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Chapter 17 - Futures Markets and Risk Management
CHAPTER 17
FUTURES MARKETS AND RISK MANAGEMENT
1. Selling a contract is a short position. If the price rises, you lose money.
3.
a. The theoretical futures price = S0 (1+ rf)T = $1,200 (1 + .02) = $1,224. At
$1,141, the gold futures contract is underpriced.
4. Margin = $115,098 .15 = $17,264.70
5. a. The required margin is 1,988.50 $50 .10 = $9,942.50
b. Total Return = (2,460 – 1,988.50) $50 = $23,575
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:
Chapter 17 - Futures Markets and Risk Management
Action
Initial Cash Flow
Cash Flow at Time T
Short sale
+S0
–ST
Short futures
0
F0 – ST
8.
a. F0 = S0 (1 + rf – d) = $2,400 (1 + .03 – .02) = $2,424
b. F0 = S0 (1 + rf – d) = $2,400 (1 + .01 – .02) =$2,376, which is less than the
current market value.
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
Short futures
0
F0 – ST
Borrow
S0
–S0(1 + r)
Total
0
F0 + D – S0(1 + r)
11.
a. F0 = S0 (1 + rf)T = $150 1.03 = $154.50
12. a. Use the spreadsheet template from Connect, input spot price, dividend yield,
interest rate, and the dates, and get the expected future prices of each maturity
dates.
Spot price
2400
Income yield (%)
2
Futures prices versus
maturity
Interest rate (%)
1
Today's date
1/1/2018
Spot price
2,400.00
Maturity date 1
2/12/2018
Futures 1
2,397.25
Maturity date 2
5/21/2018
Futures 2
2,390.64
Maturity date 3
11/18/2018
Futures 3
2,378.85
Time to maturity 1
0.11
Time to maturity 2
0.39
Time to maturity 3
0.88
Spot price
2400
Income yield (%)
2
Futures prices versus
maturity
Interest rate (%)
3
Today's date
1/1/2018
Spot price
2,400.00
Maturity date 1
2/12/2018
Futures 1
2,402.72
Maturity date 2
5/21/2018
Futures 2
2,409.31
Maturity date 3
11/18/2018
Futures 3
2,421.12
Time to maturity 1
0.11
Time to maturity 2
0.39
Time to maturity 3
0.88
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) = 2000 (1 + .005 – .002)12 = 2,073.20
15. The parity value of F0 is: S0 (1 + rf – d) = 2,000 (1 + .03 – .02) = 2,020
The actual futures price is 2,030, overpriced by 10.
Action
Initial Cash Flow
Cash Flow at Time T (one year)
Buy index
–2,000
ST + (.02 × 2,000) [CF includes 2% dividend]
Short futures
0
2,030 –ST
Borrow
2,000
–2,000 × 1.03
Total
0
10 [A riskless cash flow]
16. a. The current yield on bonds (coupon interest divided by price) plays the role of
the dividend yield.
17. The actual dollar cost of funds will be determined by LIBOR. The effective interest rate
18. The speculator who believes interest rates will fall wants to pay the floating rate and
19.
a. The dollar value of the index is: $50 2,000 = $100,000
Therefore, the position requires margin of $10,000.
20.
a. The initial futures price is: F0 = 2,000 (1 + .002 – .001)12 = 2,024.13
In one month, the maturity of the contract will be only 11 months, so the futures
21. a. The Treasurer would like to buy the bonds today, but cannot. As a proxy for
22. She must sell:
8. $
10
8
million 1$ =
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:
The contract will result in a cash flow of:
24. a. Each contract is for $50 times the index, currently valued at 2,000. Therefore,
each contract has the same exposure to the market as $100,000 worth of stock,
so to hedge a $10 million portfolio, you need:
$10 million/$100,000 = 100 contracts
b. The parity value of the futures price for a maturity of one (semiannual) period is
Action
Initial Cash Flow
Cash Flow at Time T
Short 100 futures contracts
0
100 × $50 (2,020 – ST)
Buy 5,000 “shares” of the
index (each share equals
$2,000)
–$10 million
($10 million .01) dividends
+ (5,000 ST) value of
shares at time T
Total
–$10 million
$10.20 million [which is riskless]
c. Thus the riskless return on the hedged strategy equals the T-bill rate of 2% (that
is, 10.20/10 − 1 = .02 = 2%).
25.
a. Now, the stock swings only .6 as much as the market index.
26.
a. 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:
27.
a. From parity: F0 = S0 (1 + rf – d) = [2,200 (1 + .03)] – 22 = 2,244
Actual F0 is 2,240, so the futures price is $4 below its "proper" or parity value.
b. Buy the relatively cheap futures and sell the relatively expensive stock.
Action
Initial Cash Flow
Cash Flow at Time T
Chapter 17 - Futures Markets and Risk Management
Short stock
+2,200
–(ST + 22)
Buy futures
0
ST – 2,240
Lend $2,200
–2,200
+2,266
Total
0
4
c. If you do not receive the proceeds of the short sales, then the $2,200 cannot be
invested to gain interests at the risk-free rate. Thus, the proceeds from the strategy
in part (b) becomes negative: the arbitrage opportunity no longer exists.
Action
Initial Cash Flow
Cash Flow at Time T
Short stock
+2,200
–(ST + 22)
Buy futures
0
ST – 2,240
Place $2,200 in
margin account
–2,200
+2,200
Total
0
–62
d. If we call the original futures price F0, then the proceeds from the long-futures,
short-stock strategy are:
Action
Initial Cash Flow
Cash Flow at Time T
Short stock
+2,200
–(ST + 22)
Buy futures
0
ST – F0
Place $2,200 in
margin account
–2,200
+2,200
Total
0
2,178 – F0
Therefore, F0 can be as low as 2,178 without giving rise to an arbitrage
opportunity. On the other hand, if F0 is higher than the parity value (2,240) 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: 2,178 F0 2,240
CFA 1
CFA 3
Answer:
Total losses may amount to $3,500 before a margin call is received. Each contract calls
Chapter 17 - Futures Markets and Risk Management
CFA 4
Answer:
a. Take a short position in T-bond futures, to offset interest rate risk. If rates
increase, the loss on the bond will be offset by gains on the futures.
CFA 5
Answer:
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 accept or deliver, respectively, the underlying
CFA 6
Answer:
a. The strategy that would take advantage of the arbitrage opportunity is a Reverse
Cash and Carry. A Reverse Cash and Carry arbitrage opportunity results when
the following relationship does not hold true: F0, t ≥ S0 (1 + C)
b.
Opening Transaction Now
Sell the spot commodity short
+$120.00
Buy the commodity futures expiring in 1 year
0.00
Chapter 17 - Futures Markets and Risk Management
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written
consent of McGraw-Hill Education.
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
another payment that is tied to the level of interest rates. One party in the swap
agreement pays a fixed interest rate on the notional principal of the swap. The other
party pays the floating interest rate (typically LIBOR) on the same notional
b. There are several applications of interest rate swaps. For example, suppose that a
portfolio manager is holding a portfolio of long-term bonds, but is worried that
interest rates might increase, causing a capital loss on the portfolio. This portfolio
manager can enter a swap to pay a fixed rate and receive a floating rate, thereby
CFA 8
Answer:
a. Delsing should sell stock index futures contracts and buy bond futures contracts.
This strategy is justified because buying the bond futures and selling the stock
index futures provides the same exposure as buying the bonds and selling the
stocks. This strategy assumes high correlations between the movements of the
Chapter 17 - Futures Markets and Risk Management
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written
consent of McGraw-Hill Education.
bond futures and bond portfolio and also between the stock index futures and
the stock portfolio.
b. Compute the number of contracts in each case as follows:
i. 5 $200,000,000 0.0001 = $100,000
$100,000/97.85 = 1,022 contracts
ii. $200,000,000/($1,378 250) = 581 contracts
CFA 9
Answer:
a. Short the contract. As rates rise, prices will fall. Selling the futures contract will
benefit from falling prices.
b. In 6 months the bond will accrue $25 of interest, which, when subtracted from
the price of 978.40, leaves a bond value of 953.40. This implies a YTM of
5.30%. Assuming the underlying bond on the contract also has a 5% coupon and
c. The contract drops in price by 47.98, while the bond drops in price 46.60. Both
exclude accrued interest. Thus, the combined portfolio will increase in value by
