Using the following sample average returns and standard deviations for the two investment strategies S&P 500 and the Volatility Strategy, calculate the certainty equivalent risk-free rate using mean-variance utility.

Sample Average Returns and Standard Deviations:

	Volatility Strategy	S&P 500
Average Return	9.9%	9.7%
Standard Deviation	15.2%	15.1%

A. Assume the risk aversion coefficient equals 2.

B. Assume the risk aversion coefficient equals 4.

C. If you find that for a given risk aversion level the certainty equivalent risk-free rate of the two strategies is almost the same, explain why this is so given that the two strategies behaved quite differently over the sample period.

*Please provide a mathematical explanation for the answers and not an answer from Excel