Chapter Nine - Trinity
Chapter Nine
Stock Index Futures
Multiple Choice
1. A characteristic of stock index futures is
a. they have limited risk.
b. they pay dividends monthly.
c. they are settled in cash.
d. they have a beta of zero.
ANSWER: C
2. If a stock index is 400.00, how many associated futures contracts (multiplier of $250) must be sold to hedge a $10 million stock portfolio with a beta of 1.10?
a. 50
b. 55
c. 110
d. 150
ANSWER: C
3. Which of the following statements is true regarding a stock index futures contract?
a. The basis is usually negative.
b. The basis will converge on zero as time passes.
c. The basis will only decrease; it cannot increase.
d. The basis will only increase; it cannot decrease.
ANSWER: B
4. Dynamic hedging strategies seek to
a. replicate a put option.
b. replicate a call option.
c. replicate a covered call option.
d. replicate a short put.
ANSWER: A
5. The price of a stock index futures contract is a function of all of the following except
a. dividend yield.
b. interest rates.
c. level of the index.
d. future volatility of the index
ANSWER: D
6. A synthetic index portfolio is _____ T-bills and _____ stock index futures.
a. long, long
b. long, short
c. short, long
d. short, short
ANSWER: A
7. A person buys S&P 500 futures and sells Dow Jones futures. This is an example of a(n) _____ spread.
a. bull
b. time
c. intermarket
d. credit
ANSWER: C
8. Stock index futures are used to reduce all of the following except
a. systematic risk.
b. market risk.
c. undiversifiable risk.
d. company risk.
ANSWER: D
9. A futures contract hedge ratio depends on all of the following except
a. value of the futures contract.
b. dollar value of the portfolio to be hedged.
c. beta of the portfolio to be hedged.
d. premium on the futures contract.
ANSWER: D
Short Answer/Problem
1. Attach a Wall Street Journal clipping showing OEX prices. Explain how a person could use an index option like the S&P 100 (OEX) option to provide insurance against the decline of their 250,000 stock portfolio. Use the WSJ clipping to give a specific example.
2. Attach a Wall Street Journal clipping showing SPX futures prices. A portfolio manager controls $3 million in common stock. In anticipation of a stock market decline, the decision is made to hedge the portfolio using the September S&P 500 index futures contract. The portfolio beta is 1.15. Refer to the WSJ clipping for the current value of the index and the futures contracts.
a. Calculate the number of contracts that should be bought or sold (indicate which) to hedge this portfolio.
b. Suppose that when the contracts are closed out, the portfolio has fallen in value by $350,000 and the value of the S&P 500 index is 250.00. Calculate the combined gain or loss (indicate which) on the hedged portfolio.
3. A portfolio manager controls $5 million in common stock. In anticipation of a stock market decline, the decision is made to hedge the portfolio using the S&P 500 futures contract. The portfolio's beta is 1.20, and the current value of the S&P 500 futures contract selected is 238.50.
a. Calculate the number of futures contracts that should be bought or sold.
b. Suppose that when the contracts are closed out, the portfolio has fallen in value to $4.2 million and that the S&P 500 index has fallen to 215.00. Calculate the gain or loss on the combined positions (stock portfolio and futures contracts).
c. Why does the net gain or loss not exactly equal zero?
ANSWER:
a. [pic]83.85 ( 84 contracts
b. portfolio loss = $800,000
gain on futures = 84 x (238.5 – 215) x $250 = $493,500
total = $306,500 loss
c. Rounding of the hedge ratio; beta is only an approximate measure of market sensitivity
4. Suppose the S&P 500 index is at 315.34. According to the Outlook, the dividend yield on the index is 2.89 % . If T-bills yield 8.97%, what is the fair value of an S&P futures contract that calls for delivery in 106 days?
ANSWER:
F = Se(R – D)T 315.34e(.0897 ( .0289)(106/365) = 320.97
5. In problem 4, suppose that the futures contract in question sells for 322.50. How would you take advantage of the price discrepancy?
ANSWER: The futures contract sells for more than it theoretically should. Therefore, sell the futures and buy the underlying stock.
6. Consider the following portfolio:
stock shares share price value beta
FV 12000 34 $408,000 1.25
GC 25000 22 550,000 1.00
YH 20000 17 340,000 1.07
TOTALS $1,298,000 1.10
If the S&P 500 index is about 400, how many futures contracts must be bought or sold to hedge 50% of the market risk of this portfolio?
ANSWER: [pic]14 contracts
7. You want to hedge half the market risk of a $100 million stock portfolio with a beta of 0.90. The December S&P500 stock index futures settled at 1065.25. How many futures contracts are necessary to do so? (The futures contract is $250 times the value of the index.)
ANSWER: [pic]= 170
8. Interest rates in Japan are near zero at present. Suppose the stocks in the shigotoba index (currently at 10,300) have an average dividend yield of 1.2%. Would you expect a three-month shigotoba futures contract to settle at less than, about the same, or more than 10,300? Explain your answer.
ANSWER:
F = Se(R – D)T
If D >R the exponent is negative and F< S, so the futures should sell for less than 10,300.
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