11. Suppose you are a stock portfolio manager who has already made 25% return with a current value of the portfolio worth $1,000,000,000. Assume that you are concerned about a big drop of the stock market in October because of its high valuation, and you want to hedge half of your portfolio by using the December S&P 500 futures. The following information is available to you: Beta of your portfolio B= 1.2 Value of S&P500 St = 1340 Risk-free rate r= 8% Dividend yield on S&P500 d= 3% a) Should you buy or sell futures? b) If there are 92 days from today (in September) to the December expiration, what should be the fair futures price today? c) How many contracts should you buy or sell? d) If the S&P 500 index drops 30% after 31 days on one Black Monday in October, and if your portfolio drops 1.2 times the drop in the S&P 500 index, what is the value of your entire portfolio with the hedge? And what is the value if you did not hedge? e) Alternatively, you can also sell half of your portfolio today (in September) to achieve the same hedging result as d), then why do you use futures? f) Suppose that one lucky person is going to get a huge amount of inheritance money in December and he/she wants to invest a portion of it to S&P 500 index, should he/she buy or sell futures to hedge the price risk