高等教育自学考试大纲
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 market would not
materialize. Only those commodities and financial securities with significant volatility tend to have futures contracts available for hedgers and speculators.
2. The ability to buy on margin is one advantage of futures. Another is the
ease with which one can alter one’s holdings of the asset. This is especially important if one is dealing in commodities, for which the futures market is far more liquid than the spot market.
3. Short selling results in an immediate cash inflow, whereas the
short futures position does not:
Action Short sale Short futures
Initial Final CF CF +P0 0
–PT F0 – PT
CHAPTER 22: FUTURES MARKETS
4. a. False. For any given level of the stock index, the futures
price will be lower when the dividend yield is higher. This follows from spot-futures parity:
F0 = S0 (1 + rf – d)T
b. False. The parity relationship tells us that the futures price
is determined by the stock price, the interest rate, and the dividend yield; it is not a function of beta.
c. True. The short futures position will profit when the S&P 500
Index falls. This is a negative beta position.
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高等教育自学考试大纲
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 will be a zero-NPV
agreement for each trader. Over time, however, the price of the underlying asset will change and this will affect the value of the contract.
6. Because long positions equal short positions, futures trading must
entail a “canceling out” of bets on the asset. Moreover, no cash is exchanged at the inception of futures trading. Thus, there should be minimal impact on the spot market for the asset, and futures trading should not be expected to reduce capital available for other uses.
7. a. The closing futures price for the March contract was 1,491.80,
which has a dollar value of:
$250 × 1,491.80 = $372,950
Therefore, the required margin deposit is: $37,295
b. The futures price increases by: $1,498.00 – 1,491.80 = $6.2
The credit to your margin account would be: 6.2 × $250 = $1,550 This is a percent gain of: $1,550/$37,295 = 0.04 = 4% Note that the futures price itself increased by only 0.42%.
c. Following the reasoning in part (b), any change in F is
magnified by a ratio of
(l /margin requirement). This is the leverage effect. The return will be –10%.
8. a.
b.
c.
9. a.
F0 = S0(1 + rf ) = $150 × 1.03 = $154.50 F0 = S0(1 + rf )3 = $150 × 1.033 = $163.91 F0 = 150 × 1.063 = $178.65
Take a short position in T-bond futures, to offset interest rate risk. If rates increase, the loss on the bond will be offset to some extent by gains on the futures.
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高等教育自学考试大纲
b. Again, a short position in T-bond futures will offset the
interest rate risk.
c. You want to protect your cash outlay when the bond is purchased.
If bond prices increase, you will need extra cash to purchase the bond. Thus, you should take a long futures position that will generate a profit if prices increase.
10. F0 = S0 × (l + rf – d) = 1,400 × (1 + 0.03 – 0.02) = 1,414 If the T-bill rate is less than the dividend yield, then the
futures price should be less than the spot price.
11. The put-call parity relation states that: But spot-futures parity
tells us that: XC?P?S0?(1?rf)T
F?S0?(1?rf)T
Substituting, we find that:
P?C?S0?[S0?(1?rf)T](1?rf)T?C?S0?S0?C12. According to the parity relation, the proper price for December
futures is:
FDec = FJune(l + rf )1/2 = 1500 × 1.02 1/2 = 1,514.93
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.
13. a. 120 × 1.06 = $127.20
b. The stock price falls to: 120 × (1 – 0.03) = $116.40
The futures price falls to: 116.4 × 1.06 = $123.384 The investor loses: (127.20 – 123.384) × 1,000 = $3,816
c. The percentage loss is: $3,816/$12,000 = 0.318 = 31.8%
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投资学10版习题答案22
