Suppose a hedge fund follows the following strategy. Each month it holds $100 million of an S&P 500 index fund and writes out-of-the-money put options on $100 million of the index with exercise price 5% lower than the current value of the index. Suppose the premium it receives for writing each put is $.25 million, roughly in line with the actual value of the puts.
a. Calculate the Sharpe ratio the fund would have realized in the period October 1982– September 1987. Compare its Sharpe ratio to that of the S&P 500. Use the data from the previous problem, available at the Online Learning Center, and assume the monthly risk-free interest rate over this period was .7%.
b. Now calculate the Sharpe ratio the fund would have realized if we extend the sample period by 1 month to include October 1987. What do you conclude about performance evaluation and tail risk for funds pursuing option-like strategies?