Question

1.3 (5 points) Two stocks have the following expected returns and standard deviations Stock Stock Expected return Standard Deviation A 10% 12% B 15% 20% Consider a portfolio of A and B, and let w, and wg denote the portfolio weights of these two assets, with W + W, =1. Suppose that the correlation between the expected returns on A and B is equal to 0.3. Use these data to construct the portfolio of A and B with the lowest possible variance of the portfolio return. What is the expected return of this portfolio? 1.4 (5 points) Consider the problem of portfolio choice with one risky asset (A) and one riskless asset (RF). Let r4 and 0 A denote the expected return and the standard deviation of A and let rre denote the risk free rate of return. (a) Consider a portfolio which combines A and RF, with w, denoting the weight if A in this portfolio. Find the expressions for the portfolio's expected return and standard deviation. (b) Suppose an investor has a mean-variance utility function given by U(rp,0%) = r- o , where reis the portfolio's expected return, Op is the standard deviation of the portfolio return and y is a positive constant. Find the optimal portfolio consisting of A and RF which maximizes investor's utility. Illustrate your answer on a graph and explain how the composition of this portfolio changes as the investor becomes more risk averse.

Answer 1

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