Question 7.14

If an individual's utility takes the constant relative risk aversion form (Equation 7.42), explain why this person will not change the fraction of risky assets held as his or her wealth increases. Example 7.3 we showed that a person with a CARA utility function who faces a Normally distributed risk will have expected utility of the form E[U(W)] = mu_w - (A/2) sigma^2 w, where Mw is the expected value of wealth and sima^2_w is its variance. Use this fact to solve for the optimal portfolio allocation for a person with a CARA utility function who must invest k of his or her wealth in a Normally distributed risky asset whose expected return is mu, and variance in return is sigma^2 (your answer should depend on A). Explain your results intuitively. If an individual's utility takes the constant relative risk aversion form (Equation 7.42), explain why this person will not change the fraction of risky assets held as his or her wealth increases. Example 7.3 we showed that a person with a CARA utility function who faces a Normally distributed risk will have expected utility of the form E[U(W)] = mu_w - (A/2) sigma^2 w, where Mw is the expected value of wealth and sima^2_w is its variance. Use this fact to solve for the optimal portfolio allocation for a person with a CARA utility function who must invest k of his or her wealth in a Normally distributed risky asset whose expected return is mu, and variance in return is sigma^2 (your answer should depend on A). Explain your results intuitively