9. A portfolio manager has an equity portfolio that is valued at $75 million. The portfolio has a current beta of .9 and a dividend yield of 1%. It is currently August 15 and the manager is concerned that markets are volatile and the portfolio could lose value, so they decide to hedge.

a. The manager will use the S&P 500 index contracts to hedge. The contract is settled in cash at $250 times the contract price. The current S&P index value is 1484.43 and a December S&P 500 index contract has a price of 1517.20

b. Based on these expectations, should they take a short or long futures position and why?

c. An optimal number of contracts is N* = (Dollar value of the portfolio/dollar value of one futures contract) X portfolio beta.

d. Based on (c) above, compute N* and set up the appropriate hedge.

e. On December 15 the position will be closed. The current S&P 500 index is 1410.20 and the current contract matures, so convergence takes place. Compute the percentage loss in the S&P index and the percentage loss in the portfolio, which will be (% loss in market X portfolio beta).

f. Compute the dollar loss on the portfolio, the dollar change in the futures position, and any dividends earned on the portfolio (3 months). Add these up to get the total hedged portfolio value.

g. How good was the hedge? Answer this by comparing the change in the market value of the portfolio to the change in the futures position.