It is June and a fund manager has a portfolio worth $20 million with a beta of 1.4. The manager is concerned about the performance of his stocks in August (2 months from now) and plans to use September futures contracts on the S&P 500 to hedge the risk. (He can’t use a August futures because S&P500 futures expire in March, June, September and December.) The current index level is 2,000 and one futures contract is on 250 times the index (i.e., the index multiplier is 250). The risk-free rate is 2.0% per annum and assume 0% dividend yield for simplicity. The current three-month futures price is $2,100.

To answer the following questions, you can recycle the Excel file in class demonstration. If you understand the demonstration, you will find the correct answer very fast. Do not submit the solution from last year as values given differ. If get caught, you will get 0 points for the entire homework.

a. What position should the fund manager take now to hedge exposure to the market over the next two months? In other words, how many September futures contracts does the manager have to buy or short? Specify whether it’s a long (=buy) or short (=sell) position.

b. Calculate the effect of your strategy on the fund manager’s returns if the index in two months is 1900, 2000, 2100, 2200 and 2300. Assume in 2 months (=in August), the September futures price will be 0.25% higher than the index level. For example, if the index becomes 2000 in August, the September futures price will be 1.0025*2000 = 2005.00.

c. Calculate the standard deviation of stock portfolio values and that of total portfolio (stock + futures) values. Compare these two standard deviations. How much risk is reduced by futures hedging?

d. In August, are the total values (hedged values = stock portfolio plus futures position) always greater than the stock (=unhedged) values, regardless of the index value? If not, does it mean the hedge was unsuccessful? Explain.