Consider an investor who has initial wealth w to invest, and can choose between a safe and a

risky asset. Specifically, he can put a share s of his initial wealth in the risky asset. The

investor has a strictly increasing and strictly concave utility function over final wealth y. The

safe asset has a return of zero. The risky asset has a random return R, which can take on

values {r, 0,r}, with r > 0. The probabilities of these returns are qp, 1 q, and q(1 p)

respectively, with 1 >= p, q > 0.

(a) Under what conditions on p, q will the investor invest a positive share s in the risky

asset? (5 marks)

(b) If the investor puts a share s of his wealth in the risky asset, write down expressions for

final wealth y for each of the three possible returns on the risky asset. (5 marks)

(c) If utility of final wealth u(y) = ln y, write down an expression for the expected utility of

final wealth, using your answer to (b). (5 marks)

(d) If q = 1, p > 0.5, w = 1, find the optimal value of s for the investor (Hint: it can be an

interior or a corner solution.) (5 marks)

(e) How does your answer to (d) change if 0 < q < 1? Explain. (5 marks)