Using sample average returns and standard deviations of the volatility strategy discussed in class: Vol Strategy S&P 500 Mean 9.9% 9.7% Stdev 15.2% 15.1% Skewness -8.3 -0.6 Kurtosis 104.4 4.0 a. calculate the optimal proportion that a mean-variance utility investor would invest in the volatility strategy in the following scenarios: Risk-free rate is 0.50% and gamma = 3. Enter your answer in percentage points with two decimal places. b. calculate the optimal proportion that a mean-variance utility investor would invest in the volatility strategy in the following scenarios: Risk-free rate is 0.50% and gamma = 5. Enter your answer in percentage points with two decimal places. c. calculate the optimal proportion that a mean-variance utility investor would invest in the volatility strategy in the following scenarios: Risk-free rate is 0.75% and gamma = 3. Enter your answer in percentage points with two decimal places d. Compare the answers to the previous three questions. What can be said about the effect of the risk-free rate and the risk-aversion coefficient on the optimal allocation to the volatility strategy