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 1,988.60 $250 .10 = $49,715.00
b. Total Return = (2,000 – 1,988.60) $250 = $2,850
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
Short futures
0
8.
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
11.
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
1800
Chapter 17 – Futures Markets and Risk Management
Income yield (%)
2
Interest rate (%)
1
Today’s date
1/1/2015
Spot price
1,800.00
Maturity date 1
Futures 1
1,797.94
Maturity date 2
Futures 2
1,792.98
Maturity date 3
Futures 3
1,784.14
Time to maturity 1
Time to maturity 2
Time to maturity 3
b. If the risk-free rate is higher than the dividend yield, the future price with longer
maturity will be higher than those with shorter maturities.
Spot price
1800
Income yield (%)
2
Interest rate (%)
3
Today’s date
1/1/2015
Spot price
1,800.00
Maturity date 1
Futures 1
1,802.04
Maturity date 2
Futures 2
1,806.98
Maturity date 3
Futures 3
1,815.84
Time to maturity 1
Time to maturity 2
Time to maturity 3
13.
a. F0 = S0 (1 + rf) = $120 1.06 = $127.20
14. a. The initial futures price is:
F0 = S0 (1 + rf – d) = 2000 (1 + .005 – .002)12 = 2,073.20
In one month, the futures price will be:
b. The holding period return is: $1,033.50/$10,000 = .1033 = 10.33%
Chapter 17 – Futures Markets and Risk Management
15. The parity value of F0 is: S0 (1 + rf – d) = 1,800 (1 + .03 – .02) = 1,818
The actual futures price is 1,833, overpriced by 15.
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: $250 1,800 = $450,000
b. If the futures price decreases by 1% to 1,782, then the decline in the futures price
is 18. The decrease in the margin account would be: 18 $250 = $4,500
20.
a. The initial futures price is: F0 = 1,000 (1 + .002 – .001)12 = 1,012.07
Chapter 17 – Futures Markets and Risk Management
this purchase, T-bond futures contracts can be purchased.
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 $250 times the index, currently valued at 1,800. Therefore,
each contract has the same exposure to the market as $450,000 worth of stock,
and to hedge a $9 million portfolio, you need:
$9 million/$450,000 = 20 contracts
b. The parity value of the futures price = 1,800 (1 + .02 – .01)2 = 1,836.18
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
27.
a. From parity: F0 = S0 (1 + rf – d) = [1,800 (1 + .03)] – 25 = 1,829
b. Buy the relatively cheap futures and sell the relatively expensive stock.
Action
Initial Cash Flow
Cash Flow at Time T
Short stock
+1,800
–(ST + 25)
c. If you do not receive the proceeds of the short sales, then the $1,800 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
+1,800
–(ST + 25)
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
Chapter 17 – Futures Markets and Risk Management
Short stock
+1,800
–(ST + 25)
Therefore, F0 can be as low as 1,775 without giving rise to an arbitrage
CFA 1
Answer:
CFA 2
Answer:
CFA 3
Answer:
Total losses may amount to $3,500 before a margin call is received. Each contract calls
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:
Chapter 17 – Futures Markets and Risk Management
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
Contract to lend $120 at 8% for 1 year
Total cash flow
Closing Transaction One Year from Now
Accept delivery on expiring futures
Cover short commodity position
0.00
Collect on loan of $120
+$129.60
Total arbitrage profit
CFA 7
Answer:
Chapter 17 – Futures Markets and Risk Management
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
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
b. Compute the number of contracts in each case as follows:
i. 5 $200,000,000 0.0001 = $100,000
CFA 9
Answer:
a. Short the contract. As rates rise, prices will fall. Selling the futures contract will
benefit from falling prices.
Chapter 17 – Futures Markets and Risk Management
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
c. The contract drops in price by 47.98, while the bond drops in price 46.60. Both