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only dates each year when futures contracts settle.




F I G U R E 16.6
Spot and forward
prices in foreign
exchange
Source: From The Wall Street
Journal, January 16, 2002.
Reprinted by permission of
Dow Jones & Company, Inc.,
via Copyright Clearance
Center, Inc. © Dow Jones &
Company, Inc. All Rights
Reserved Worldwide.
Bodie’Kane’Marcus: V. Derivative Markets 16. Futures Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




589
16 Futures Markets


Interest Rate Futures
The late 1970s and 1980s saw a dramatic increase in the volatility of interest rates, leading to
investor desire to hedge returns on fixed-income securities against changes in interest rates.
As one example, thrift institutions that had loaned money on home mortgages before 1975
suffered substantial capital losses on those loans when interest rates later increased. An inter-
est rate futures contract could have protected banks against such large swings in yields. The
significance of these losses has spurred trading in interest rate futures.
The major U.S. interest rate contracts currently traded are on Eurodollars, Treasury bills,
Treasury notes, and Treasury bonds. The range of these securities provides an opportunity to
hedge against a wide spectrum of maturities from very short (T-bills) to long term (T-bonds).
In addition, futures contracts tied to interest rates in Europe (euro-denominated), Japan, the
United Kingdom, and several other countries trade and are listed in The Wall Street Journal.
Figure 16.2 shows listings of some of these contracts in The Wall Street Journal.
The Treasury contracts call for delivery of a Treasury bond, bill, or note. Should interest
rates rise, the market value of the security at delivery will be less than the original futures
price, and the deliverer will profit. Hence, the short position in the interest rate futures contract
gains when interest rates rise and bond prices fall.
Similarly, Treasury bond futures can be useful hedging vehicles for bond dealers or under-
writers. We saw earlier, for example, how the T-bond contract could be used by an investor to
hedge the value of a T-bond portfolio or by a pension fund manager who anticipates the pur-
chase of a Treasury bond.
An episode that occurred in October 1979 illustrates the potential hedging value offered by
T-bond contracts. Salomon Brothers, Merrill Lynch, and other underwriters brought out a $1
billion issue of IBM bonds. As is typical, the underwriting syndicate quoted an interest rate at
which it guaranteed the bonds could be sold. This underwriting arrangement is called a “firm
commitment,” and is discussed in more detail in Chapter 3. (In essence, the syndicate buys the
company™s bonds at an agreed-upon price and then takes the responsibility of reselling them
in the open market. If interest rates increase before the bonds can be sold to the public, the
syndicate, not the issuer, bears the capital loss from the fall in the value of the bonds.)
In this case, the syndicate led by Salomon Brothers and Merrill Lynch brought out the IBM
debt to sell at yields of 9.62% for $500 million of 7-year notes and 9.41% for $500 million of
25-year bonds. These yields were only about four basis points above comparable maturity
U.S. government bond yields, reflecting IBM™s excellent credit rating. The debt issue was
brought to market on Thursday, October 4, when the underwriters began placing the bonds
with customers. Interest rates, however, rose slightly that Thursday, making the IBM yields
less attractive, and only about 70% of the issue had been placed by Friday afternoon, leaving
the syndicate still holding between $250 million and $300 million of bonds.
Then on Saturday, October 6, the Federal Reserve Board announced a major credit-
tightening policy. Interest rates jumped by almost a full percentage point. The underwriting
syndicate realized the balance of the IBM bonds could not be placed to its regular customers
at the original offering price and decided to sell them in the open bond market. By that time,
the bonds had fallen nearly 5% in value, so that the underwriter™s loss was about $12 million
on the unsold bonds. The net loss on the underwriting operation came to about $7 million, af-
ter the profit of $5 million that had been realized on the bonds that were placed.
As the major underwriter with the lion™s share of the bonds, Salomon lost about $3.5 mil-
lion on the bond issue. Yet, while most of the other underwriters were vulnerable to the inter-
est rate movement, Salomon had hedged its bond holdings by shorting about $100 million in
Government National Mortgage Association (GNMA) and Treasury bond futures. Holding a
short position, Salomon Brothers realized profits on the contract when interest rates increased.
Bodie’Kane’Marcus: V. Derivative Markets 16. Futures Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




590 Part FIVE Derivative Markets


The profits on the short futures position resulted because the value of the bonds required to be
delivered to satisfy the contract decreased when interest rates rose. Salomon Brothers proba-
bly about broke even on the entire transaction, making estimated gains on the futures position
of about $3.5 million, which largely offset the capital loss on the bonds it was holding.
How could Salomon Brothers have constructed the proper hedge ratio, that is, the proper
number of futures contracts per bond held in its inventory? The T-bond futures contract nom-
inally called for delivery of an 8% coupon, 20-year maturity government bond in return for the
futures price. (In practice, other bonds may be substituted for this standard bond to settle the
contract, but we will use the 8% bond for illustration.) Suppose the market interest rate is 10%
and Salomon is holding $100 million worth of bonds, with a coupon rate of 10% and 20 years
to maturity. The bonds currently sell at 100% of par value. If the interest rate were to jump to
11%, the bonds would fall in value to a market value of $91.98 per $100 of par value, a loss
of $8.02 million. (We use semiannual compounding in this calculation.)
To hedge this risk, Salomon would need to short enough futures so that the profits on the
futures position would offset the loss on the bonds. The 8%, 20-year bond of the futures con-
tract would sell for $82.84 at an interest rate of 10%. If the interest rate were to jump to 11%,
the bond price would fall to $75.93, and the fall in the price of the 8% bond, $6.91, would ap-
proximately equal the profit on the short futures position per $100 par value.7 Because each
contract calls for delivery of $100,000 par value of bonds, the gain on each short position
would equal $6,910. Thus, to offset the $8.02 million loss on the value of the bonds, Salomon
theoretically would need to hold $8.02 million/$6,910 1,161 contracts short. The total gain
on the contracts would offset the loss on the bonds and leave Salomon unaffected by interest
rate swings.
The actual hedging problem is more difficult for several reasons, most of which are due to
the fact that this is really a cross-hedge: Salomon is hedging its IBM bonds by selling con-
tracts on Treasury bonds and, to a lesser extent, GNMA bonds. Some of the complications in
this hedging strategy are: (1) Salomon probably would hold more than one issue of bonds in
its inventory; (2) interest rates on government and corporate bonds will not be equal and need
not move in lockstep; (3) the T-bond contract may be settled with any of several bonds instead
of the 8% benchmark bond; and (4) taxes could complicate the picture. Nevertheless, the prin-
ciples illustrated here underlie all hedging activity.




SUMMARY • Forward contracts are arrangements that call for the future delivery of an asset at a
currently agreed-upon price. The long trader is obligated to purchase the good, and the
short trader is obligated to deliver it. If the price at the maturity of the contract exceeds the
forward price, the long side benefits by virtue of acquiring the good at the contract price.
• A futures contract is similar to a forward contract, differing most importantly in the
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aspects of standardization and marking to market, which is the process by which gains and
losses on futures contract positions are settled daily. In contrast, forward contracts call for
no cash transfers until contract maturity.
• Futures contracts are traded on organized exchanges that standardize the size of the
contract, the grade of the deliverable asset, the delivery date, and the delivery location.
Traders negotiate only the contract price. This standardization creates increased liquidity


7
We say approximately because the exact figure depends on the time to maturity of the contract. We assume here that
the maturity date is less than a month away so that the futures price and the bond price move in virtual lockstep.
Bodie’Kane’Marcus: V. Derivative Markets 16. Futures Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




591
16 Futures Markets


in the marketplace and means buyers and sellers can easily find many traders for a desired
purchase or sale.
• The clearinghouse acts as an intermediary between each pair of traders, acting as the short
position for each long, and as the long position for each short, so traders need not be
concerned about the performance of the trader on the opposite side of the contract. Traders
are required to post margins in order to guarantee their own performance on the contracts.
• The gain or loss to the long side for a futures contract held between time 0 and t is
Ft F0 . Because FT PT at maturity, the long™s profit if the contract is held until
maturity is PT F0 , where PT is the spot price at time T and F0 is the original futures
price. The gain or loss to the short position is F0 PT .
• Futures contracts may be used for hedging or speculating. Speculators use the contracts to
take a stand on the ultimate price of an asset. Short hedgers take short positions in
contracts to offset any gains or losses on the value of an asset already held in inventory.
Long hedgers take long positions in futures contracts to offset gains or losses in the
purchase price of a good.
• The spot-futures parity relationship states that the equilibrium futures price on an asset
providing no service or payments (such as dividends) is F0 P0(1 rf )T. If the futures
price deviates from this value, then market participants can earn arbitrage profits.
• If the asset provides services or payments with yield d, the parity relationship becomes
F0 P0 (1 rf d )T. This model is also called the cost-of-carry model, because it states
that the futures price must exceed the spot price by the net cost of carrying the asset until
maturity date T.
• Futures contracts calling for cash settlement are traded on various stock market indexes.
The contracts may be mixed with Treasury bills to construct artificial equity positions,
which makes them potentially valuable tools for market timers. Market index contracts
also are used by arbitrageurs who attempt to profit from violations of the parity
relationship.
• Interest rate futures allow for hedging against interest rate fluctuations in several different
markets. The most actively traded contract is for Treasury bonds.

KEY
basis, 579 forward contract, 566 short position, 567
TERMS
basis risk, 579 futures price, 567 spot-futures parity
cash delivery, 576 index arbitrage, 587 theorem, 582
clearinghouse, 572 long position, 567 spread, 579
convergence property, 575 maintenance margin, 574 triple-witching hour, 587
cost-of-carry marking to market, 574
relationship, 582 program trading, 587

PROBLEM
1. The open interest on a futures contract at any given time is the total number of
SETS
outstanding:
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a. Contracts.
b. Unhedged positions.
c. Clearinghouse positions.
d. Long and short positions.
2. In futures trading, the minimum level to which an equity position may fall before
requiring additional margin is most accurately termed the:
a. Initial margin.
b. Variation margin.
c. Cash flow margin.
d. Maintenance margin.
Bodie’Kane’Marcus: V. Derivative Markets 16. Futures Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




592 Part FIVE Derivative Markets


3. A silver futures contract requires the seller to deliver 5,000 Troy ounces of silver. Jerry
Harris sells one July silver futures contract at a price of $8 per ounce, posting a $2,025
initial margin. If the required maintenance margin is $1,500, what is the first price per
ounce at which Harris would receive a maintenance margin call?
4. a. Using Figure 16.2, compute the dollar value of the stocks traded on one contract on
the Standard & Poor™s 500 index. The closing spot price of the S&P index is given
in the last line of the figure. If the margin requirement is 10% of the futures price
times the multiplier of $250, how much must you deposit with your broker to trade
the March contract?
b. If the March futures price were to increase to $1,200, what rate of return would you
earn on your net investment if you entered the long side of the contract at the price
shown in the figure?
c. If the March futures price falls by 1%, what is the percentage gain or loss on your
net investment?
5. Why is there no futures market in cement?
6. Why might individuals purchase futures contracts rather than the underlying asset?
7. What is the difference in cash flow between short-selling an asset and entering a short
futures position?
8. Consider a stock that will pay a dividend of D dollars in one year, which is when a
futures contract matures. Consider the following strategy: Buy the stock, short a
futures contract on the stock, and borrow S0 dollars, where S0 is the current price of
the stock.
a. What are the cash flows now and in one year? (Remember the dividend the stock
will pay.)
b. Show that the equilibrium futures price must be F0 S0(1 r) D to avoid
arbitrage.
c. Call the dividend yield d D/S0, and conclude that F0 S0(1 r d ).
9. a. A hypothetical futures contract on a nondividend-paying stock with current price
$150 has a maturity of one year. If the T-bill rate is 6%, what should the futures
price be?
b. What should the futures price be if the maturity of the contract is three years?
c. What if the interest rate is 8% and the maturity of the contract is three years?
10. Your analysis leads you to believe the stock market is about to rise substantially. The
market is unaware of this situation. What should you do?
11. In each of the following cases, discuss how you, as a portfolio manager, could use
financial futures to protect a portfolio.
a. You own a large position in a relatively illiquid bond that you want to sell.
b. You have a large gain on one of your long Treasuries and want to sell it, but you
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would like to defer the gain until the next accounting period, which begins in four
weeks.
c. You will receive a large contribution next month that you hope to invest in long-term
corporate bonds on a yield basis as favorable as is now available.
12. Suppose the value of the S&P 500 stock index is currently $1,300. If the one-year T-bill

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