ka,0) D) Max (Sa-Ka,0) Answer: D

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6) Which of the following examples does not involve different numeraire?

A) Currency translation B) Quantity uncertain C) Backward equation D) All-or-nothing options Answer: C 7) Mary wagers to pay one share of stock to Matt if the price at expiration in 1 year is above $75.00. Assume S(0) = 60.00, σ = 0.15, r = 0.04, and dividend rate = 0.01. What is the value of Mary's bet?

A) $6.55 B) $7.55 C) $8.55 D) $9.55 Answer: B 8) Assume S = $60, K = $65, σ = 0.15, r = 0.05, T - t = 122 days, div = 0.015, and a jump probability = 0.003. What is the value of a call?

A) $0.67 B) $1.67 C) $2.67 D) $3.67 Answer: A 9) Assume S = $52.50, K = $55, σ = 0.20, r = 0.045, T - t = 130 days, div = 0.01, and a jump probability = 0.007. What is the value of a put option?

A) $3.63 B) $2.63 C) $1.63 D) $0.63 Answer: A 10) Assume S = $48.35, K = 45, σ = 0.23, r = 0.04, T - t = 60 days, div = 0, and a jump probability = 0.005. What is the increase in the value of a call over a no-jump call?

A) $0.04 B) $0.03 C) $0.02 D) $0.01 Answer: B

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11) Lapel Inc. stock price is $32.00. Joe bets Sarah that the price will be above $35.00 in 6 months (180 days). The standard deviation of the stock is 0.25 and the risk free interest rate is 5.0%. If Joe wins the bet, he wishes to be paid with one share of stock. What is the value of the wager to Joe? A) $3.00 B) $9.65 C) $12.44 D) $19.58 Answer: C 12) Lapel Inc. stock price is $32.00. Joe bets Sarah that the price will be above $35.00 in 6 months (180 days). The standard deviation of the stock is 0.25 and the risk free interest rate is 5.0%. If Joe wins the bet, he wishes to be paid with one share of stock. If Sarah agrees to the bet, what is the value of her wager?

A) $3.00 B) $9.65 C) $12.44 D) $19.58 Answer: D 13) Lapel Inc. stock price is $32.00. Joe bets Sarah that the price will be above $35.00 in 6 months (180 days). The standard deviation of the stock is 0.25 and the risk free interest rate is 5.0%. If Joe wins the bet, he wishes to be paid with one share of stock. At approximately what stock price will the wager be of equal value to both Joe and Sarah?

A) $32.00 B) $33.30 C) $34.25 D) $35.00 Answer: B 21.2 Short Answer Essay Questions 1) Explain the relationship between strike prices and implied volatilities under a price jump scenario.

Answer: At lower strike prices implied volatility rises, particularly when time to expiration is low.

2) How does a dividend payment impact the option price?

Answer: The stock price represents the present value of future dividends, thus, in essence, modifies the return and will adjust the option price.

3) Briefly define a terminal boundary condition.

Answer: European options fall into this category and are characterized by the fact that they are satisfied by an asset at expiration.

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4) Define a power option.

Answer: An option whose payoff, at maturity, is based upon the stock price at maturity raised to some exponential figure.

5) Give an example of currency translation that is a change in numeraire.

Answer: A firm has income in yen from overseas operations that may be valued in dollars.

21.3 Class Discussion Question 1) How does the Black-Scholes equation explain the pricing of derivatives? Ask the class to explain the variety of ways in which the Black-Scholes model can be modified in order to price various derivatives.

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Derivatives Markets, 3e (McDonald) Chapter 22 Risk-Neutral and Martingale Pricing 22.1 Multiple Choice 1) For a utility function that exhibits decreasing martingale utility, the martingale utility is high when: A) Consumption and utility are low B) Consumption and utility are high C) Consumption is low and utility is high D) Consumption is high and utility is low Answer: A 2) For a utility function that exhibits decreasing martingale utility, the martingale utility is low when: A) Consumption and utility are low B) Consumption and utility are high C) Consumption is low and utility is high D) Consumption is high and utility is low Answer: B 3) The ratio of the future uncertain martingale utility to the present known martingale utility is called: A) Brownian motion B) Change of measure C) Stochastic discount factor D) Utility function Answer: C 4) The process of moving from one probability distribution to another is called: A) Brownian motion B) Change of measure C) Stochastic discount factor D) Utility function Answer: B 5) The risk-neutral measure arises when we select ________ as the numeraire.

A) Asset portfolio B) Corporate bond C) Treasury bond D) Money market account Answer: D

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6) In martingale pricing, the observed price of a stock follows a process which substitutes what variable for alpha?

A) Delta B) Epsilon C) Money market rate D) Risk-free rate Answer: D 7) The pricing of derivatives is linked to the decisions investors make relative to: A) Black-Scholes variables B) Money markets C) Portfolios D) T-bills Answer: C 8) When defining a change in measure, a redefining of the units in which a payoff is measured is called: A) Brownian motion B) Change of numeraire C) Stochastic discount factor D) Utility function Answer: B 9) It can be said that Girsanov's theorem shows the equivalence of which two items?

A) Change of drift and change of measure B) Change of numeraire and change of measure C) Change of drift and change of numeraire D) Change of numeraire and change of process Answer: A 10) The primary link between Brownian motion and Girsanov's theorem relates to which variable?

A) Drift B) Numeraire C) Returns D) Standard deviation Answer: A 11) Which of the following is not commonly used as a numeraire?

A) Futures contract B) Money market account C) Risky asset D) Zero coupon bond Answer: A

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12) The case where the zero coupon bond is selected as the numeraire under a risky asset method results in a measure called the: A) Drift measure B) Forward measure C) Money market measure D) Spread measure Answer: B 13) In the case of a European Outperformance Option, we assume the strike asset is: A) Cash B) A money market fund C) A stock or an index D) A zero-coupon bond Answer: C 22.2 Short Answer Essay Questions 1) What aspect of risk-neutral pricing valuation links it to portfolio selection?

Answer: Investors must select a portfolio by valuing assets. This requires the determination of discount rates and payoffs. This valuation is the link between portfolio selection and risk-neutral pricing.

2) How do asset values differ between using a traditional DCF approach and a stochastic discount factor approach?

Answer: When implemented correctly, the two approaches will give the same present value. The DCF uses asset-specific state-dependent discount rates and the stochastic approach uses assetindependent, state-dependent discount rates.

3) How do probabilities change with a change of measure?

Answer: The new measure has the effect of increasing the probability in those states where the product of marginal utility and the asset price is greater than average.

4) What does Girsanov's theorem tell us about drift and Brownian motion?

Answer: If we add drift to Brownian motion we can alter the probability distribution so as to convert the Brownian motion plus drift into a Brownian motion which has no drift under the new distribution.

5) In the first-order condition for portfolio selection, explain the meaning of equilibrium.

Answer: The aggregate demand and supply of assets will be equal. Given an investor's chosen portfolio and the market prices for assets, investors will not change their investment position. If not true, high valuation investors would buy from low valuation investors and create equilibrium.

22.3 Class Discussion Question 1) Randomly divide the class into two groups. Give one group the task of defending Warren Buffet's position on valuing put options. Have the other group disagree with Buffet's position.

Moderate a discussion of the two, listing the pros and cons on the board.

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Derivatives Markets, 3e (McDonald) Chapter 23 Exotic Options: II 23.1 Multiple Choice 1) In a specific wager, Pat is paid $5.00 if the price of ABC Corp. is above $85.00. Currently, ABC Corp. price is $75.00, σ = 0.25, r = 0.04, div = 0 and the wager lasts 6 months. Pat receives nothing if the price is below $85.00. What is the value of her wager?

A) $1.20 B) $2.20 C) $3.20 D) $4.20 Answer: A 2) In a specific wager, Pat is paid $5.00 if the price of ABC Corp. is above $85.00. Currently, ABC Corp. price is $75.00, σ = 0.25, r = 0.04, div = 0 and the wager lasts 6 months. If the price is below $85.00, Pat must pay $5.00. What is the net value of Pat's wager?

A) -$2.49 B) +$2.49 C) -$1.50 D) +$1.50 Answer: A 3) Eugene holds a collect-on-delivery call with S = $36.50, K = $35, σ = 0.22, r = 0.04, div = 0 and 270 days until expiration. What is the value of the European COD call?

A) $5.90 B) $6.90 C) $7.90 D) $8.90 Answer: B 4) In a specific wager, Pat is paid $5.00 if the price of ABC Corp. is above $85.00. Currently, ABC Corp. price is $75.00, σ = 0.25, r = 0.04, div = 0 and the wager lasts 6 months. Pat is paid one share of ABC Corp. stock if the price is below $85.00. What is the value of her wager?

A) $21.80 B) $22.80 C) $23.80 D) $24.80 Answer: B

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5) The Buckingham Casino offers to give every gambler one share of Buckingham Casino Corp. stock if the price drops below $40.00, as an incentive to spur business. If S = $45.25, σ = 0.15, r = 0.05 and div = 0, how much is this offer worth if it expires in 30 days?

A) $0.36 B) $0.26 C) $0.16 D) $0.06 Answer: D 6) The Buckingham Casino offers to give every gambler one share of Buckingham Casino Corp. stock if the price drops below $40.00, as an incentive to spur business. If S = $45.25, σ = 0.15, r = 0.05 and div = 0, how much profit or loss is Buckingham incurring if they charge $0.25 to participate in this wager?

A) $0.31 loss B) $0.31 profit C) $0.19 loss D) $0.19 profit Answer: D 7) Suppose S = $52.50, K = $50, σ = 0.25, r = 0.04 and div = 0.01. What is the price of a gap option with 156 days until expiration and K1 = $32.00?

A) $14.00 B) $15.00 C) $16.00 D) $17.00 Answer: C 8) Cyril is purchasing a down-and-in cash call. H = $45.00, S = $38.24, K = $35, σ = 0.33, r = 0.05, div = 0 and it expires in 140 days. What is the value of the option if the payment is $1.00?

A) $0.80 B) $1.80 C) $2.80 D) $3.80 Answer: A 9) Albert has accepted a wager to receive $5.00 if the price of Will Co. is above $35.00 per share. This right only exists if Will Co. drops below $33.00 sometime over the coming 100 days.

Currently, Will Co. stock price is $38.24, r = 0.05, σ = 0.33, and div = 0. What is the value of Albert's position?

A) $0.35 B) $0.25 C) $0.15 D) $0.05 Answer: C

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10) The current Nikkei index price is 21,200. Assume σ = 0.13, r = 0.05 and div = 0.015. If K = 20,000 yen and yen per dollar spot rates are 103, what is the dollar value of a 2-year call?

A) $13.97 B) $18.97 C) $23.97 D) $28.97 Answer: D 11) The Nikkei index is 22,550, K = 21,000, σ = 0.19, rf = 0.04, S = 0.10, r = 0.08 and div = 0.01. The yen to dollar spot rate is 104 and the correlation coefficient is 0.30. What would be the dollar price of a 2-year equity-linked foreign exchange call?

A) $45.02 B) $35.02 C) $25.01 D) $15.02 Answer: A 12) The concept created by Hakannson in 1976 to describe the exotic option like payoffs that could result without the need for a delta hedging requirement is known as: A) Exotics B) Multioptions C) Quantos D) Supershares Answer: D 13) A multivariate option that has a claim with a payoff dependent upon the price of two different assets is known as: A) Exotics B) Multioptions C) Quantos D) Supershares Answer: C 14) A multivariate option that has a claim with a payoff determined by the average of two or more asset prices is known as: A) Basket options B) Multioptions C) Quantos options D) Rainbow options Answer: A

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23.2 Short Answer Essay Questions 1) Donald Trump offers to give you a partnership share in his casinos if the price of his shares drops below a certain level. He charges a nominal fee for this right. What is he offering you and is he wise?

Answer: You are being offered an asset-or-nothing put. If his fee is more than the value of the put, the offer is advantageous to him.

2) What is the risk a U.S. investor faces when investing in foreign index securities, besides index fluctuations?

Answer: Due to currency fluctuations, investors can lose money despite being correct about the movement of the index.

3) How does a quanto hedge the currency risk a U.S. investor encounters when investing in foreign indexes?

Answer: A quanto is a synthetic investment in the foreign index in which a currency forward hedge exists and the quantity of the currency hedge is linked to the index performance.

4) What purpose do currency linked options serve?

Answer: Cross-country investors can use currency-linked options to vary their exposure to currency and equity risks by changing the denomination of their strike and assets.

5) What is the characteristic that makes options, like quantos, multivariate options?

Answer: Any options that involve the interaction of two or more different assets are considered multivariate options.

23.3 Class Discussion Question 1) Ask students to define Exotic options. Ask students to give examples of Exotic options. Have students define their example in terms of basic calls on puts. Demonstrate how all Exotic options are merely modified versions of basic options.

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Derivatives Markets, 3e (McDonald) Chapter 24 Volatility 24.1 Multiple Choice 1) A stock has a historical volatility of 39%. The data shows significantly increased volatility in recent data and significantly lower volatility in older data. The implied estimate of the unconditional volatility using the GARCH model is most likely to be which of the following?

A) 12% B) 25% C) 45% D) 85% Answer: D 2) A stock price has a historical volatility of 24%. If an anomalous event occurs to the company in the next past two days, which was not anticipated, what is the most likely implied estimate of the unconditional volatility using the GARCH model?

A) 12% B) 20% C) 27% D) 45% Answer: D 3) During periods when measured volatility is high, the typical day tends to exhibit high volatility. This behavior is referred to as volatility: A) Clustering B) EWMA C) Smile D) Stochasticity Answer: A 4) The S&P 100 Index implied volatility prior to 2003 is published by the CBOE under the ticker symbol: A) IVX B) SP1X C) VIX D) VXO Answer: D 5) The S&P 100 Index implied volatility since 2003 is published by the CBOE under the ticker symbol: A) IVX B) SP1X C) VIX D) VXO Answer: C 1 Copyright © 2013 Pearson Education, Inc.

6) Plotting the volatility of a security in a three dimensional graph, using time to maturity on one axis and strike price on another, is referred to as volatility: A) Skew B) Smile C) Smirk D) Surface Answer: D 7) When the volatility of an asset is higher at the deep in the money and deep out of the money positions, than at the money, the plot is called a volatility: A) Skew B) Smile C) Smirk D) Surface Answer: B 8) The process of emphasizing more recent observations of data in calculating volatility is commonly known as: A) ARCH B) EWMA C) GARCH D) Realized quadratic variation Answer: B 9) The sum of the squared, continuously compounded returns used to calculate a volatility is referred to as: A) ARCH B) EWMA C) GARCH D) Realized quadratic variation Answer: D 10) A forward contract that pays the difference between a forward price and some measure of the realized stock variance is called a Variance: A) Skew B) Smile C) Surface D) Swap Answer: D 11) A forward contract that pays ln(ST/S0) and can be used to hedge or speculate on variance is called a ________ contract.

A) Growth B) Log C) Variance D) Volatility Answer: B 2 Copyright © 2013 Pearson Education, Inc.

12) The negative correlation between stock prices and volatility is referred to as the: A) Correlation effect B) Correlation risk C) Leverage effect D) Leverage risk Answer: C 24.2 Short Answer Essay Questions 1) Explain the pattern of implied volatility that is often referred to as a smirk. (Use a call as your example.)

Answer: Implied volatility tends to be higher for in the money options and lower for out of the money options. The effect is magnified when time to expiration is lower.

2) What is the one aspect of volatility that is assumed in the Black-Scholes model and why might that assumption be in error?

Answer: The BS model assumes that the standard deviation of the asset is a constant. Historical computations of implied volatility indicate that the standard deviation changes, thus raising questions about the accuracy of the BS model.

3) Why would an exponentially weighted moving average be a more accurate means of calculating volatility than a simple sampling of historical data?

Answer: Historical observations show that volatility is constantly changing. This makes historical data less relevant than recent data. As such, EWMA places more emphasis on recent data.

4) What concept helped Robert Engle win the Nobel Prize for economics in 2003 and what was its basic tenant?

Answer: The ARCH model of price movements showed how volatility changed. While price movements are random, the volatility of a particular stock tends to cluster around high and low levels of volatility. High volatility was followed by high volatility and low volatility was followed by low volatility.

5) What is the primary difference between ARCH models and GARCH models?

Answer: GARCH is a variant of the ARCH model with one major difference. The GARCH model allows for infinite lags and can still be estimated with a small number of parameters.

24.3 Class Discussion Question 1) Ask students to provide a definition of forecasted volatility and market efficiency. Begin a discussion of the consistency or inconsistency that may exist between these two concepts. Is it possible that markets are inefficient if volatility can be forecasted? If so, how can someone take advantage of this inefficiency to make excess returns?

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Derivatives Markets, 3e (McDonald) Chapter 25 Interest Rate and Bond Derivatives 25.1 Multiple Choice 1) Zero-coupon bonds maturing in 1, 2, and 3 years have prices of 0.9345, 0.8766, and 0.8212, respectively. What is the forward price for a 1-year bond purchased in year 2?

A) 0.6866 B) 0.7234 C) 0.8787 D) 0.9368 Answer: D 2) Bonds maturing in 1, 2, and 3 years have prices of 0.9345, 0.8766, and 0.8212, respectively.

What is the price of a call option that expires in two years and gives you the right to pay 0.8600 to buy the 1-year bond? Assume σ = 0.15.

A) $0.015 B) $0.105 C) $0.205 D) $0.305 Answer: B 3) Zero-coupon bonds maturing in 1, 2, and 3 years have prices of 0.9020, 0.8320, and 0.7620, respectively. What is the implied forward rate from year 2 to year 3?

A) 7.94% B) 9.19% C) 09.68% D) 10.21% Answer: B 4) Bonds maturing in 1, 2, and 3 years have prices of 0.9020, 0.8320, and 0.7620, respectively.

What is the price of a put option that expires in 1 year that gives you the right to sell a 1-year bond for a price of 0.9200? Assume σ = 0.18.

A) $0.35 B) $0.25 C) $0.15 D) $0.05 Answer: D 5) Bonds maturing in 1, 2, and 3 years have prices of 0.9600, 0.9153 and 0.8620, respectively. A 0.9300 strike call on a 1-year bond matures in 1 year with σ = 0.20. What is the price of an 8.0% interest rate caplet that expires in 1 year?

A) $0.66 B) $0.76 C) $0.86 D) $0.96 Answer: A 1 Copyright © 2013 Pearson Education, Inc.

6) Bonds maturing in 1, 2, and 3 years have prices of 0.9323, 0.8762, and 0.8002, respectively. A 0.8900 call on a 1-year bond matures in 1 year with σ = 0.25. What is the price of a 10.0% interest rate caplet that expires in 1 year?

A) $0.50 B) $0.60 C) $0.70 D) $0.80 Answer: C 7) A series of 1-year interest rate caplets for 4 years have values of $0.05, $0.07, $0.08, and $0.10, respectively. What is the value of a 3-year interest rate cap?

A) $0.08 B) $0.12 C) $0.20 D) $0.30 Answer: C 8) Assume a = 0.10, b = 0.15, r = 0.04 and σ = 0.35. Using the CIR model, calculate the price of a zero coupon bond maturing in 6 years.

A) 0.6042 B) 0.7042 C) 0.8042 D) 0.9042 Answer: B 9) Assume a = 0.15, b = 0.08, r = 0.05, and 0.30. Using the CIR model, calculate the delta of a zero coupon bond maturing in 5 years.

A) -4.08 B) -3.08 C) -2.08 D) -1.08 Answer: C 10) Assume a = 0.25, b = 0.13, r = 0.06, and σ = 0.25. Using the CIR model, calculate the gamma of a zero coupon bond maturing in 3 years.

A) 2.14 B) 2.34 C) 2.54 D) 2.74 Answer: D

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11) If next year's bond prices for 2-year zero coupon bonds may be either 0.9454 or 0.9233, what is the yield volatility?

A) 18% B) 16% C) 14% D) 12% Answer: A 12) If next year's bond prices for 3-year zero coupon bonds may be either 0.8923 or 0.8644, what is the yield volatility?

A) 12.7% B) 13.7% C) 14.7% D) 15.7% Answer: A 13) The price of a bond that matures in 1 year is 103.34, using base 100 pricing. The price of a bond that matures in two years is 101.90, using base 100 pricing. What is the 1-year bond forward price in year 1?

A) 98.56 B) 98.61 C) 101.90 D) 103.34 Answer: B 14) Using base 100 pricing, the price of bonds that mature in years 1, 2, and 3 is 101.92, 100.87, and 99.34, respectively. Given this data, what is the 2-year forward price for a 1-year bond?

A) 98.48 B) 99.34 C) 100.22 D) 100.87 Answer: A 15) Using base 100 pricing, the price of bonds that mature in years 1, 2, 3, and 4 is 93.46, 92.22, 91 98 and 90.23, respectively. Given this data, what is the 2-year forward price for a 2-year bond?

A) 97.84 B) 98.92 C) 99.74 D) 160.45 Answer: B

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25.2 Short Answer Essay Questions 1) What is the transaction that results within an interest rate cap to make the holder's rate "capped"?

Answer: The interest rate cap pays the difference between the realized interest rate in a period and the cap rate.

2) How does the node configuration in interest rates and bonds differ from stocks?

Answer: In bonds the nodes do not, necessarily, recombine. In stocks they do recombine.

3) Describe the effectiveness of duration as a tool in hedging bonds.

Answer: Duration is good, but not perfect. Duration changes as bond prices change and it assumes all YTM shift in concert. This assumption is false.

4) Under what conditions does delta-gamma-theta approximate the exact bond price change?

Answer: This only occurs when the interest rate shift equals one standard deviation.

5) What is calibration?

Answer: This is the process of finding a model that matches the available data.

25.3 Class Discussion Question 1) What are the various models in bond pricing and behavior? Ask students to describe the various models along with an explanation of each model's strengths and weaknesses.

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Derivatives Markets, 3e (McDonald) Chapter 26 Value at Risk 26.1 Multiple Choice 1) Your portfolio is worth $200,000. The standard deviation of its annual returns is 0.20 and the expected return is 11.0%. What is the probability of a loss over 10 business days?

A) 39.84% B) 49.84% C) 59.84% D) 69.84% Answer: B 2) Your portfolio is worth $200,000. The standard deviation of its annual returns is 0.20 and the expected return is 11.0%. What is the 2-week value at risk at a 95% confidence level?

A) $12,058 B) $13,058 C) $14,058 D) $15,058 Answer: A 3) You own $4 million of Jacko Corp. The expected return is 14.0% and σ = 0.20. What is the value at risk over 4 weeks at a 99% confidence level?

A) $383,000 B) $413,000 C) $453,000 D) $473,000 Answer: D 4) Your $1 million portfolio consists of 50% of Jacko with = 0.14, σ = 0.20 and 50% of Macko with = 0.10, σ = 0.15. The correlation coefficient is 0.25. What is the value at risk over 1 week at a 95% confidence level?

A) $23,447 B) $26,447 C) $29,447 D) $32,447 Answer: C 5) Your $2 million portfolio consists of 25% Evans stock with = 0.16, σ = 0.22 and 75% Indy stock with = 0.09, σ = 0.12. The correlation coefficient is 0.13. What is the value at risk over 1 day at a 99% confidence level? Assume 252 days per year.

A) $21,792 B) $31,792 C) $41,792 D) $51,792 Answer: B 1 Copyright © 2013 Pearson Education, Inc.

6) Your $2 million portfolio consists of 25% Evans stock with = 0.16, σ = 0.22 and 75% Indy stock with = 0.09, σ = 0.12. The correlation coefficient is 0.65. What is the value at risk over 1 day at a 99% confidence level? Assume 252 days per year.

A) $27,976 B) $37,976 C) $47,976 D) $57,976 Answer: B 7) Harold owns 10,000 shares of IBM at $54.50 per share. He writes $55 strike covered call on all the shares. Assume = 0.14, σ = 0.18, rf = 0.04, and the options expire in 90 days. What is the value at risk for 1 day, using the delta approximation at a 95% confidence level?

A) $4,717 B) $5,717 C) $6,717 D) $7,717 Answer: A 8) Kelly owns 50,000 shares of Microsoft at $63.60 per share. She buys 20,000 $60 strike calls.

Assume = 0.12, σ = 0.23, rf = 0.05, and the options expire in 170 days. What is the value at risk for 2 weeks, using the delta approximation at a 99% confidence level?

A) $311,463 B) $411,463 C) $511,463 D) $611,463 Answer: B 9) Matt owns 5,000 share of Matrix at $52.50. To arbitrage this he shorts 5,000 calls and longs 5,000 puts at a strike of $50.00. Assume = 0.16, σ = 0.30, rf = 0.06, and the options expire in 170 days. What is the value at risk for 1 week at a 95% confidence level?

A) $0 B) $16,433 C) $18,433 D) $20,433 Answer: A 10) A bond maturing in 5 years has a YTM = 0.065 and an annual yield volatility of 2.0%. Given a $15 million portfolio, what is the value at risk over 2 weeks at a 95% confidence level?

A) $283,917 B) $383,917 C) $483,917 D) $583,917 Answer: C

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11) You own two bonds; 25% of a 30-year bond with σ = 0.02 and 75% of a 20-year bond with σ = 0.015. The correlation coefficient is 0.82. What is the 2-week value at risk at a 95% confidence level? (Assume portfolio value = $15 million.)

A) $0 B) $234,357 C) $734,357 D) $1,734,357 Answer: D 12) A stock has a price of $50 and pays no dividend. The historical standard deviation of the stock is 25% and the expected return on the stock is 12%. At the 95% confidence level, what is the Tail VaR over the next 6 months?

A) $2.50 B) $13.63 C) $22.36 D) $47.50 Answer: B 13) A stock has a price of $42.63 and pays no dividend. The historical standard deviation of the stock is 18% and the expected return on the stock is 11%. At the 95% confidence level, what is the Tail VaR over the next 270 days?

A) $2.13 B) $6.56 C) $9.71 D) $40.50 Answer: C 14) Use VaR techniques to determine the cost of insurance on a risky investment. The investment asset has a value of $150 and pays no dividend. The historical standard deviation of the asset is 20% and the expected return on the asset is 15%. At the 95% confidence level, what is the price of a put option that insures the asset over the next 6 months?

A) $0.33 B) $1.25 C) $2.65 D) $6.56 Answer: A 15) Use VaR techniques to determine the cost of insurance on a risky investment. The investment asset has a value of $80 and pays no dividend. The historical standard deviation of the asset is 15% and the expected return on the asset is 8%. At the 95% confidence level, what is the price of a put option that insures the asset over the next year?

A) $2.56 B) $1.25 C) $0.86 D) $0.15 Answer: D 3 Copyright © 2013 Pearson Education, Inc.

26.2 Short Answer Essay Questions 1) What is implied volatility?

Answer: It is the standard deviation of an asset extracted from actual option prices and then imputed from an option pricing formula.

2) Why is recent data more relevant than older data when calculating volatility?

Answer: Research shows that future near term volatility more closely approximates the recent past volatility.

3) What is bootstrapping and what is its use?

Answer: This is the process of using observed past returns to create an empirical probability distribution of returns that can be used in simulations.

4) How is VaR used in credit risk scenarios?

Answer: VaR is used to evaluate market risk due to price changes and can lead to a determination of the credit risk needing to be hedged.

5) What is a default swap and what is its use?

Answer: A default swap pays very small amounts and a large amount during default. They are used to protect bondholders against default by a bond issuer.

26.3 Class Discussion Question 1) Why is VaR an important tool in measuring risk? What are some of its shortcomings? Ask the class to explain the rationale for a company to rely heavily on VaR in the absence of other measurement tools.

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Derivatives Markets, 3e (McDonald) Chapter 27 Credit Risk 27.1 Multiple Choice 1) The difference between the yield to maturity on a defaultable bond and an otherwise equivalent default-free bind is called the: A) Credit risk B) Credit spread C) Loss given default D) Recovery rate Answer: B 2) The chance that a counter party may fail to meet a contractual obligation on a debt instrument is referred to as: A) Credit risk B) Credit spread C) Loss given default D) Recovery rate Answer: A 3) A bond has a current value of $950 and promises to pay $1,000 at the end of 4 years. The expected return on the asset is 12% and the risk free rate is 3%. If the actual cash payout in case of default is 0, what is the true default probability given that the asset has a standard deviation of 18%?

A) 15.2% B) 21.5% C) 33.2% D) 49.6% Answer: B 4) A bond has a current value of $950 and promises to pay $1,000 at the end of 4 years. The expected return on the asset is 12% and the risk free rate is 3%. If the actual cash payout in case of default is 0, what is the risk neutral default probability given that the asset has a standard deviation of 18%?

A) 15.2% B) 21.5% C) 33.2% D) 49.6% Answer: D

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5) Suppose that B = $500 and A0 = $470, α = 9%, r = 4%, σ = 17%, and δ = 0. If T = 8, what is the true default probability?

A) 13.0% B) 20.5% C) 38.3% D) 44.4% Answer: A 6) Suppose that B = $500 and A0 = $470, α = 9%, r = 4%, σ = 17%, and δ = 0. If T = 8, what is the risk neutral default probability?

A) 13.0% B) 20.5% C) 38.3% D) 44.4% Answer: C 7) Suppose that B = $500 and A0 = $470, α = 9%, r = 4%, σ = 17%, and δ = 0. If T = 8, what is the recovery rate assuming true default probability?

A) $369 B) $400 C) $470 D) $500 Answer: B 8) Suppose that B = $500 and A0 = $470, α = 9%, r = 4%, σ = 17%, and δ = 0. If T = 8, what is the recovery rate assuming risk neutral default probability?

A) $369 B) $400 C) $470 D) $500 Answer: A 9) A firm has a single issue of a zero coupon debt that promises to pay $90 in 4 years, and the A0 = $100, r = 5%, σ = 15%, and δ = 0. If the asset has no chance of total default, what is the value of the debt?

A) $67.10 B) $75.19 C) $85.62 D) $90.00 Answer: B

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10) A firm has a single issue of a zero coupon debt that promises to pay $90 in 4 years, and the A0 = $100, r = 4%, σ = 25%, and δ = 0. If the asset has a 2% chance of total default, what is the value of the debt?

A) $67.10 B) $75.19 C) $85.62 D) $90.00 Answer: A 11) A firm has a single issue of a zero coupon debt that promises to pay $90 in 4 years, and the A0 = $100, r = 4%, σ = 25%, and δ = 0. If the asset has a 2% chance of total default, what is the yield on the bond?

A) 8.32% B) 12.33% C) 24.36% D) 36.85% Answer: D 12) A firm has a single issue of a zero coupon debt that promises to pay $40 in 5 years, and the A0 = $50, r = 4%, σ = 12%, and δ = 0. If the asset has a 5% chance of total default, what is the value of the debt?

A) $30.83 B) $42.68 C) $55.21 D) $62.41 Answer: A 27.2 Short Answer Essay Questions 1) What are the two ways that the payoff conditional on default can be expressed?

Answer: The recovery rate is the amount the debt holders receive as a fraction of what they are owed. The loss given default is the difference between the amount owed and the amount received.

2) What does a transition matrix indicate about a bond's future credit risk?

Answer: A transition matrix tells us the probability that a firm in a given ratings category will switch to another ratings category over the course of a year.

3) What is the recovery rate?

Answer: The recovery rate is the percentage figure that indicates how much of the money owed to the bondholders is likely to be paid in the case of a bond default.

4) What is meant by the phrase "tranche" when referring to collateralized debt obligations?

Answer: The process of creating a tranche relates to dividing the cash flows from debt into different categories. Relative to CDOs, it means to place a different priority, with respect to cash flows, on each of the different categories.

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5) What is a credit default swap and what function does it serve?

Answer: A CDS makes a payment when a specific credit event occurs. A CDS serves to provide insurance against credit risk, specifically default. An insuring party provides payment in case of default.

27.3 Class Discussion Question 1) Credit risk has always existed. Since the early 1990s, credit derivatives have become dominant in the capital markets. How do these instruments serve to reduce and/or transfer risk?

Can you think of ways in which the existence of credit derivatives has made the financial markets more efficient?

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Test Bank for

DERIVATIVES MARKETS Third Edition

Robert L. McDonald

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