22. Static hedging strategies using BSM model A fund manager has a well-diversified portfolio that more or less mirrors the performance of the S&P 500 and is worth $360 million. Actually, the beta of the portfolio with respect to the S&P 500 is 1.1. The S&P 500 quotes 3,400, the multiplier is $250, and the portfolio manager would like to buy insurance against a reduction of more than 5% in the value of the portfolio over the next 6 months. The continuous risk-free interest rate is 2% per annum. The continuous dividend yield on both the portfolio and the S&P 500 is 3%, and the volatility of the index is 16% per annum. 1. If the fund manager buys traded European put options, how much would the insurance cost? 2. Explain carefully an alternative strategy open to the fund manager involving traded European call options and show that it leads to the same result. 3. If the fund manager decides to provide insurance by keeping part of the portfolio in risk- free bonds, what should the initial position be? 4. If the fund manager decides to provide insurance by using 6-month index futures, what should the initial position be? 22. Static hedging strategies using BSM model A fund manager has a well-diversified portfolio that more or less mirrors the performance of the S&P 500 and is worth $360 million. Actually, the beta of the portfolio with respect to the S&P 500 is 1.1. The S&P 500 quotes 3,400, the multiplier is $250, and the portfolio manager would like to buy insurance against a reduction of more than 5% in the value of the portfolio over the next 6 months. The continuous risk-free interest rate is 2% per annum. The continuous dividend yield on both the portfolio and the S&P 500 is 3%, and the volatility of the index is 16% per annum. 1. If the fund manager buys traded European put options, how much would the insurance cost? 2. Explain carefully an alternative strategy open to the fund manager involving traded European call options and show that it leads to the same result. 3. If the fund manager decides to provide insurance by keeping part of the portfolio in risk- free bonds, what should the initial position be? 4. If the fund manager decides to provide insurance by using 6-month index futures, what should the initial position be