Suppose there are two assets available to an investor. One is risk-free and has a return of 1 percent. The other is risky and has an expected return of 0.05 (5%) and a variance of 0.16 (16%). The investor’s utility is given by U(r) = 2/5 E(r) −1/2AVar(r) and his risk aversion coefficient is 1.
A. The investor is trying to decide what fraction of his wealth he will invest in the risky asset. Write down the investor’s maximization problem.
B. Take the first order conditions for the investor’s problem. Find a formula for y∗, the optimal fraction of wealth that the investor will invest in the risky asset.
C. Find the value of y∗ given the characteristics of both assets and the risk-aversion of the investor.