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Chapter 2. Futures Markets Rangarajan K. Sundaram Stern School of Business New York University


Outline Introduction Standardized Contract Terms Unilateral Reversal of Positions Default Risk and Margin Accounts Futures Pricing Case Study: The GNMA CDR Futures Contract Case Study: Metallgesellschaft AG 3



Objectives Futures contracts are the exchange-traded counterparts of forward contracts. Key features distinguishing futures contracts from forward contracts: The standardization of futures contracts. The ability to unilaterally reverse positions. The use of margin accounts or \performance bonds" to control default by investors in the market.


The Origins As economic mechanisms, forward markets are very old. Futures Industry Association traces the origin of forward trading to India around 2,000 BC. Substantial evidence of forward markets in Greco-Roman and medieval Europe. World's first futures market was quite possibly the Dojima Rice Market (Osaka, 1730). 6

The 19th Century Modern futures markets are most associated with 19th century America, particularly the grain markets of Chicago. The Chicago Board of Trade (CBoT) was established in 1848. Swiftly followed by a number of other exchanges (New York, Milwaukee, St. Louis, Kansas City, ... ). Over a thousand commodity exchanges sprang up in the US by the end of the 19th century.


Three Major Trends  Consolidation A worldwide phenomenon.  NYMEX-COMEX (1994); CME-CBoT (2007);CME-NYMEX (2008).  Creation of Eurex, Euronext; Euronext-LIFFE (2002);NYSEEuronext (2007).  In emerging markets too: e.g., BM&FBovespa (2008).  Increasing role of financial futures.  Until the 1970's: asset underlying futures was a commodity (e.g., wheat, gold, oil).  In 1972, first financial futures (currency futures) were introduced at the CME.  Interest-rate futures followed in mid 70's, and stock-index futures in early 80's.  Increasing role of technology: the trading "pit" is dying out. 8

Volume of Trading on CBoT  Financial Futures were introduced in 1972.  Trading volume on the CBoT in millions of contracts in the first two decades since that point:


The Top 15 Futures Contracts Worldwide: 2008


Standardized Contract Terms



Contract terms must be standardized, since buyer and seller do not interact directly. Standardization is perhaps the most important task performed by the exchange. Essential in promoting liquidity and improving quality of hedge. Apart from contract maturity dates, standardization involves three components: 1.Quantity (size of contract). 2.Quality (standard deliverable grade). 3.Delivery options (other deliverable grades + price adjustment mechanism). 12

Example: Commodity Futures Contracts


Example: Financial Futures Contracts


Example: "Mini" Futures Contracts


Example: The Corn Futures Contract Exchange: Chicago Board of Trade (CBoT). Contract months: March, May, July, September, December. Size: 5,000 bushels. Quality: No. 2 Yellow Corn. Delivery options:  No. 1 Yellow and No. 3 Yellow may also be delivered.  If No. 1 Yellow is delivered, the short position receives 1.5 cents per bushel more than the contract price.  If No. 3 Yellow is delivered, the short position receives 1.5 cents per bushel less than the contract price.


Example: The Yen Futures Contract

Exchange: Chicago Mercantile Exchange (CME) Contract months: March, June, September, December. Size: 12,500,000 Yen. Quality: Not relevant. Delivery options: None.


Example: The T-Bond Futures Contract Exchange: CBoT. Contract months: March, June, September, December. Size: $100,000 in face value of US Treasury Bonds. Quality: Coupon of 6%. Must have at least 15 years to maturity or first call. Delivery options: Any other coupon can be delivered. Cash flows from delivered bond will be discounted at 6% rate to obtain conversion factor for price adjustment.


Conversion Factor: An Example Suppose delivered bond is 20 years, 8% coupon. Coupons are paid semi-annually. Assume the last coupon was just paid. Thus, present value of cash flows when discounted at 6%:

So long position will pay the short position 1.2311 times the agreed-upon delivery price.


Consequences of Delivery Options  Why provide delivery options in futures contracts?  It makes corners and squeezes more difficult.  Enhance market liquidity.  However, there is an important cost: the quality of the hedge is degraded. The delivered grade is not the standard grade, but the cheapest-to-deliver grade.  Case study: The GNMA futures contract.


Unilateral Reversal of Positions


Reversal of Positions

 Unlike forward contracts, holders of futures contracts can unilaterally reverse (or "close out") their positions.  Reversal involves taking the opposite position to the original.  For example, suppose an investor has a long position in 10 COMEX gold contracts for delivery in April.  To reverse this position, the investor has to take a short position in 10gold contracts for delivery in April. 22

Reversal of Positions

 Of course, reversal may not be costless.  For example, suppose the long position in the 10 COMEX gold contracts was taken at a futures price of $1,045 per oz.  Suppose that the price at the time of close-out is $1,037 per oz.  Then, effectively the investor has agreed to buy at $1,045/oz and sell at$1,037/oz, for a net loss of $8/oz.  Since one contract is for 100 oz, this leads to a total loss on the 10contracts of 10 x 100 x 8 = $8, 000.  This loss is settled through the margin account discussed below.


Why Allow Reversal?

 Why is reversal important?  May simply not want physical delivery (say, investor in California using wheat futures on the CBoT).  Standardization of delivery dates creates "delivery basis risk:" the risk that the delivery dates on the contract may not match the market commitment dates of the hedger.  Allowing for reversal allows elimination of part of this delivery basis risk: the contract can be closed out on the market commitment date.


An Example

 A US firm will receive £20 million on February 28, and wants to hedge against changes in the $/£ exchange rate using March futures contracts.  Current futures delivery price for March delivery: $1.64/£.  Consider the following strategy:  Take a short position in the March futures contract with the delivery price of $1.64/£.  On February 28, close out the short futures position by taking a long futures position.  Sell the £20 million in the spot market on February 28.


Convergence of Futures to Spot

 Why will this strategy help?  Key observation: On the delivery date, the spot price and the futures price must coincide.  Since February 28 is "close" to the delivery date, the spot and futures prices will be close to each other.  Therefore, the spot sale and long futures positions will approximately offset each other, leaving the firm with a cash flow of (20, 000, 000 x 1.64) = $32, 800, 000.  Remark: In Chapter 5, we examine hedging in the presence of basis risk and derive optimal (i.e., variance-minimizing) strategies in such cases. 26

Default Risk and Margin Accounts


Margin Accounts

 Since buyers and sellers do not interact directly, there is an incentive for either party to default if prices move adversely.  To inhibit default, futures exchanges use margin accounts. This is effectively the posting of collateral against default.  The level at which margins are set is crucial for liquidity. Too high levels eliminate default, but inhibit market participation. Too low levels increase default risk.  In practice, margin levels are not set very high.


The Margining Procedure

 Initial margin.  Amount initially deposited by investor into margin account.  Marking-to-market.  Daily adjustment of margin account balances to reflect gains/losses from futures price movements over the day.  Maintenence margin.  Floor level of margin account. 29

Margining: An Example

 Investor takes long position in 10 wheat futures contracts at a futures price of $3.60 per bushel.  Size of one futures contract: 5,000 bushels.  Thus, futures price: $18,000 per contract.  Suppose that  Initial margin = $878 per contract.  Maintenence margin = $650 per contract.


Example: Marking-to-Market

 Settlement price on day 1: $3.58 per bushel = $17,900 per contract.  "Loss" from holding long contract at $3.60: $100/contract.  Total "loss" = $1,000: debited from the margin account.  Margin account balance: $7,780.  Effectively:  Original contract at $3.60/bushel has been replaced with new contract at $3.58/bushel.  Difference is debited from the margin account.  Of course, margin account of corresponding short position would increase by $1,000.


Example: Marking-to-Market

 Settlement price on day 2: $3.54 per bushel = $17,700 per contract.  "Loss" per contract: $(17, 900 — 17, 700) = $200 per contract.  Total loss = $2,000; debited from the margin account.  New margin account balance: $5,780.  Since balance is less than maintenance margin, margin call results.  If account is topped up (to initial margin levels), situation continues.  If not, investor's position is closed out.


Margining: Summary  To reiterate: marking-to-market essentially involves:  Rewriting the customer's futures contract at the current settlement price, and  settling immediately the gains or losses to the customer from the rewiting.  Basic idea: If an investor is not able to meet "small" losses (from price movements over a day), it is unlikely he will be able to meet larger losses that might result.  Historically, margining has worked very well in inhibiting default.  Exchanges also retain right to change margin at any time.  Used to defuse potentially market-threatening situations (e.g., 1980silver crisis).


Margin Levels: Examples


Futures Pricing


Futures vs. Forward Prices

 Analytical valuation of futures contracts complicated by two considerations: 1. Delivery options provided to the short position. 2. Margining which creates uncertain interim cash flows.  These features will have an impact on futures prices compared to another wise identical forward contract.  The question is: how much of an effect? Is it quantitatively significant?  For most futures contracts (especially short-dated ones), it turns out the effect is minimal: such contracts can be priced as if they are forward contracts.


Case Study: The GNMA CDR Futures Contract


Case Study: GNMA Futures  The GNMA CDR futures contract offers an excellent case study in contract design. A detailed analysis is in E. Johnston and J. McConnell (1989, Review of Financial Studies.  The contract was introduced in 1975 on the CBoT. First interest-rate futures contract traded on an exchange. Volumes Grew explosively over first five years, Declined slightly over 1980-82. Collapsed back to near-zero levels by 1985.  The initial success and subsequent failure of the contract can be traced to the poor specification of delivery options.


GNMA CDR Futures: Trading Volumes


Hedging Spot Risk: The Role of Correlation  An obvious but important point:  Hedging is an offsetting of risks.  For a futures contract to provide a good hedge for a spot risk, futures price must bear close relationship to spot price of asset being hedged.  That is, futures price changes and spot price changes must be highly correlated.  In many cases, the underlying risk is well defined (oil, lumber, corn, exchange rates, etc.).  For interest-rate securities, one must be careful in identifying which risk it is that investors are seeking to hedge.


Hedging Demand in Mortgages

 GNMA CDR futures contracts are futures on mortgage-backed securities.  But which mortgage-backed securities are investors seeking to hedge?  Hedging demand is concentrated in current-coupon mortgages.  Primary source of hedging demand: mortgage bankers.  Mortgage bankers are exposed to interest rate risk on mortgages written at current coupon rates, between the time the loans are made and the time they are sold on the secondary market.

 Conclusion:

For the futures to be a successful hedge vehicle, futures price must bear a close relationship to current coupon mortgages.


The Role of Delivery Options

 Futures contracts also have delivery options that provide for alternative deliverable grades and the price adjustments for each grade. The actual delivered grade will be not the standard grade, but the cheapest-to-deliver grade.  This means the futures price will always bear a close relationship to the price of the cheapest-to-deliver grade.  However, we want the futures price to be closely related to the price of current-coupon mortgages.  Conclusion:

The delivery options must be specified such that the current coupon mortgages are typically the cheapest-to-deliver.


The GNMA Contract Specification

 Did the GNMA CDR futures contract meet this criterion?  Specification of the contract:  Underlying asset: GNMA mortgage backed securities.  Contract size: $100,000 in face value of mortgages.  Standard grade:  Coupon: 8%.  Maturity: 29–30 years.  Deliverable grades:  Any coupon in place of the standard 8%.  Price adjustment:  Cash flows from delivered grade discounted at 8% for 12 years.  Implicit assumption: all mortgages are prepaid in 12 years.


The Problem

 High-coupon mortgages are more likely to be prepaid early than lowcoupon mortgages.  Holder of mortgage has an option to "call" (repay) the mortgage at any time.  Right is more valuable to holder of high-coupon mortgage.  The 12-years-for-all-mortgages assumption undervalues the call in high-coupon mortgages relative to low-coupon mortgages.  Equivalently, it overstates the adjustment factor for high-coupon mortgages relative to that for low-coupon mortgages.  Conclusion: In general, high-coupon mortgages will be the cheapest-to-deliver grade.


To Summarize ...

 For the contract to be a good hedge, the futures price must be closely related to the price of current-coupon mortgages.  In general, for any futures contract, the futures price is closely related to the price of the cheapest-to-deliver grade.  Thus, the delivery options must be such that current coupons are closely related to the cheapest-to-deliver prices.  However, the specification of the delivery options in the GNMA CDR futures contract makes high-coupon mortgages typically the cheapest-todeliver grade.


The Consequence ...

 Thus, as long as high coupons are also current coupons (i.e., interest rates are constant or rising), the contract will be a good hedge. This was actually the case between 1975 and 1982. Coupon rates were around 8% in 1975, rose to 17% in late 1981, and remained at 16–17% until early 1982. As a consequence, trading in the contract grew rapidly.  However, in late 1982, interest rates declined steeply. The contract was no longer a useful hedge vehicle. Trading in the contract dropped to near-zero levels by 1987. Interest in the contract never revived as Treasury futures and other contracts supplanted it as the hedge vehicles of choice.


Case Study: Metallgesellschaft AG


Case Study: Metallgesellschaft

 Protagonist: Metallgesellschaft Refining & Marketing (MGRM), a subsidiary of Metallgesellschaft AG.  Begining in 1992, MGRM began selling 5–year and 10–year fixed-price oil supply contracts to a number of customers.  The customers were also provided with an option that allowed them to void the contract (at a profit) if oil spot prices rose rapidly.  The contracts were marketed aggresively and very successfully.  By Nov '93, MGRM had build up long-term supply commitments of over 150 million barrels.  This was 8 times the commitment of Oct '92, and more than twice the commitments of May '93.


The Need to Hedge

 These contracts left MGRM exposed to increases in the price of oil.  MGRM hedged its exposure using exchange-traded futures contracts via a "stack-and-roll" hedging strategy.  Such a strategy involves the following steps: 1. The firm takes long positions in futures contracts to cover its entire exposure. 2. All positions are in the nearby futures contract, i.e., for delivery at the end of the current month. (This is the "stack" part.) 3. At the end of each month, the company closes out its position, and opens new long positions to cover its remaining exposure. (This is the "roll" part.)


In Principle ...

 Theoretically, a stack-and-roll strategy should provide a good hedge for an exposure like MGRM's.  If oil prices rise, there would be a loss on the forward contracts, but a gain on the long futures positions.  If oil prices fall, there would be losses on the long futures positions, but these would be offset by the increased economic value of the forward commitments.


Between Cup and Lip ...

 In practice, a number of cash-flow related problems may arise.  There were three specific risks that MGRM's strategy entailed: 1. A steep fall in oil prices. 2. A change in the oil market from backwardation to contango. 3. Basis risk from the futures/forward mismatch.  We examine each of these in turn.


A Background Factor

 One factor that robbed MGRM of its anonymity was the sheer size of the positions involved.  Position limits made it impossible to completely hedge MGRM's total commitments of 160 million barrels using only futures contracts.  MGRM had long futures positions of 55 million barrels on NYMEX.  It also entered into OTC swaps arrangements to hedge the remaining exposure.


A Fall in Oil Prices

 Every $1 fall in oil prices would lead to a $55 million cash outflow on the futures margin accounts alone.  A steep oil price fall would thus create an immediate and large cash requirement to meet margin calls.  The corresponding gains on the short forward positions would not translate into cash inflows until some date in the future.  Thus, although the economic value of the position is unaffected (it remains hedged), a severe short-term cash flow requirement is created.


Nightmare Scenario No. 1

 Unfortunately for MGRM, this scenario came true: oil prices plummeted in late 1993.  This led to a cash requirement of around $900 million to meet margin calls (on the futures positions) and extra collateral (on the OTC positions).


Oil Prices in 1993-94


Backwardation to Contango

 A futures market is said to be in backwardation if futures prices are below spot.  It is said to be in contango if futures prices are above spot.  In a typical commodity market with a positive cost-of-carry, the futures will be above spot, i.e., the market will be in contango.  However, in some commodity markets (especially oil) futures prices have remained below spot for long periods of time.  This phenomenon is commonly attributed to the presence of a large "convenience yield" from holding the spot commodity.


The Problem with Contango

 Recall MGRM employed a stack-and-roll strategy.  Rolling over futures positions at the end of each month involves 1. Closing out the existing long futures position by taking a short futures position in the expiring contract. 2. Taking a long futures position in the new nearby contract.  This is effectively selling at the current spot price and buying at the current futures price.  In backwardation, rollover creates cash inflows.  However, in contango, rollover creates cash outflows.


Nightmare Scenario No. 2

 Through much of the mid and late 1980's, the oil futures market was in backwardation.  If this situation had continued, MGRM could have expected to make large profits on rollover.  Unfortunately for MGRM, in late 1993, the oil market went into contango.  As a consequence, by end-1993, MGRM was incurring a cash outflow of up $30 million each month on rollover costs alone.


The Problem of Basis Risk

 A final technical issue that may have hurt MGRM is basis risk.  MGRM was hedging long-term forwards with short-term futures.  Since these two prices may not move in lockstep, there is basis risk in hedging.  In the presence of basis risk, a well-developed theory shows that it is not, in general, optimal to use a hedge ratio of unity (i.e., to hedge exposure one-forone).  However, MGRM does appear to have used a hedge ratio of unity which may have further degraded the quality of the hedge, adding to losses.


The Denouement

 When MGRM's cash requirements became public information, their problems got compounded. NYMEX doubled their margin requirements. Later, NYMEX also removed MGRM's hedger's exception, effectively halving their position limits. Counterparties on their OTC contracts also demanded increased collateral for rolling over contracts.  In response, MG's senior management then decided to close out their positions and terminate the hedging strategy in place.


Arguments in Favor

 Cash requirements had become excessive.  Rollover costs were around $30 million a month.  The long-term forward contracts were not "watertight," i.e., significant creditrisk existed.  Basis risk also existed from mismatch in assets underlying forward and futures contracts.


Arguments Against

 Termination of hedge converted paper losses into real ones.  If market went back into backwardation (which had been the market's normal" state for several years), rollover profits would arise.  Removal of hedge left MGRM vulnerable to price increases.


Timing is Everything

 As it happens, MGRM's positions were unwound near the bottom of the market: oil prices rebounded during 1994.  By waiting a few months to unwind, the company could have recouped a substantial portion of its losses.


Financial Engineering chapter 02  

Financial Engineering chapter 02