Forwards and Futures
1. A stock has a current price of $65. A dividend of $3.25 is expected to be paid in 6 months. The
risk-free interest rate is 10% effective per annum. Xis the forward price of a one-year forward contract
that has the stock as the underlying asset. Determine X.
2. Ted expects to purchase a portfolio of stocks in 3 months. In order to hedge against price
movements, the portfolio manager enters into a long position on a 3-month forward contract on the
S&P stock index. The index is currently at 900, the continuously compounded dividend yield is 2%,
and the continuously compounded risk free rate is 4%. What is the payoff on the forward contract if the
index value is 1025 at expiration?
3. Suppose that the current spot price of corn is $3.55 per bushel, and a six-month forward contract on
corn has a forward price of $3.70 per bushel. A farmer decides to hedge the price you will get for his
corn crop six months from now by shorting a 1,000-bushel forward contract on corn today. Suppose
that the spot price of corn at maturity of the forward is $3.80. Based on this information, what is the
profit or loss to his short position at maturity?
4. A one-year forward contract on a stock has a price of $75. The stock is expected to pay a dividend of
$1.50 at two future times, six months from now and one year from now, and the annual effective
risk-free interest rate is 6%.
Calculate the current stock price.
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Forwards and Futures
5. Interest is 4% per year converted continuously. A stock currently sells for $16 a share and pays a
dividend of 8 cents a quarter per share. A dividend has just been paid.
What is the Prepaid Forward Price of 100 shares purchased 6 months from now (just after the
dividend).
6. The spot price for an index is 1000. The continuous interest rate is 5%, and the index pays no
dividends. You observe a 3-month forward price of 1020. What arbitrage profit can be made in 3
months on one contract?
7. The price for one share of stock was $120 on December 21, 2010.
The business decides to pay a dividend of $1.80 every 3 months for the next year (i.e. on March 21,
2011; June 21, 2011; September 21, 2011; and December 21, 2011).
The quarterly effective interest rate is 1.25%.
What is the forward price for one share of stock to be paid immediately after the December 21, 2008
dividend?
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Forwards and Futures
8. A stock paying a continuous dividend at a constant annual rate of d has a current spot price of $90,
and the price of a nine-month prepaid forward contract is $88. The continuously-compounded annual
interest rate is 10%.
Find the annualized forward premium.
9. Suppose a stock index is currently priced at $1,500, and the 12-month forward price on that index is
$1,550. Let the annualized continuous dividend yield on the index be 2%, and let the continuously
compounded annual rate of (risk-free) interest be 8%. What would be the profit or loss at forward
maturity (12 months from now) under a cash-and-carry strategy?
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