Question

8.3

Quantitative Problem: You are holding a portfolio with the following investments and betas: Stock Dollar investment Beta $300,000 200,000 500,000 1.15 1.70 0.70 -0.15 Total investment $1,000,000 The market's required return is 9% and the risk-free rate is 5%. What is the portfolio's required return? Do not round intermediate calculations. Round your answer to three decimal places.

Answer 1

Beta of portfolio is weighted average of the beta of constituents.

Beta of portfolio = Beta1 * Weight1 + Beta2 * Weight2 + Beta3 * Weight3 + + Beta4 * Weight4

Weight A = 300,000/1,000,000 =30%

Weight B = 200,000/1,000,000 =20%

Weight C = 500,000/1,000,000 =50%

Beta of portfolio = 1.15 * 30% + 1.70 * 20% + 0.70 * 50%

Beta of portfolio = 1.035

Based on CAPM,

Expected return on portfolio = risk free rate + beta * (Expected market return - Risk free rate)

Expected return on portfolio = 5% + 1.035 * (9% - 5%) = 9.140%