Question

Quantitative Problem:

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

Stock	Dollar investment			Beta
A		$300,000		1.20
B		150,000		1.50
C		400,000		0.75
D		150,000		-0.30
Total investment		$1,000,000

The market's required return is 10% and the risk-free rate is 3%.

What is the portfolio's required return?

Answer 1

Market Required Return (Rm) = 10%

Risk free Return (Rf) = 3%

Computing Expected return using CAPM Approach

Expected Retuen (R) = Rf + β (Rm - Rf)

Computation of Portfolio Beta(β):

Stock	Dollar Investment	Beta
(i)	(ii)	(iii)	(ii)*(iii)
A	300,000	1.2	360,000
B	150,000	1.5	225,000
C	400,000	0.75	300,000
D	150,000	-0.3	(45,000)
	1,000,000		840,000

Portfolio Beta = 840,000/ 1,000,000

Portfolio Beta = 0.84

Expected Return (R) = 3% + 0.84 (10% - 3%)

Expected Return (R) = 0.03 + 0.0588

Expected Return (R) = 8.88%