Please prove it step by step. I am pretty confused. =-=

2. (2 points). Consumption CAPM. Assume utility is of the quadratic form U(C) = ac - C2 and a representative investor chooses a portfolio to solve the two-period utility maximization problem N max U(Co) + >SMU(CD) N s.t. Co+ Laici = Wo where the terms are defined as in class lecture 9. Assume all C's are low enough that marginal utility is positive. Let g = (C1-Co)/Co, the growth in consumption. Let i be the return to a portfolio that is uncorrelated with g. Show that, in equilibrium, the expected return to any portfolio, "*, equals the sum of the expected return of f plus the beta from a regression of the portfolio return on consumption growth times some constant Z: E[ ] = E[+9] + BEZ Where COV(*,g) BE = var(9) Useful facts: For any constants d. f, and h and random variables v and w cov(do, w) = dcov(v, w) and cov(v + f, w th) = cov(v, w)