2. Suppose you want to use S&P 500 index options to hedge your portfolio. Your portfolio has a beta of 2.0 and it is currently worth $500,000. The current value of S&P 500 is 1000. Interest rate is 6% per annum. Both your portfolio and the index have dividend yield of 4% per annum. You want to use index option to avoid the portfolio value falling below $425,000 in the next six months. (a) What strike price would you choose? (b) What is the value of the hedged portfolio if S&P 500 decreases to 800? (20 points)