11. A portfolio manager has a portfolio that mirrors the performance of the S&P500. It is...

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11. A portfolio manager has a portfolio that mirrors the performance of the S&P500. It is worth $360 million. The S&P500 index is 1200. The portfolio manager would like to buy insurance against a reduction in the value of the portfolio greater than 0.05 (or 5%) in the next 6 months. The annual risk-free interest rate is r = 0.06 (or 6%). The annual dividend yield on the portfolio and the S&P500 is q = 0.03 (or 3% per year). The annual volatility of the index, = 0.30 (or 30%). a) Suppose that the fund manager buys European put options. (i) Recall that = 1. Find the value of K. (ii) Use the Black Scholes Merton model to find the price of a put option on the index, P. (iii) Remembering that each put option contract is on 100 times the index, find the number of put option contracts to protect the portfolio against a fall of 10% in its value over the next 6 months. (iv) Find the cost of the insurnce. b) What other strategy could be used to protect the value of the portfolio which involves the use of European call options? c) Suppose that the manager decides to insure the value of the portfolio by buying risk-free assets. How much should be invested in risk-free securities? 11. A portfolio manager has a portfolio that mirrors the performance of the S&P500. It is worth $360 million. The S&P500 index is 1200. The portfolio manager would like to buy insurance against a reduction in the value of the portfolio greater than 0.05 (or 5%) in the next 6 months. The annual risk-free interest rate is r = 0.06 (or 6%). The annual dividend yield on the portfolio and the S&P500 is q = 0.03 (or 3% per year). The annual volatility of the index, = 0.30 (or 30%). a) Suppose that the fund manager buys European put options. (i) Recall that = 1. Find the value of K. (ii) Use the Black Scholes Merton model to find the price of a put option on the index, P. (iii) Remembering that each put option contract is on 100 times the index, find the number of put option contracts to protect the portfolio against a fall of 10% in its value over the next 6 months. (iv) Find the cost of the insurnce. b) What other strategy could be used to protect the value of the portfolio which involves the use of European call options? c) Suppose that the manager decides to insure the value of the portfolio by buying risk-free assets. How much should be invested in risk-free securities?