2. (25 points) You manage a portfolio of stocks worth $10M. The beta of your portfolio is 0.8. You fear a market decline over the next three months. You would like to use S\&P 500 index options to protect against the value of your portfolio falling below $9.5N. To simplify the computation, assume that the dividend yield of both your portfolio and the S\&P 500 portfolio is 0%. Suppose that the S\&P 500 index is currently at 4604 . The following is the current information on S\&P 500 index options with three month expiration traded on the exchange. B=0.8 (a) Which option should you buy? You need to specify the type of option (call or put) and the strike price. (b) How many "index shares" of this option should you buy? (c) What is the cost of your portfolio insurance? (d) Suppose the S\&P 500 falls by 5% over the next three months. How much money are you expected to lose on your portfolio of stocks? How much money will you gain on your options position? Is your insurance wasted? Explain