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SOLUTIONS TO CONCEPT CHECKS
1. According to interest rate parity, F
0
should be $1.981. Because the futures price is too high, we
should reverse the arbitrage strategy just considered.
CF Now ($)
CF in 1 Year
1.
Borrow $2.00 in the U.S. Convert to 1 U.K. pound.
1
2.00
2
2.00(1.04)
2.
Lend the 1 pound in the U.K.
2
2.00
1.05E
1
3.
Enter a contract to sell 1.05 pounds at a futures
price of $2.01/£.
0
(£1.05)($2.01/£ 2 E
1
)
TOTAL
0
$.0305
2. Because the firm does poorly when the dollar depreciates, it hedges with a futures contract that
will provide profits in that scenario. It needs to enter a long position in pound futures, which
means that it will earn profits on the contract when the futures price increases, that is, when more
dollars are required to purchase one pound. The specific hedge ratio is determined by noting that
if the number of dollars required to buy one pound rises by $.05, profits decrease by $200,000 at
the same time that the profit on a long future contract would increase by $.05 3 62,500 5 $3,125.
The hedge ratio is
$200,000 per $.05 depreciation in the dollar
$3,125 per contract per $.05 depreciation
5 64 contracts long
3. Each $1 increase in the price of corn reduces profits by $1 million. Therefore, the firm needs to
enter futures contracts to purchase 1 million bushels at a price stipulated today. The futures posi-
tion will profit by $1 million for each increase of $1 in the price of corn. The profit on the contract
will offset the lost profits on operations.
4.
In General
(per unit of index)
Our Numbers
Hold 100,000 units of indexed stock portfolio with
S
0
5 1,400.
S
T
100,000 S
T
Sell 400 contracts.
F
0
2 S
T
400 3 $250 3 (1,414 2 S
T
)
TOTAL
F
0
$141,400,000
The net cash flow is riskless, and provides a 1% monthly rate of return, equal to the risk-free rate.
5. The price value of a basis point is still $9,000, as a 1-basis-point change in the interest rate
reduces the value of the $20 million portfolio by .01% 3 4.5 5 .045%. Therefore, the number
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834
P A R T V I
Options, Futures, and Other Derivatives
of futures needed to hedge the interest rate risk is the same as for a portfolio half the size with
double the modified duration.
6.
LIBOR
7%
8%
9%
As debt payer (LIBOR 3 $10 million)
2
700,000
2
800,000
2
900,000
As fixed payer receives $10 million 3 (LIBOR 2 .08)
2
100,000
0
1
100,000
Net cash flow
2
800,000
2
800,000
2
800,000
Regardless of the LIBOR rate, the firm’s net cash outflow equals .08 3 principal, just as if it had
issued a fixed-rate bond with a coupon of 8%.
7. The manager would like to hold on to the money market securities because of their attractive rela-
tive pricing compared to other short-term assets. However, there is an expectation that rates will
fall. The manager can hold this particular portfolio of short-term assets and still benefit from the
drop in interest rates by entering a swap to pay a short-term interest rate and receive a fixed inter-
est rate. The resulting synthetic fixed-rate portfolio will increase in value if rates do fall.
8. Stocks offer a total return (capital gain plus dividends) large enough to compensate investors for
the time value of the money tied up in the stock. Agricultural prices do not necessarily increase
over time. In fact, across a harvest, crop prices will fall. The returns necessary to make storage
economically attractive are lacking.
9. If systematic risk were higher, the appropriate discount rate, k, would increase. Referring to
Equation 23.4, we conclude that F
0
would fall. Intuitively, the claim to 1 pound of orange juice
is worth less today if its expected price is unchanged, while the risk associated with the value of
that claim increases. Therefore, the amount investors are willing to pay today for future delivery
is lower.
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