Page < 2 > of 4 ZOOM + A representative investor maximizes lifetime utility that depends only on current consumption (C) and future consumption (C1). The expected utility from future consumption is discounted by a discount factor, . In a two-period model, lifetime utility is given by: U(C,,C,)=U(C.)+ E,[U(C,.])] Assume that the investor's endowment is given by (et, et+1). That is, at time t the investor receives an exogenous endowment of resources, denoted as et, which is allocated between consumption and assets; at time t+1 the investor receives et+1. The number of assets that he will buy is denoted by and the price for each unit of the assets is pt. At time t + 1 assets pay a dividend d++1 that can be used, along with a new exogenous endowment of resources (e++1), for consumption purposes in period t + 1. (a) If the investor's choice variable is , use the above information to write out the investor's maximization problem. (3) (c) Use the above information and answers in (a) and (b) to show that: (b) Derive the investor's necessary first order condition (FOC) resulting from the above maximization problem. (3) 1=BE m+1 P:+1+d++1 P: U(C) where m+1 U'(C.) (d) Further derive the following consumption CAPM (CCAPM) equation: (6) E(P)- 1 Cov,[U'(C1), 1+rj, t-1] E,[U'(C++1)] (e) Provide an intuitive meaning of the above equation. (4) (c) Use the above information and answers in (a) and (b) to show that: Page < 1= BE m P:+1+d++1 P: U'(C) where m+1 = U'(C) (d) Further derive the following consumption CAPM (CCAPM) equation: (6) E()-=- 1 EU(C)] Cov[U'(C1), 1+r;, -1] 2 of 4 ZOOM + (4) Provide an intuitive meaning of the above equation. (4) (f) If asset A is highly correlated with consumption then it is less risky than asset B which is negatively related to consumption. Is this statement true? Explain your answer? (5) 2