Question

Stock A has an annual expected return of 8%, a beta of .9, and a firm-specific volatility of 50% Stock B has an annual expected return of 9%, a beta of 1.3, and a firm-specific volatility of 40% The market has a standard deviation of 20%, and the risk-free rate is is 2%. Suppose we construct a portfolio built out of 50% stock A, 30% stock B, and 20% government t-bills.

What is the expected return of this portfolio? (in %, round to 1 decimal place) [b]

What is the beta of this portfolio? (round to 2 decimal places)

Answer 1

Stock A

Expected return on stock A = R_A = 8%

Beta of stock A = β_A = 0.9

Weight of stock A in the portfolio = w_A = 50%

Stock B

Expected return on stock B = R_B = 9%

Beta of stock B = β_B = 1.3

Weight of stock B in the portfolio = w_B = 30%

T-Bill

T-Bills are risk-free asset

Return on T-Bills = Risk free rate = R_T = 2%

Beta of T-bills = β_T = 0 [T-bills are risk-free]

Weight of T-bills in the portfolio = w_T = 20%

Portfolio

Expected return on the portfolio is calculated using the formula:

E[R_P] =w_A*R_A + w_B*R_B + w_T*R_T

Expected return on portfolio = E[R_P] = (50%*8%) + (30%*9%) + (20%*2%) = 7.1%

Beta of the portfolio is calculated using the formula:

β_P = w_A*β_A + w_A*β_B + w_T*β_T = (50%*0.9) + (30%*1.3) + (20%*0) = 0.84

Answers

a. Expected return on the portfolio = 7.1%

b. Beta of the portfolio = 0.84