Question

uppose you are the money manager of a $4.68 million investment fund. The fund consists of four stocks with the following investments and betas:

Stock Investment Beta

A $ 260,000 1.50

B 720,000 (0.50)

C 1,300,000 1.25

D 2,400,000 0.75

If the market's required rate of return is 12% and the risk-free rate is 6%, what is the fund's required rate of return? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

The question is solved by first computing the portfolio beta.

Weight of stock A = $260,000 / $4,680,000

= 0.0556

Weight of stock B = $720,000 / $4,680,000

= 0.1538

Weight of stock C = $1,300,000 / $4,680,000

= 0.2778

Weight of stock D = $2,400,000 / $4,680,000

= 0.5128

Portfolio beta = 0.0556*1.50 + 0.1538*-0.50 + 0.2778*1.25 + 0.5128*0.75

= 0.0834 - 0.0769 + 0.3473 + 0.3846

= 0.7384

The required return on the stock 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.

b= Stock’s beta

Ke= 6% + 0.7384*(2% - 6%)

= 6% + 4.4304%

= 10.4304%.

Therefore, the required return of the fund is 10.43%.