Question

1. a. An individual plans to invest in Stock A and/or Stock B. The expected returns are 9% and 10% for Stocks A and B, respectively. The betas are 0.95 and 1.25 for Stocks A and B, respectively. Find the expected return and beta for the portfolio if the individual invests 75% of his funds in Stock A. (E(R_p) = 9.25%, β_p = 1.025)

b. Suppose the individual described in Part a, forms a portfolio consisting of three assets: 10% invested in Stock A, 30% invested in Stock B, and 60% invested in a risk-free asset with a return of 6%. What is the expected return and beta for this portfolio?

Answer 1

Expected return and expected beta of a portfolio is the weighted average of expected returns and betas of the stocks of the portfolio

a)

So, Expected Return

= Expected return of stock A x Weight of stock A + Expected Return of stock B x Weight of stock B

Since the portfolio consists of only these two stocks, weight of stock B = 1 – Weight of stock A

= 1 – 0.75 = 0.25

= 9% x 0.75 + 10% x (1 – 0.75)

= 9% x 0.75 + 10% x 0.25

= 9.25%

Similarly, Expected Beta

= 0.95 x 0.75 + 1.25 x 0.25

= 1.025

b)

Beta of a risk free asset is 0

So, Expected Return

= 9% x 0.10 + 10% x 0.30 + 6% x 0.60

= 7.5%

Beta of the portfolio

= 0.95 x 0.10 + 1.25 x 0.30 + 0 x 0.60

= 0.47