3. Suppose the average return of the S&P 500 over the last 50 years has been 7.8% with a standard deviation of 20% per year. Also assume the risk free rate is 3.5%. a. Find the optimal weight of the risky asset in a complete portfolio for an individual with a risk aversion coefficient of 2.5. Additionally, calculate the return, standard deviation and utility for the following portfolios. Weight Index = 1 Weight Index .75 Weight Index =.35 Weight Index = 0 F8 4 1 2 Ret Sp 500 3 Risk Premium 4 Rf 5 6 7 Y Star 8 9 10 W_index 11 12 13 14 A 1 0.75 0.35 0 B X fx 7.80% W_rf 3.50% var C Std.dev D 20% Return 8% 5.850% E A F Std.Dev Utility 20% 15% G 2 H