Chapter 17 – Futures Markets and Risk Management
CHAPTER 17
FUTURES MARKETS AND RISK MANAGEMENT
2. Futures price = S0 (1+ rf − d)T = $1,200 (1 + .01 – .02) = $1,188
3. The theoretical futures price = S0 (1+ rf)T = $1,700 (1 + .02) = $1,734. At $1,641, the
gold futures contract is underpriced. To benefit from the mispricing, we sell gold short
$1,700 today, lend the money at risk-free rate, and long gold future of $1,641. One year
4. Margin = $115,098 .15 = $17,264.70
5.
a. The required margin is 1,164.50 $250 .10 = $29,112.50
6. The ability to buy on margin is one advantage of futures. Another is the ease with
7. Short selling results in an immediate cash inflow, whereas the short futures position
does not:
Action Initial Cash Flow Cash Flow at Time T
Short sale
+S0
–ST
Short futures 0 F0 – ST
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8. F0 = S0 (1 + rf – d) = $1,200 (1 + .03 – .02) = $1,212
9. According to the parity relationship, the proper price for December futures is:
10.
a.
Action Initial Cash Flow Cash Flow at Time T
Buy stock
–S0
ST + D
11.
12.
a. Use the spreadsheet template from www.mhhe.com/bkm, input spot price,
dividend yield, interest rate, and the dates, and get the expected future prices of
each maturity dates.
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13.
a. F0 = S0 (1 + rf) = $120 1.06 = $127.20
b. The stock price falls to: $120 (1 – .03) = $116.40
14.
a. The initial futures price is:
F0 = S0 (1 + rf – d) = 800 (1 + .005 – .002)12 = 829.28
7.85 $250 = $1,962.50
b. The holding period return is: $1,962.50/$10,000 = .1963 = 19.63%
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15. The parity value of F0 is: S0 (1 + rf – d) = 1,200 (1 + .03 – .02) = 1,212
The actual futures price is 1,233, overpriced by 21.
19.21 $250 = $4,802.50
b. The holding period return is: $4,802.50/$10,000 = .48025 = 48.03%
21. The Treasurer would like to buy the bonds today, but cannot. As a proxy for this
22. She must sell:
$1 million×8
10 =$.8
million of T-bonds
23. If yield changes on the bond and the contracts are each 1 basis point, then the bond
value will change by:
24.
a. Each contract is for $250 times the index, currently valued at 1,200. Therefore,
each contract has the same exposure to the market as $300,000 worth of stock,
and to hedge a $6 million portfolio, you need:
$6 million/$300,000 = 20 contracts
Chapter 17 – Futures Markets and Risk Management
25. The firm should enter a swap in which it pays a 7% fixed rate and receives LIBOR on
$10 million of notional principal. Its total payments will be as follows:
26.
a. From parity: F0 = S0 (1 + rf – d) = [1,200 (1 + .03)] – 15 = 1,221
Actual F0 is 1,218, so the futures price is $3 below its “proper” or parity value.
b. Buy the relatively cheap futures and sell the relatively expensive stock.
Total
0
3
c. If you do not receive the proceeds of the short sales, then the $1,200 cannot be
Total
–33
d. If we call the original futures price F0, then the proceeds from the long-futures,
Total
1,185 – F0
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whole or part.
Chapter 17 – Futures Markets and Risk Management
Therefore, F0 can be as low as 1,185 without giving rise to an arbitrage
opportunity. On the other hand, if F0 is higher than the parity value (1,218) an
arbitrage opportunity (buy stocks, sell futures) will open up. There is no short-
selling cost in this case. Therefore, the no-arbitrage region is: 1,185 F0
1,218CFA 1
CFA 2
CFA 3
Answer:
CFA 4
Answer:
b. Again, a short position in T-bond futures will offset the bond price risk.
CFA 5
Answer:
contract.
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Chapter 17 – Futures Markets and Risk Management
CFA 6
Answer:
a. The strategy that would take advantage of the arbitrage opportunity is a Reverse
If the futures price is less than the spot price plus the cost of carrying the goods
b.
Opening Transaction Now
Sell the spot commodity short +$120.00
Buy the commodity futures expiring in 1 year 0.00
Contract to lend $120 at 8% for 1 year –$120.00
Total cash flow $0.00
Closing Transaction One Year from Now
Accept delivery on expiring futures –$125.00
Cover short commodity position 0.00
Collect on loan of $120 +$129.60
Total arbitrage profit $4.60
CFA 7
Answer:
a. In an interest rate swap, one firm exchanges (or “swaps”) a fixed payment for
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Chapter 17 – Futures Markets and Risk Management
b. There are several applications of interest rate swaps. For example, suppose that a
CFA 8
Answer:
a. Delsing should sell stock index futures contracts and buy bond futures contracts.
b. Compute the number of contracts in each case as follows:
CFA 9
Answer:
a. Short the contract. As rates rise, prices will fall. Selling the futures contract will
b. In 6 months the bond will accrue $25 of interest, which, when subtracted from
17-9