Question

Stock X has an expected return of 15%, standard deviation of 20%, beta of 0.8. Stock Y has an expected return of 20%, a standard deviation of 40% and a beta of 0.3, and a correlation with stock X of 0.6. Assume the CAPM holds. a. If you are a typical, risk-averse investor with a well-diversified portfolio, which stock would you prefer? b. What are the expected return and standard deviation of a portfolio consisting of 30% of stock X and 70% of stock Y? d. What is the beta of the portfolio in (b)?

Answer 1

a.

Lets calculate the Coefficient of variation for both stocks

coefficient of varaiation fo Stock X = standard deviation / expected return = 20/15 = 1.33  

COV for stock Y = 40 /20 = 2

A risk averse investor will choose stock X as it has lesser COV. ie risk per unit of return is lesser for stock X.

b.

Expected return of portfolio = weight of X * return of X + weight of Y * return of Y = 0.3 * 15 +0.7*20 = 18.50%

Standard deviation of portfolio = [ weight of X^2 * standard deviation of X^2 + weight of Y ^2 * standard deviation of Y^2 + 2 * Weight of X* weight of Y * correlation * sd of X * sd of Y ] ^0.50

= [0.3^2*20^2 + 0.7^2*40^2 + 2*0.3*0.7*0.6*20*40 ]^0.50

= 31.96%

C.

Portfolio beta = weight of X * beta of X + weight of Y * beta of Y = 0.3 * 0.8 + 0.7*0.3 = 0.45