Question

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

Stock Dollar investment Beta

A $250,000 1.25

B 100,000 1.60

C 300,000 0.80

D 350,000 -0.20

Total investment $1,000,000

The market's required return is 11% 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

Weight of stock A= $250,000 / $1,000,000

= 0.25

Weight of stock B= $100,000 / $1,000,000

= 0.10

Weight of stock C= $300,000 / $1,000,000

= 0.30

Weight of stock D= $350,000 / $1,000,000

= 0.35

Portfolio beta = 0.25*1.25 + 0.10*1.60 + 0.30*0.80 + 0.35*-0.20

= 0.3125 + 1.16 + 0.24 - 0.07

= 1.6425

The required return of the portfolio is calculated using the Capital Asset Pricing Model (CAPM)

The formula is given below:

Ke= Rf+b[E(Rm)-Rf]

where:

Rf= risk-free rate of return

Rm= expected rate of return on the market.

Rm-Rf= Market risk premium

b= Stock’s beta

Ke= 4% + 1.6425*(11% - 4%)

= 4% + 11.4975%

= 15.4975% 15.50%.