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Below are some practice problems covering options and futures.
1.
Suppose there is a financial asset XYZ, which is the underlying asset for a futures contract
with settlement 1 year from now.
You know the following about this financial asset and
futures contract:
in the cash market XYZ is selling for $100; XYZ pays $4 per year (4%
dividend yield); and the current 1 year interest rate at which funds can be loaned or borrowed
is 7%. The futures contract calls for delivery of 100 shares of XYZ.
1)
What is the theoretical futures price?
2)
What action would you take if the futures price were $120?
3)
What action would you take if the futures price were $80?
Solution:
To find the theoretical price recall the “fair value” equation
F = P * {1 + (ry)}
Plug in P =100, r = .07, y = .04 to get F = 100*{1+(.07.04)} = 103
Theoretical futures price = 103
If the futures price is $120, the future is overpriced, thus you would want to sell
futures and buy XYZ. To do this you would borrow at the riskfree rate r and buy
100 shares of XYZ for each futures contract you sell short (futures call for
delivery of 100 shares).
If the futures price is $80, the future is underpriced, thus you would want to buy
futures, sell XYZ and invest the money in the risk free asset. To do this you
would short 100 shares of XYZ and invest this money at the riskfree rate r. For
each 100 shares you sell short, you would buy one futures contract (futures call
for delivery of 100 shares).
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View Full Document2.
The riskfree rate of interest is 7% per annum and the dividend yield on a stock index is 3%
per annum.
The current value of an index is 150.
What is the index futures price for a
contract that expires in one year?
Solution:
F = P * {1 + (ry)}
Plug in P =150, r = .07, y = .03 to get F = 150*{1+(.07.03)} = 156
3.
A company has a $10 million portfolio with a beta of 1.2.
The S&P is currently 1400 and one
futures contract is $250 times the index. The futures contract expires in 6 months
1)
How can the company use futures contracts on the S&P 500 to completely hedge its
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 Fall '08
 CHABOT
 Economics

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