Question

Exercise 2. Suppose that there is one risk free asset with return rf and one risky asset with normally distributed returns, r ~ N(u,02). Show that the CARA utility u(r) = -e-Ar gives the same optimal allocation of wealth to the risky asset as the mean-variance utility function we used in class. That is, show that E[r] – rf OCARA = AO2 Hint: Use the fact that if a random variable x is distributed normally with mean Mx and variance oz, then E[ear] = eqHx+žao? Exercise 3. There exists only two risky assets with returns rı and r2 and a risk free rate rf. You are splitting your wealth only between the two risky assets. Compute the portfolio with the highest Sharpe ratio. (Hint: The algebra is easier if you do this problem in terms of expected excess returns instead of in terms of expected returns). Show your work.

Answer 1

According to HomeworkLib policy only one question per post

3)

There is nothing in question which says which assets has higher sharpey ratio. Let it be 1st. The ratio for 1st is rp-rf/standard deviation. In case if first it us 10-2/5=1.6.In case of 2nd it is 4-2/3=0.67 . note rp is portfolio risk and rf risk free return