Question

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

Stock	Dollar investment	Beta
A	$300,000	1.35
B	150,000	1.5
C	500,000	0.75
D	50,000	-0.25
Total investment	1,000,000

The market's required return is 10% and the risk-free rate is 5%. What is the portfolio's required return? Round your answer to 3 decimal places. Do not round intermediate calculations.
%

Answer 1

Stock	Dollar investment	Beta	Weight	Weighted Beta
A	300000	1.35	0.3	0.405
B	150000	1.5	0.15	0.225
C	50000	0.75	0.05	0.0375
D	50000	-0.25	0.05	-0.0125
Total investment	1000000	Portfolio Beta	=sum =	0.655

where weight = dollar investment/total investment

weighted beta = beta*weight

As per CAPM

expected return = risk-free rate + beta * (expected return on the market - risk-free rate)

Expected return% = 5 + 0.655 * (10 - 5)

Expected return% = 8.275