CONSUMPTION CAPM CCAPM equation - 7 consuption . www.savvyuni.com 12 www.savvypro.ca 18052072503 SAVVYUNI rise premi ER - R/= P.UC)A E RK = stock k # P Tag expected gross retum U'(c) = marginal utility of consumption aft s) - Tire O . u'(co) = marginal utility of consumption BC= 0. Ps = state S ASI143 (state SAJ stock k pg price CHE A.*) 6 = investor's discount factor qx = stock price of k at time 0 Expected risk premi- $ marginal utility of consuuptonzing waynal2. Consider the CCAPM. Let r be the interest rate at which an investor borrows. Assume the investor chooses (co, (1, . . ., 0x ) such that S K Co + 1+r EA;OK = y k=1 where y is initial wealth. (10) a. Suppose there are only two states at time one and two assets. Use the usual discounted two period expected utility of the CCAPM but suppose instantaneous utility is u(c) = c" where o > 0 is a parameter. Using the first order conditions for optimization find an equation for the optimal 61 in terms of the optimal 02. (10) b. Now consider the CCAPM with a general utility function u. Ex- plain the effect on the risk premium for an arbitrary asset k if the subjective discount rate 8 rises. Recall u'(c) is marginal utility of consumption. It satisfies u'(c) > 0 for all c and if c rises u'(c) falls