The utility function for a risk averse investor is given by: =()122=+[()]1222 Maximizing utility and solving for y, yields the optimal position (allocation), y*, for a risk averse investor who invests in a risky asset: =()2 a) Assume that there are two investors, Investor 1 and Investor 2. Investor 1 has a risk aversion parameter of 2 whereas Investor 2 has a risk aversion parameter of 3.75, such that 2>1 where A is the risk aversion parameter. Assume that the return on a portfolio of risky assets is 12.5% and that this portfolio has a standard deviation of 24%. Estimate the proportion of capital that will be allocated to an investment in the risk-free asset if the risk free asset offers a return of 4.3%.

b) With reference to risk preferences of the two investors above and assuming that preferences for both investors can be represented by upward sloping (convex) indifference curves, show and explain how their choice of the optimal complete portfolio will differ. Make use of the appropriate diagram(s) and be sure to draw and label the appropriate diagram clearly and briefly outline the relevant components.