1. Consider an investor faced with the following problem. Holding the wealth level Wo, the investor maximizes the expected utility by finding optimal portfolio weight(a) on the risky asset. max E[U(W1)] s.t. W = W.(a(1 + 2) + (1 - a)(1+r)) (a) Assume that U is differentiable. Derive FOC. (b) Show that the optimizing a should be positive if E[Z] > rf. (c) Let U be a CRRA utility function. Show that the optimizing a is independent of Wo. (d) Let U be a CARA utility function. Show that the optimizing a is decreasing with respect to Wo. (e) Discuss how the optimizing a is linked with the RRA. 1. Consider an investor faced with the following problem. Holding the wealth level Wo, the investor maximizes the expected utility by finding optimal portfolio weight(a) on the risky asset. max E[U(W1)] s.t. W = W.(a(1 + 2) + (1 - a)(1+r)) (a) Assume that U is differentiable. Derive FOC. (b) Show that the optimizing a should be positive if E[Z] > rf. (c) Let U be a CRRA utility function. Show that the optimizing a is independent of Wo. (d) Let U be a CARA utility function. Show that the optimizing a is decreasing with respect to Wo. (e) Discuss how the optimizing a is linked with the RRA