Question

Quantitative Problem: You are holding a portfolio with the following investments and betas:

Stock	Dollar investment		Beta
A	$300,000		1.15
B	150,000		1.70
C	500,000		0.85
D	50,000		-0.35
Total investment	$1,000,000

The market's required return is 9% and the risk-free rate is 4%. What is the portfolio's required return? Do not round intermediate calculations. Round your answer to three decimal places.

  %

Answer 1

Based on CAPM,

Expected Return on Security = Risk free rate + Beta * (Expected Market Return - Risk free rate)

Beta of portfolio is weighted average of beta of constituents.

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

Weight1 = 300,000/1,000,000 = 30%

Weight2 = 150,000/1,000,000 = 15%

Weight3 = 500,000/1,000,000 = 50%

Weight4 = 50,000/1,000,000 = 5%

Beta of Portfolio = 30% * 1.15 + 15% * 1.70 + 50% * 0.85 + 5% * -0.35

Beta of portfolio = 1.0075

Based on CAPM,

Expected return on portfolio = 4% + 1.0075 * (9% - 4%)

Expected return on portfolio = 4% + 5.0375%

Expected return on portfolio = 9.0375% = 9.038%