Forward contracts are agreements negotiated directly between two parties in the OTC (i.e., nonexchange-traded) markets. A typical participant in a forward contract is a commercial or investment bank that, serving the role of the market maker, is contacted directly by the customer (although customers can form an agreement directly with one another). Forward contracts are individually designed agreements and can be tailored to the specific needs of the ultimate end user. Futures contracting, on the other hand, is more complicated. An investor wishing either to buy or to sell in the futures market gives his order to a broker (a futures commission merchant), who then passes it to a trader on the floor of an exchange (the trading pit). After a trade has been agreed on, details of the deal are passed to the exchange clearinghouse, which catalogs the transaction. The ultimate end users in a futures contract never deal with each other directly. Rather, they always transact with the clearinghouse, which is also responsible for overseeing the delivery process, settling daily gains and losses, and guaranteeing the overall transaction. Exhibit 22.1 high- lights the differences in how these contracts are created.1
As an example, let us consider the traditional agricultural commodity futures that have been traded for more than 130 years beginning with the creation of the Chicago Board of Trade (CBT), the world’s oldest and largest derivatives exchange. Futures contracts based on a wide array of commodities and securities have been created and now trade on almost 100 exchanges worldwide. Exhibit 22.2 lists the leading futures exchanges in the United States and the world, ranked by relative trading volume. Notice that two of the top three and three of the top five exchanges in the world are located in the United States. Additionally, Exhibit 22.3 shows price and trade activity data for a representative sample of commodity futures contracts; financial futures will be described in detail later in the chapter. Each of these commodity contracts is stan- dardized in terms of the amount and type of the commodity involved and the available dates on which it can be delivered. As we will see, this standardization can lead to an important source of risk that may not exist in forward contracts.
To interpret the display in Exhibit 22.3, consider the gold futures contract traded on the Com- modity Exchange (COMEX), a division of the New York Mercantile Exchange (NYM). Each contract calls for the long position to buy, and the short position to sell, 100 troy ounces of gold in the appointed months. With commodity futures, it usually is the case that delivery can take place any time during the month at the discretion of the short position. Contracts are available with settlement dates every other month for the next 16 months. An investor committing on this particular date to a long position in the June 2002 contract is obligated to buy 100 ounces of gold 4 months later for the contract price of $301.20 per ounce. The volume statistics show that Futures Contract
Mechanics
1For a more detailed discussion of the futures trading process, see Roger G. Clarke. Options and Futures: A Tutorial (Charlottesville, Va.: Research Foundation of the Institute of Chartered Financial Analysts, 1992). Some of this discus- sion is based on this book.
906 CHAPTER 22 FORWARD AND FUTURESCONTRACTS
Customer (Long)
A. Forward Contracts
Market Maker
Customer (Short)
EXHIBIT 22.1 FORWARD AND FUTURES TRADING MECHANICS
Brokerage Firm
Brokerage Firm
Exchange Clearinghouse
• Guarantor
• Oversees Delivery
• Bookkeeper
• Settlement Treasurer B. Futures Contracts
Customer (Long)
Customer (Short)
Pit Traders
LEADING FUTURES EXCHANGES RANKED BY RELATIVE TRADING VOLUME A. U.S. Futures Exchanges (2000 Data)
EXCHANGENAME& ABBREVIATION % OFTRADINGVOLUME
Chicago Mercantile Exchange, CME 39.8%
Chicago Board of Trade, CBT 38.7
New York Mercantile Exchange, NYM 17.6
New York Board of Trade, NYBT 3.1
Kansas City Board of Trade, KC 0.5
Mid-America Commodity Exchange, MCE 0.3
B. International Futures Exchanges (2000 Data)
EXCHANGE& COUNTRY % OFTRADINGVOLUME
EUREX, Germany & Switzerland 24.6%
CME, United States 16.5
CBT, United States 16.1
London Intl. Financial Futures Exchange, United Kingdom 9.0
NYMEX, United States 7.3
BM&F, Brazil 6.8
Paris Bourse SA, France 5.3
London Metal Exchange, United Kingdom 5.2
Tokyo Commodity Exchange, Japan 4.3
Euronext Brussels Derivative Market, Belgium 2.6
Sydney Futures Exchange, Australia 2.4
EXHIBIT 22.2
Source: Futures Industry Association. Reprinted with permission.
EXHIBIT 22.3COMMODITY FUTURES QUOTATIONS Source:The Wall Street Journal,8 February 2002. Printed with permission from The Wall Street Journal,Dow Jones & Co. Inc.
almost 70,000 gold contracts changed hands on the last reported trading day. Open interest—the total number of outstanding contracts of any maturity—was 136,441, down 1,929 contracts from the previous day.2
Another important difference between forward and futures contracts is how the two types of agreements account for the possibility that a counterparty will fail to honor its obligation. Forward contracts may not require either counterparty to post collateral, in which case each is exposed to the potential default of the other during the entire life of the contract. In contrast, the futures exchange requires each customer to post an initialmargin accountin the form of cash or gov- ernment securities when the contract is originated. (The futures exchange, as a well-capitalized corporation, does not post collateral to protect customers from its potential default.) This margin account is then adjusted, or marked to market, at the end of each trading day according to that day’s price movements. All outstanding contract positions are adjusted to the settlement price, which is set by the exchange after trading ends to reflect the midpoint of the closing price range.
The marked-to-market process effectively credits or debits each customer’s margin account for daily trading gains or losses as if the customer had closed out her position, even though the contract remains open. For example, Exhibit 22.3 indicates that the settlement price of the June 2002 gold contract increased by $2.20 per ounce from the previous trading day. This price increase benefits the holder of a long position by $220 (=$2.20 per ounce ×100 ounces). Specif- ically, if she had entered into the contract yesterday, she would have a commitment to buy gold for $299.00, which she could now sell for $301.20. Accordingly, her margin account will be increased by $220. Conversely, any party who is short June gold futures will have his margin account reduced by $220 per contract. To ensure that the exchange always has enough protec- tion, collateral accounts are not allowed to fall below a predetermined maintenance level, typi- cally about 75 percent of the initial level. If this $220 adjustment reduced the short position’s account beneath the maintenance margin, he would receive a margin calland be required to restore the account to its full initial level or face involuntary liquidation.
To summarize, the main trade-off between forward and futures contracts is design flexibility ver- sus credit and liquidity risks, as highlighted by the following comparison.
These differences represent extremes; some forward contracts, particularly in foreign exchange, are quite standard and liquid while some futures contracts now allow for greater flexibility in the terms of the agreement. Also, forwards require less managerial oversight and intervention—
especially on a daily basis—because of the lump-sum settlement at delivery (i.e., no margin accounts or marked-to-market settlement), a feature that is often important to unsophisticated or infrequent users of these products.
FUTURES FORWARDS
Design flexibility: Standardized Can be customized Credit risk: Clearinghouse risk Counterparty risk Liquidity risk: Depends on trading Negotiated exit Comparing Forward
and Futures Contracts
908 CHAPTER 22 FORWARD AND FUTURESCONTRACTS
2New contracts are created when a new customer comes to the exchange at a time when no existing contract holder wishes to liquidate his position. On the other hand, if an existing customer wants to close out her short position and there is not a new customer to take her place, the contract price will be raised until an existing long position is enticed to sell back his agreement, thereby canceling the contract and and reducing open interest by one.
HEDGING WITH FORWARDS AND FUTURES
The goal of a hedge transaction is to create a position that, once added to an investor’s portfolio, will offset the price risk of another, more fundamental holding. The word “offset” is used here rather than “eliminate” because the hedge transaction attempts to neutralize an exposure that remains on the balance sheet. In Chapter 21, we expressed this concept with the following chart, which assumes that the underlying exposure results from a long commodity position:
In this case, a short position in a forward contract based on the same commodity would provide the desired negative price correlation. By virtue of holding a short forward position against the long position in the commodity, the investor has entered into a short hedge. A long hedge, on the other hand, is created by supplementing a short commodity holding with a long forward position.
The basic premise behind either a short or a long hedge is that as the price of the underlying commodity changes, so too will the price of a forward contract based on that commodity. Fur- ther, the implicit hope of the hedger is that the spot and forward prices change in a predictable way relative to one another. For instance, the short hedger in the preceding example is hoping that if commodity prices fall and reduce the value of her underlying asset, the forward contract price also will fall by the same amount to create an offsetting gain on the derivative. Thus, a crit- ical feature that affects the quality of a hedge transaction is the way in which the spot and for- ward prices change over time.
Defining the Basis To understand better the relationship between spot and forward price movements, it is useful to develop the concept of the basis. At any Date t, the basis is the spot price minus the forward price for a contract maturing at Date T:
➤22.1 Bt,T=St– Ft,T
where:
St=the date t spot price
Ft,T=the date t forward price for a contract maturing at date T
Potentially, a different level of the basis may exist on each trading date t. Two facts always are true, however. First, the initial basis at Date 0 (B0,T) always will be known since both the current spot and forward contract prices can be observed. Second, the maturity basis at Date T (BT,T) always is zero whenever the commodity underlying the forward contract matches the asset held exactly. For this to occur, the forward price must converge to the spot price as the contract expires (FT,T=ST).
Consider again the investor who hedged her long position in a commodity by agreeing to sell it at Date T through a short position in a forward contract. The value of the combined position is (F0,T– S0). If the investor decides to liquidate her entire position (including the hedge) prior to maturity, she will not be able to deliver the commodity to satisfy her forward obligation as orig- inally intended. Instead, the investor will have to (1) sell her commodity position on the open
ECONOMICEVENT ACTUALCOMMODITYEXPOSURE DESIREDHEDGEEXPOSURE
Commodity prices fall Loss Gain
Commodity prices rise Gain Loss
Hedging and the Basis
market for St, and (2) “buy back” her short forward position for the new contract price of Ft,T.3 The profit from the short hedge liquidated at Date t is
➤22.2 Bt,T– B0,T=(St– Ft,T) – (S0– F0,T)
The term Bt,Toften is called the cover basis because that is when the forward contract is closed out, or covered.
Equation 22.2 highlights an important fact about hedging. Once the hedge position is formed, the investor no longer is exposed to the absolute price movement of the underlying asset alone. Instead, she is exposed to basis riskbecause the terminal value of her combined position is defined as the cover basis minus the initial basis. Notice, however, that only the cover basis is unknown at Date 0, and so her real exposure is to the correlationbetween future changes in the spot and forward con- tract prices. If these movements are highly correlated, the basis risk will be quite small. In fact, it is usually possible to design a forward contract based on a specific underlying asset and deliver- able on exactly the desired future date. This sort of customized design reduces basis risk to zero, since FT,T=ST. Conversely, basis risk is a possibility when contract terms are standardized and is most likely to occur in the futures market where standardization is the norm.
To illustrate the concept of basis risk, suppose the investor wishes in February to hedge a long position of 100,000 pounds of cotton she is planning to sell in April. Exhibit 22.3 shows that cot- ton futures contracts do exist but with delivery months in either March or May. With each contract requiring the delivery of 50,000 pounds of cotton, she decides to short two of the May contracts, specifically intending to liquidate her position a month early. Suppose that on the date she initiates her short hedge, the spot cotton price was $0.3733 per pound and the May futures contract price was $0.3968 per pound. This means that her initial basis was –2.35 cents, which she hopes will move toward zero in a smooth and predictable manner. Suppose, in fact, that when she closes out her combined position in April, cotton prices have declined so that St=$0.3660 and Ft,T=$0.3753, leaving a cover basis of –0.93 cent. This means the basis has increased in value, or strengthened, which is to the short hedger’s advantage. The net April selling price for her cotton is $0.3875 per pound, which is equal to the spot price of $0.3660 plus the net futures profit of $0.0215 (= 0.3968 – 0.3753). Notice that this is lower than the original futures price but considerably higher than the April spot price. Thus, the short hedger has benefited by exchanging pure price risk for basis risk.
Although it is difficult to generalize, substantial indirect evidence exists that minimizing basis risk is the primary goal of most hedgers. For example, Brown and Smith noted that the phe- nomenal growth of OTC products to manage interest rate risk—despite the existence of exchange-traded contracts—is a response to the desire to create customized solutions.4Further, a survey by Jesswein, Kwok, and Folks showed that corporate risk managers preferred to hedge their firms’ foreign exchange exposure with forward contracts rather than with futures by a ratio of about five to one.5Finally, Edwards and Canter as well as Pirrong chronicled the severe dif- ficulties the German firm Metallgesellschaft A. G. had in trying to hedge the energy-related posi- tions on its balance sheet with exchange-traded futures positions.6
Understanding Basis Risk
910 CHAPTER 22 FORWARD AND FUTURESCONTRACTS
3The mechanics of liquidating a forward or futures contract prior to maturity will be described in the next section.
4Keith C. Brown and Donald J. Smith, Interest Rate and Currency Swaps: A Tutorial (Charlottesville, Va.: Research Foundation of the Institute of Chartered Financial Analysts, 1995).
5Kurt Jesswein, Chuck C. Y. Kwok, and William R. Folks, “What New Currency Risk Products Are Companies Using and Why?” Journal of Applied Corporate Finance 8, no. 3 (Fall 1995): 103–114.
6Franklin R. Edwards and Michael S. Canter, “The Collapse of Metallgesellschaft: Unhedgeable Risks, Poor Hedging Strategy, or Just Bad Luck?” Journal of Applied Corporate Finance 8, no. 1 (Spring 1995): 86–105, and Stephen C. Pir- rong, “Metallgesellschaft: A Prudent Hedger Ruined or a Wildcatter on NYMEX?” Journal of Futures Markets 17, no. 5 (August 1997): 543–578.
In the preceding example, the decision to short two cotton futures contracts was a simple one because the investor held exactly twice as much of the same commodity as was covered by a sin- gle contract. In most cases, calculating the appropriate hedge ratio, or the number of futures con- tracts per unit of the spot asset, is not that straightforward. The approach suggested by both John- son and Stein is to choose the number of contracts that minimizes the variance of net profit from a hedged commodity position. The determination of the required number of contracts can be established as follows.7
Consider the position of a short hedger who is long one unit of a particular commodity and short N forward contracts on that commodity. Rewriting Equation 22.2 for the profit from a short hedge and allowing for a variable number of contracts, the net profit (Πt) of this position at Date t can be written
Πt=(St– S0) – (Ft,T– F0,T) (N) =(∆S) – (∆F)(N) The variance of this value is then given as
where:
COV =the covariance of changes in the spot and forward prices
Minimizing this expression and solving for N leaves
➤22.3
where:
q =the correlation coefficient between the spot and forward price changes8
The optimal hedge ratio (N*) can be interpreted as the ratio of the spot and forward price stan- dard deviations multiplied by the correlation coefficient between the two series. Recalling from Chapter 1 that standard deviation is a measure of a position’s total risk, this means that the opti- mal number of contracts is determined by the ratio of total volatilities deflated by ρto account for the systematic relationship between the spot and forward prices. (It is, in fact, directly com- parable to the beta coefficient of a common stock.) An important implication of this is that the best contract to use in hedging an underlying spot position is the one that has the highest value of ρ. What if, for instance, a clothing manufacturer wanted to hedge the eventual purchase of a large quantity of wool, a commodity for which no exchange-traded futures contract exists? The expression for N* suggests that it may be possible to form an effective cross hedgeif prices for a contract based on a related commodity (e.g., cotton) are highly correlated with wool prices. In fact, the expected basis risk of such a cross hedge can be measured as (1 – ρ2). Finally, note that the value for N* also can be calculated as the slope coefficient of a regression using ∆S and ∆F
N S F
F
S F
*= , =
COV∆ ∆
∆
∆
σ ∆
σ
σ ρ
2
σΠ2 =σ∆2S +(N2)σ∆2F – (2 N)COV∆ ∆S, F
Calculating the Optimal Hedge Ratio
7Leland L. Johnson, “The Theory of Hedging and Speculation in Commodity Futures,” Review of Economic Studies 27 (1959–60): 139–160; and Jerome L. Stein, “The Simultaneous Determination of Spot and Futures Prices,” American Economic Review 51, no. 5 (December 1961): 1012–1025.
8Given data for spot and forward prices,σ2Πin the variance equation is a function of just one variable, N. Thus differen- tiating this equation with respect to N leaves [dσΠ2/dN] = 2(N)σ2∆F– 2COV∆S, ∆F, which can be set equal to zero and solved for N*. It is easily confirmed that the second derivative of this function is positive and so N* is a minimizing value.
912 CHAPTER 22 FORWARD AND FUTURESCONTRACTS
as the dependent and independent variables, respectively.9In the regression context,ρ2is called the coefficient of determination or, more commonly, R2. Some examples of these calculations are presented in subsequent sections.