Question 1 A representative investor maximizes lifetime utility that depends only on current consumption (Ct) and future consumption (Cti). The expected utility from future consumption is discounted by a discount factor, B. In a two-period model, lifetime utility is given by: U(G,()=U(C)+ BE,[U(C..)] Assume that the investor's endowment is given by (er , er+/). That is, at time / the investor receives an exogenous endowment of resources, denoted as er, which is allocated between consumption and assets; at time t+ 1 the investor receives enI. The number of assets that he will buy is denoted by 2 and the price for each unit of the assets is pr. At time / + / assets pay a dividend dy that can be used, along with a new exogenous endowment of resources (et+1), for consumption purposes in period f + 1. (a) If the investor's choice variable is A, use the above information to write out the investor's maximization problem. (3) (b) Derive the investor's necessary first order condition (FOC) resulting from the above maximization problem. (3) (c) Use the above information and answers in (a) and (b) to show that: (4) 1 = BE, my Pul + d, U'(C ) where my U'(C,) (d) Further derive the following consumption CAPM (CCAPM) equation: (6) E,[U'(C,)] Cov,[U'(C.), 1+5,all (e) 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)Question 2 The following CAPM equation was estimated: r -r, =0, + B[E(r.)-r,]+5, Parameter Coefficient t-Stat P-value R-squared 70.15 3.25 0.002 0.15 Bi 0.50 2.31 0.010 (1) If CAPM correctly describes the data one is using, are the results confirming your expectations concerning CAPM? Explain your answer. (4) Issues around linearity and the use of a single factor have been raised in the literature as weaknesses of the CAPM model. How would you modify the above expression/model if you wanted to test for linearity and the possibility of several factors? (6) (mi) Some investors have argued that they would choose APT over CAPM. What are some of the reasons offered in the literature for this? Please refer to Van Rensburg (1997), and Martikainen and Yli-Olli (1990) for this. (10) (iv) The CAPM is a special case of an APT model. Briefly discuss this statement