This is incorrect… wouldnt you need the correllation to determine the standard deviations of the portfolios and then plug that into the Utility function? The following information is available regarding corner portfolios from an efficient frontier Corner Portfolio Expected Return Exp. Std. Dev. Sharpe Ratio Asset Class Weights 1 2 3 4 5 1 14.00% 18.00% 0.639 0.00% 0.00% 100.00% 0.00% 0.00% 2 13.66% 16.03% 0.696 0.00% 0.00% 86.36% 0% 14.00% 3 13.02% 13.58% 0.775 21.69% 0.00% 56.56% 0.00% 21.76% 4 12.79% 13.00% 0.792 21.48% 0.00% 52.01% 5.24% 21.27% 5 10.54% 8.14% 0.988 9.40% 51.30% 26.55% 0.00% 12.76% 6 8.70% 6.32% 0.981 0.00% 89.65% 4.67% 0.00% 5.68% The following portfolios are under consideration by an investor: Portfolio Expected Return A 11.0% B 13.5% For an investor with a risk-aversion of 6, which portfolio would have the highest utility? A) Portfolio A with a utility of 0.092. B) Portfolio A with a utility of 0.085. C) Portfolio B with a utility of 0.115. Your answer: B was correct! For portfolios A and B we first need the approximate standard deviation. Portfolio A with an expected return of 11% lies between corner portfolios 4 and 5. Let w denote the weight of corner portfolio 5, we solve for w in the following equation: 11 = (10.54)(w) + (12.79)(1-w) w = 0.80 Approximate standard deviation of portfolio A = (0.80)(8.14)+(0.20)(13) = 9.11. Similarly, Portfolio B with an expected return of 13.50% lies between corner portfolios 2 and 3. Let w denote the weight of corner portfolio 2, we solve for w in the following equation: 13.50 = (13.66)(w) + (13.02)(1-w) w = 0.75 Approximate standard deviation of portfolio B = (0.75)(16.03)+(0.25)(13.58) = 15.418. RZ =6 UA = E(RA) – 0.5(RZ)(σ2A) = 0.11 – 0.5(6)(0.0911)2 = 0.085 UB = E(RB) – 0.5(RZ)(σ2B) = 0.135 – 0.5(6)(0.154)2 = 0.064