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Action Today (time 0) S \$95 S \$110
Buy .4656 shares at price S \$100 \$44.232 \$51.216
Write 1 call at price C 0 6.984
Total \$44.232 \$44.232

The portfolio must have a market value equal to the present value of \$44.232.
e. \$44.232/1.05 \$42.126
f. .4656 \$100 C \$42.126
C \$46.56 \$42.126 \$4.434
5. Higher. For deep out-of-the-money options, an increase in the stock price still leaves the option
unlikely to be exercised. Its value increases only fractionally. For deep in-the-money options,
exercise is likely, and option holders benefit by a full dollar for each dollar increase in the stock,
as though they already own the stock.
2
6. Because 0.6, 0.36.
ln(100/95) (0.10 0.36/2)0.25
d1 0.4043
0.6 0.25
d2 d1 0.6 0.25 0.1043

Using Table 15.2 and interpolation, or a spreadsheet function,
N(d1) 0.6570
N(d2) 0.5415
0.10 0.25
C 100 0.6570 95e 0.5415 15.53

7. Implied volatility exceeds 0.5. Given a standard deviation of 0.5, the option value is \$13.70.
A higher volatility is needed to justify the actual \$15 price.
8. A \$1 increase in stock price is a percentage increase of 1/122 0.82%. The put option will fall by
(0.4 \$1) \$0.40, a percentage decrease of \$0.40/\$4 10%. Elasticity is 10/0.82 12.2. www.mhhe.com/bkm
Bodieâˆ’Kaneâˆ’Marcus: V. Derivative Markets 16. Futures Markets Â© The McGrawâˆ’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

16
FUTURES MARKETS

AFTER STUDYING THIS CHAPTER
YOU SHOULD BE ABLE TO:

> Calculate the profit on futures positions as a function of
current and eventual futures prices.

> Formulate futures market strategies for hedging or
speculative purposes.

> Compute the futures price appropriate to a given price on
the underlying asset.

> Design arbitrage strategies to exploit futures market
mispricing.

564
Bodieâˆ’Kaneâˆ’Marcus: V. Derivative Markets 16. Futures Markets Â© The McGrawâˆ’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

http://www.mgex.com (Minneapolis Grain
Related Websites
Exchange)
http://www.nybot.com (New York Board of Trade)
http://www.numa.com
http://www.nymex.com (New York Mercantile
The above sites are good places to start when looking
Exchange)
for websites in futures and derivatives. They contain
information on services and other links. http://www.cme.com (Chicago Mercantile
Exchange)
http://www.cme.com
http://www.cbot.com
http://www.kcbt.com (Kansas City Board of Trade)
The above sites have extensive information available on
financial futures, including index products. Most of the These sites are exchange sites.
the futures markets.

utures and forward contracts are like options in that they specify the purchase

F or sale of some underlying security at some future date. The key difference is
that the holder of an option to buy is not compelled to buy and will not do so if
the trade is unprofitable. A futures or forward contract, however, carries the obliga-
tion to go through with the agreed-upon transaction.
A forward contract is not an investment in the strict sense that funds are paid for
an asset. It is only a commitment today to transact in the future. Forward arrange-
ments are part of our study of investments, however, because they offer a powerful
means to hedge other investments and generally modify portfolio characteristics.
Forward markets for future delivery of various commodities go back at least to
ancient Greece. Organized futures markets, though, are a relatively modern develop-
ment, dating only to the 19th century. Futures markets replace informal forward con-
tracts with highly standardized, exchange-traded securities.
Figure 16.1 documents the tremendous growth of trading activity in futures mar-
kets since 1976. The figure shows that trading in financial futures has grown partic-
ularly rapidly and that financial futures now dominate the entire futures market.
This chapter describes the workings of futures markets and the mechanics of
trading in these markets. We show how futures contracts are useful investment vehi-
cles for both hedgers and speculators and how the futures price relates to the spot
price of an asset. Finally, we take a look at some specific financial futures contractsâ€”
those written on stock indexes, foreign exchange, and fixed-income securities.
Bodieâˆ’Kaneâˆ’Marcus: V. Derivative Markets 16. Futures Markets Â© The McGrawâˆ’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

566 Part FIVE Derivative Markets

16.1 THE FUTURES CONTRACT
To see how futures and forwards work and how they might be useful, consider the portfolio
diversification problem facing a farmer growing a single crop, let us say wheat. The entire
planting seasonâ€™s revenue depends critically on the highly volatile crop price. The farmer canâ€™t
easily diversify his position because virtually his entire wealth is tied up in the crop.
The miller who must purchase wheat for processing faces a portfolio problem that is the
mirror image of the farmerâ€™s. He is subject to profit uncertainty because of the unpredictable
future cost of the wheat.
Both parties can reduce this source of risk if they enter into a forward contract requiring
forward contract
the farmer to deliver the wheat when harvested at a price agreed upon now, regardless of the
An arrangement
market price at harvest time. No money need change hands at this time. A forward contract is
calling for future
simply a deferred-delivery sale of some asset with the sales price agreed upon now. All that is
delivery of an asset at
an agreed-upon price. required is that each party be willing to lock in the ultimate price to be paid or received for de-
livery of the commodity. A forward contract protects each party from future price fluctuations.

300
281.1
280
260.3
260 254.5
Financial Futures and Options 242.7
Agricultural Futures and Options
240 233.5
222.4
219.5
Metals and Energy
210.7
220

200
178.6
Contracts (in millions)

180
153.3
160 149.7
141.8
138.7
137.2
140
124.5
120
99.0
100

80
65.4
60.8
60 60.3
62
58.7 59.4
40 50.3
42.3
43.1 42.2
37.0 36.9
38.8
35.4
26.8
20 22.1
.8 .7 .7 .4 .2 .1 .1 .1 .1 .1 .1 .07 .1 .05 .03 .02 .02
0
1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

F I G U R E 16.1
CBOT trading volume in futures contracts
Bodieâˆ’Kaneâˆ’Marcus: V. Derivative Markets 16. Futures Markets Â© The McGrawâˆ’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

567
16 Futures Markets

Futures markets formalize and standardize forward contracting. Buyers and sellers do not
have to rely on a chance matching of their interests; they can trade in a centralized futures
market. The futures exchange also standardizes the types of contracts that may be traded: It es-
tablishes contract size, the acceptable grade of commodity, contract delivery dates, and so
forth. While standardization eliminates much of the flexibility available in informal forward
contracting, it has the offsetting advantage of liquidity because many traders will concentrate
on the same small set of contracts. Futures contracts also differ from forward contracts in that
they call for a daily settling up of any gains or losses on the contract. In contrast, in the case
of forward contracts, no money changes hands until the delivery date.
In a centralized market, buyers and sellers can trade through brokers without personally
searching for trading partners. The standardization of contracts and the depth of trading in
each contract allows futures positions to be liquidated easily through a broker rather than per-
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