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A fund manager has a well-diversified portfolio that mirrors the performance of the S&P 500 and is worth $360 million. The value of the S&P 500 is 1,200, 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 six months. The risk-free interest rate is 6% per annum. The dividend yield on both the portfolio and the S&P 500 is 3%, and the volatility of the index is 30% per annum.
Problem 1) If the fund manager buys traded European put options to insure its existing position, how much would the insurance cost?
Problem 2) What is the delta of one put option? If the fund manager decides to provide insurance by keeping part of the portfolio in risk-free securities, how much of the portfolio needs to be invested in risk-free securities?
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