Suppose the S&P 500 currently has a level of $1,000. You wish to hedge a

$5,000.000 portfolio that has a beta of 1.5 with the S&P 500. In order to hedge the

portfolio, a 4-month futures contract is used over the next 3 months. The current

price of the future contract is $1,010. The index also pays a dividend yield of 1%

per annum, while the continuously compounded return on a 1-year T-bill is 4%.

(a) How many S&P 500 futures contracts should you short to hedge your

portfolio? Assume each futures contract is for delivery of $250 times the

index.

(b) Suppose now that in 3 months the value of S&P 500 index drops to $900,

while the futures contracts price drops to $902.

(i) What is the gain from shorting the futures contracts?

(ii) What is the expected value of the portfolio at the end of the

3 months?

(iii) What is the expected value of your overall position including the

gain from the hedge? Briefly, discuss the actual return generated

from the overall hedged position.