Suppose a portfolio has assets that are worth $60 million, and the S&P 500 index is at 1200. Assume that the beta of the portfolio is 2.0, and there is no alpha. The expense ratio of the portfolio is 3% per year. The dividend yield of the index is also 3% per year. The risk-free interest rate is 5% per year. (The expense ratio, dividend yield, and interest rate are simple rate in yearly compounding.)
(a) How many contracts of put options should be purchased to hedge the risk that the value of the portfolio falls below a floor value in one year?