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perceived changes in the price volatility of the contract. Price limits often are eliminated as
contracts approach maturity, usually in the last month of trading.
Price limits traditionally are viewed as a means to limit violent price fluctuations. This rea-
soning seems dubious. Suppose an international monetary crisis overnight drives up the spot
price of silver to $8.00. No one would sell silver futures at prices for future delivery as low as
$5.10. Instead, the futures price would rise each day by the $1 limit, although the quoted price
would represent only an unfilled bid order”no contracts would trade at the low quoted price.
After several days of limit moves of $1 per day, the futures price would finally reach its equi-
librium level, and trading would occur again. This process means no one could unload a posi-
tion until the price reached its equilibrium level. This example shows that price limits offer no
real protection against fluctuations in equilibrium prices.

Because of the mark-to-market procedure, investors do not have control over the tax year in
which they realize gains or losses. Instead, price changes are realized gradually, with each
Bodie’Kane’Marcus: V. Derivative Markets 16. Futures Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

16 Futures Markets

daily settlement. Therefore, taxes are paid at year-end on cumulated profits or losses regard-
less of whether the position has been closed out.

Hedging and Speculation
Hedging and speculating are two polar uses of futures markets. A speculator uses a futures con-
tract to profit from movements in futures prices, a hedger to protect against price movements.
If speculators believe prices will increase, they will take a long position for expected prof-
its. Conversely, they exploit expected price declines by taking a short position.

Let™s consider the use of the T-bond futures contract, the listings for which appear in Figure
16.2. Each T-bond contract on the Chicago Board of Trade (CBT) calls for delivery of
$100,000 par value of bonds. The listed futures price of 103-29 (that is, 10329„32) means the
market price of the underlying bonds is 103.90625% of par, or $103,906.25. Therefore, for Speculating with
every increase of one point in the T-bond futures price (e.g., to 104-29), the long position T-Bond Futures
gains $1,000, and the short loses that amount. Therefore, if you are bullish on bond prices,
you might speculate by buying T-bond futures contracts.
If the T-bond futures price increases by one point to 104-29, you profit by your speculation
by $1,000 per contract. If the forecast is incorrect, and T-bond futures prices decline, you lose
$1,000 times the decrease in the futures price for each contract purchased. Speculators bet
on the direction of futures price movements.

Why would a speculator buy a T-bond futures contract? Why not buy T-bonds directly?
One reason lies in transaction costs, which are far smaller in futures markets.
Another reason is the leverage futures trading provides. Recall that each T-bond contract
calls for delivery of $100,000 par value, worth about $103,906 in our example. The initial
margin required for this account might be only $15,000. The $1,000 per contract gain
translates into a 6.67% ($1,000/$15,000) return on the money put up, despite the fact
that the T-bond futures price increases only 0.96% (1/103.906). Futures margins, therefore,
allow speculators to achieve much greater leverage than is available from direct trading in
a commodity.
Hedgers, by contrast, use futures markets to insulate themselves against price movements.
An investor holding a T-bond portfolio, for example, might anticipate a period of interest rate
volatility and want to protect the value of the portfolio against price fluctuations. In this case,
the investor has no desire to bet on price movements in either direction. To achieve such pro-
tection, a hedger takes a short position in T-bond futures, which obligates the hedger to deliver
T-bonds at the contract maturity date for the current futures price. This locks in the sales price
for the bonds and guarantees that the total value of the bond-plus-futures position at the ma-
turity date is the futures price.3

To keep things simple, we will assume that the T-bond futures contract calls for delivery of a bond with the same
coupon and maturity as that in the investor™s portfolio. In practice, a variety of bonds may be delivered to satisfy the
contract, and a “conversion factor” is used to adjust for the relative values of the eligible delivery bonds. We will ig-
nore this complication.
Bodie’Kane’Marcus: V. Derivative Markets 16. Futures Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

578 Part FIVE Derivative Markets

Suppose as in Figure 16.2 that the T-bond futures price for March 2002 delivery is
$103.90625 (per $100 par value), which we will round off to $103.91, and that the only
16.3 EXAMPLE three possible T-bond prices in March are $102.91, $103.91, and $104.91. If investors cur-
rently hold 200 bonds, each with par value $1,000, they would take short positions in two
Hedging with
contracts, each for $100,000 value. Protecting the value of a portfolio with short futures po-
T-Bond Futures
sitions is called short hedging.
The profits in March from each of the two short futures contracts will be 1,000 times any
decrease in the futures price. At maturity, the convergence property ensures that the final fu-
tures price will equal the spot price of the T-bonds. Hence, the futures profit will be 2,000
times (F0 PT), where PT is the price of the bonds on the delivery date, and F0 is the original
futures price, $103.91.
Now consider the hedged portfolio consisting of the bonds and the short futures positions.
The portfolio value as a function of the bond price in March can be computed as follows:

T-Bond Price in March 2002
$102.91 $103.91 $104.91

Bond holdings (value 2,000 PT) $205,820 $207,820 $209,820
Futures profits or losses 2,000 0 2,000
Total $207,820 $207,820 $207,820

The total portfolio value is unaffected by the eventual bond price, which is what the
hedger wants. The gains or losses on the bond holdings are exactly offset by those on the two
contracts held short.
For example, if bond prices fall to $102.91, the losses on the bond portfolio are offset by
the $2,000 gain on the futures contracts. That profit equals the difference between the fu-
tures price on the maturity date (which equals the spot price on that date, $102.91) and the
originally contracted futures price of $103.91. For short contracts, a profit of $1 per $100 par
value is realized from the fall in the spot price. Because two contracts call for delivery of
$200,000 par value, this results in a $2,000 gain that offsets the decline in the value of the
bonds held in the portfolio. In contrast to a speculator, a hedger is indifferent to the ultimate
price of the asset. The short hedger, who has in essence arranged to sell the asset for an
agreed-upon price, need not be concerned about further developments in the market price.
To generalize the example, note that the bond will be worth PT at the maturity of the fu-
tures contract, while the profit on the futures contract is F0 PT. The sum of the two posi-
tions is F0 dollars, which is independent of the eventual bond price.

A long hedge is the analogue to a short hedge for a purchaser of an asset. Consider, for ex-
ample, a pension fund manager who anticipates a cash inflow in two months that will be in-
vested in fixed-income securities. The manager views T-bonds as very attractively priced now
and would like to lock in current prices and yields until the investment actually can be made
two months hence. The manager can lock in the effective cost of the purchase by entering the
long side of a contract, which commits her to purchasing at the current futures price.

3. Suppose that T-bonds will be selling in March at $102.91, $103.91, or $104.91.
Show that the cost in March of purchasing $200,000 par value of T-bonds net of
CHECK the profit/loss on two long T-bond contracts will be $207,820 regardless of the
eventual bond price.
Exact futures hedging may be impossible for some goods because the necessary futures
contract is not traded. For example, a portfolio manager might want to hedge the value of a
Bodie’Kane’Marcus: V. Derivative Markets 16. Futures Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

16 Futures Markets

diversified, actively managed portfolio for a period of time. However, futures contracts are
listed only on indexed portfolios. Nevertheless, because returns on the manager™s diversified
portfolio will have a high correlation with returns on broad-based indexed portfolios, an ef-
fective hedge may be established by selling index futures contracts. Hedging a position using
futures on another asset is called cross-hedging.

4. What are the sources of risk to an investor who uses stock index futures to hedge Concept
an actively managed stock portfolio?

Basis Risk and Hedging
The basis is the difference between the futures price and the spot price.4 As we have noted, on basis
the maturity date of a contract, the basis must be zero: The convergence property implies that The difference
FT PT 0. Before maturity, however, the futures price for later delivery may differ sub- between the futures
stantially from the current spot price. price and the spot
We discussed the case of a short hedger who holds an asset (T-bonds, in our example) and
a short position to deliver that asset in the future. If the asset and futures contract are held un-
til maturity, the hedger bears no risk, as the ultimate value of the portfolio on the delivery date
is determined by the current futures price. Risk is eliminated because the futures price and
spot price at contract maturity must be equal: Gains and losses on the futures and the com-
modity position will exactly cancel. If the contract and asset are to be liquidated early, before
contract maturity, however, the hedger bears basis risk, because the futures price and spot basis risk
price need not move in perfect lockstep at all times before the delivery date. In this case, gains Risk attributable to
and losses on the contract and the asset need not exactly offset each other. uncertain movements
Some speculators try to profit from movements in the basis. Rather than betting on the di- in the spread between
a futures price and a
rection of the futures or spot prices per se, they bet on the changes in the difference between
spot price.
the two. A long spot“short futures position will profit when the basis narrows.

Consider an investor holding 100 ounces of gold, who is short one gold futures contract. Sup-
pose that gold today sells for $291 an ounce, and the futures price for June delivery is $296
an ounce. Therefore, the basis is currently $5. Tomorrow, the spot price might increase to
$294, while the futures price increases to $298.50, so the basis narrows to $4.50. The in- Speculating on
vestor™s gains and losses are as follows: the Basis
Gain on holdings of gold (per ounce): $294 $291 $3.00
Loss on gold futures position (per ounce): $298.50 $296 $2.50
The investor gains $3 per ounce on the gold holdings, but loses $2.50 an ounce on the short
futures position. The net gain is the decrease in the basis, or $0.50 an ounce.

A related strategy is a spread position, where the investor takes a long position in a futures spread (futures)
contract of one maturity and a short position in a contract on the same commodity, but with a Taking a long position
different maturity. Profits accrue if the difference in futures prices between the two contracts in a futures contract
changes in the hoped-for direction; that is, if the futures price on the contract held long in- of one maturity and a
short position in a
creases by more (or decreases by less) than the futures price on the contract held short. Like
contract of a different
basis strategies, spread positions aim to exploit movements in relative price structures rather
maturity, both on the
than to profit from movements in the general level of prices. same commodity.

Usage of the word basis is somewhat loose. It sometimes is used to refer to the futures-spot difference, F P, and
other times it is used to refer to the spot-futures difference, P F. We will consistently call the basis F P.
Bodie’Kane’Marcus: V. Derivative Markets 16. Futures Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

580 Part FIVE Derivative Markets

Consider an investor who holds a September maturity contract long and a June contract
short. If the September futures price increases by 5 cents while the June futures price in-
16.5 EXAMPLE creases by 4 cents, the net gain will be 5 cents 4 cents, or 1 cent.
Speculating on
the Spread

Spot-Futures Parity
There are at least two ways to obtain an asset at some date in the future. One way is to pur-
chase the asset now and store it until the targeted date. The other way is to take a long futures
position that calls for purchase of the asset on the date in question. As each strategy leads to
an equivalent result, namely, the ultimate acquisition of the asset, you would expect the
market-determined cost of pursuing these strategies to be equal. There should be a predictable
relationship between the current price of the asset, including the costs of holding and storing
it, and the futures price.
To make the discussion more concrete, consider a futures contract on gold. This is a par-
ticularly simple case: Explicit storage costs for gold are minimal, gold provides no income
flow for its owners (in contrast to stocks or bonds that make dividend or coupon payments),
and gold is not subject to the seasonal price patterns that characterize most agricultural com-
modities. Instead, in market equilibrium, the price of gold will be at a level such that the ex-
pected rate of capital gains will equal the fair expected rate of return given gold™s investment
risk. Two strategies that will assure possession of the gold at some future date T are:
Strategy A: Buy the gold now, paying the current or “spot” price, S0, and hold it until time
T, when its spot price will be ST.
Strategy B: Initiate a long futures position, and invest enough money now in order to pay
the futures price when the contract matures.
Strategy B will require an immediate investment of the present value of the futures price in a
riskless security such as Treasury bills, that is, an investment of F0 /(1 rf)T dollars, where rf
is the rate paid on T-bills. Examine the cash flow streams of the following two strategies.5

Action Initial Cash Flow Cash Flow at Time T
Strategy A: Buy gold S0 ST
Strategy B: Enter long position 0 ST F0
Invest F0 /(1 rf)T in bills T
F0 /(1 rf) F0
Total for strategy B F0 /(1 ST


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