Consider an investor with preferences given by the utility function U = E(r) – 0.5Aσ2 and there are two portfolios with the following characteristics:
Portfolio A Portfolio B
E(r) = 0.06 σ = 0.07 E(r) = 0.10 σ = 0.17
(a) Suppose that the investor has a level of risk aversion of A = 4. Which portfolio should the investor choose?
(b) Suppose that the investor has a level of risk aversion of A = 2. Which portfolio should the investor choose? Briefly explain why your answer is different from Part (a).
(c) Suppose the investor has a level of risk aversion of A = 4. What must the return be on a risk-free asset in order for the investor to be indifferent between investing in the risk-free asset and Portfolio B?
(d) Suppose the investor has a level of risk aversion of A = 4. Calculate the risk-premium associated with Portfolio B. Assume that the risk-free rate is the same as your answer in Part(c).