please show how to do this the long way and not with excel

2. Using sample average returns and standard deviations of the two investment strategies provided in class slides (S&P 500 and Volatility Strategy), calculate the certainty equivalent risk-free rate using mean-variance utility. 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, 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 (based on the graph) over the sample period. 2. Using sample average returns and standard deviations of the two investment strategies provided in class slides (S&P 500 and Volatility Strategy), calculate the certainty equivalent risk-free rate using mean-variance utility. 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, 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 (based on the graph) over the sample period