5. 16 POINTS A portfolio manager has a portfolio that mirrors the performance of the S&P500. It is worth $600 million. The S&P500 index is 2000. The portfolio manager would like to buy insurance against a reduction in the value of the portfolio of 5% in the next 3 months. The risk-free interest rate, r = : 6% per year. The dividend yield on the portfolio and the S&P500 is q = 4% per year. The volatility of the index, o = 20% per year. (a) Suppose that the fund manager buys European put options. Find the value of a put option and the total cost of the insurance. (6) 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? 5. 16 POINTS A portfolio manager has a portfolio that mirrors the performance of the S&P500. It is worth $600 million. The S&P500 index is 2000. The portfolio manager would like to buy insurance against a reduction in the value of the portfolio of 5% in the next 3 months. The risk-free interest rate, r = : 6% per year. The dividend yield on the portfolio and the S&P500 is q = 4% per year. The volatility of the index, o = 20% per year. (a) Suppose that the fund manager buys European put options. Find the value of a put option and the total cost of the insurance. (6) 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