CHAPTER 22: FUTURES MARKETS
CHAPTER 22: FUTURES MARKETS
PROBLEM SETS
1. There is little hedging or speculative demand for cement futures, since cement prices
are fairly stable and predictable. The trading activity necessary to support the futures
2. The ability to buy on margin is one advantage of futures. Another is the ease with which
3. Short selling results in an immediate cash inflow, whereas the short futures
position does not:
Action Initial CF Final CF
4. a. False. For any given level of the stock index, the futures price will be lower
5. The futures price is the agreed-upon price for deferred delivery of the asset. If that
price is fair, then the value of the agreement ought to be zero; that is, the contract
6. Because long positions equal short positions, futures trading must entail a
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CHAPTER 22: FUTURES MARKETS
7. a. The closing futures price for the September contract was 2082.70, which has a
dollar value of:
b. The futures price increases by: $2090.00 – 2082.70 = $7.30
c. Following the reasoning in part (b), any change in F is magnified by a ratio of
8. a. F0 = S0(1 + rf ) = $150 × 1.03 = $154.50
9. a. Take a short position in T-bond futures, to offset interest rate risk. If rates
c. You want to protect your cash outlay when the bond is purchased. If bond
b. If the T-bill rate is less than the dividend yield, then the futures price should be
11. The put-call parity relation states that: But spot-futures parity tells us that:
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0(1 )T
f
X
C P S r
= + – +
0
(1 )
T
f
F S r= ´ +
CHAPTER 22: FUTURES MARKETS
Substituting, we find that:
12. According to the parity relation, the proper price for December futures is:
The actual futures price for December is low relative to the June price. You should
take a long position in the December contract and short the June contract.
b. The stock price falls to: 120 × (1 – 0.03) = $116.40
The increase in the futures price is 15.09, so the cash flow will be:
15. The treasurer would like to buy the bonds today but cannot. As a proxy for this
purchase, T-bond futures contracts can be purchased. If rates do in fact fall, the
Arbitrage Portfolio CF now CF in 1 year
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0
0 0 0
[ (1 ) ]
(1 )
T
f
T
f
S r
P C S C S S C
r
´ +
= – + = – + =
+
CHAPTER 22: FUTURES MARKETS
17. a. Futures prices are determined from the spreadsheet as follows:
Spot Futures Parity and Time Spreads
Spot price 2,000
Income yield (%) 2.0 Futures prices versus maturity
Interest rate (%) 3.0
LEGEND:
Enter data
Value calculated
See comment
b. The spreadsheet demonstrates that the futures prices now decrease with
increased income yield:
Spot Futures Parity and Time Spreads
Spot price 2,000
Income yield (%) 4.0 Futures prices versus maturity
Interest rate (%) 3.0
LEGEND:
Enter data
Value calculated
See comment
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CHAPTER 22: FUTURES MARKETS
18. a. The current yield for Treasury bonds (coupon divided by price) plays the role of
the dividend yield.
b. When the yield curve is upward sloping, the current yield exceeds the short
19. a.
Cash Flows
Action Now T1T2
Long futures with maturity T1 0 P1 – F( T1)0
b. Since the T2 cash flow is riskless and the net investment was zero, then any
profits represent an arbitrage opportunity.
c. The zero-profit no-arbitrage restriction implies that
CFA PROBLEMS
1. a. The strategy that would take advantage of the arbitrage opportunity is a “reverse
F0 ≥ S0 (1+ C)
If the futures price is less than the spot price plus the cost of carrying the goods to
the futures delivery date, then an arbitrage opportunity exists. A trader would be
b.
Cash Flows
Action Now One year from now
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CHAPTER 22: FUTURES MARKETS
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CHAPTER 22: FUTURES MARKETS
Buy the commodity futures expiring in 1 year $0.00 $0.00
2. a. The call option is distinguished by its asymmetric payoff. If the Swiss franc
rises in value, then the company can buy francs for a given number of dollars
to service its debt and thereby put a cap on the dollar cost of its financing. If
the franc falls, the company will benefit from the change in the exchange rate.
b. The call option gives the company the ability to benefit from depreciation in the
franc but at a cost equal to the option premium. Unless the firm has some special
3. The important distinction between a futures contract and an options contract is that the
futures contract is an obligation. When an investor purchases or sells a futures contract,
the investor has an obligation to either accept or deliver, respectively, the underlying
Futures and options modify a portfolio’s risk in different ways. Buying or selling a
futures contract affects a portfolio’s upside risk and downside risk by a similar
4. a. The investor should sell the forward contract to protect the value of the bond
against rising interest rates during the holding period. Because the investor
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CHAPTER 22: FUTURES MARKETS
b. The value of the forward contract on expiration date is equal to the spot price of
the underlying asset on expiration date minus the forward price of the contract:
The contract has a negative value. This is the value to the holder of a long position
in the forward contract. In this example, the investor should be short the forward
c. The value of the combined portfolio at the end of the six-month holding period is:
The change in the value of the combined portfolio during this six-month
The value of the combined portfolio is the sum of the market value of the
bond and the value of the short position in the forward contract. At the start
of the six-month holding period, the bond is worth $1,000 and the forward
The fact that the combined value of the long position in the bond and the short
position in the forward contract at the forward contract’s maturity date is equal
to the forward price on the forward contract at its initiation date is not a
These results support VanHusen’s statement that selling a forward contract on the
underlying bond protects the portfolio during a period of rising interest rates. The
5. a. Accurate. Futures contracts are marked to the market daily. Holding a short
position on a bond futures contract during a period of rising interest rates
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CHAPTER 22: FUTURES MARKETS
b. Inaccurate. According to the cost-of-carry model, the futures contract price is
adjusted upward by the cost of carry for the underlying asset. Bonds (and other
financial instruments), however, do not have any significant storage costs.
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