You are trying to help your client, James Bond, construct a portfolio. James has a quadratic utility function. There are three assets in the economy, labeled X, Y, and Z. James’s agent has already suggested three possible combinations of X, Y, and Z for him. One of these risky portfolios will be eventually combined with the risk-free asset.
Portfolio Asset X Asset Y Asset Z E(r) σ
1 0.1723 0.5324 0.2953 0.1166 0.2372
2 0.3372 0.3237 0.3391 0.1135 0.2372
3 0.4567 0.2567 0.2866 0.1078 0.2235
(a) Which portfolio can we eliminate as a candidate for the optimal risky portfolio? Explain.
(b) Now, suppose that the risk-free rate is 0.04. Which portfolio is the optimal (Tangency) risky portfolio? (Assume that one of them (Portfolio 1, 2 or 3) is indeed the optimal risky portfolio.) Explain.
(c) Suppose that after asking James a series of preference questions, you determine that his coefficient of risk aversion is 2. What is the best portfolio for James (weights in each of the four assets)?
(d) James's sister, Julie comes to you, seeking advice on her portfolio. Julie also has a quadratic utility function, but is more risk-averse than James. Explain how the weights in Julie's portfolio would differ from James’s. In particular, discuss how the weights in the risky assets would change relative to each other and relative to the risk-free asset.