Question

Suppose you are the money manager of a $4.94 million investment fund. The fund consists of four stocks with the following investments and betas: Stock Investment Beta A $ 240,000 1.50 B 380,000 (0.50) C 1,420,000 1.25 D 2,900,000 0.75 If the market's required rate of return is 12% and the risk-free rate is 4%, what is the fund's required rate of return? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

The fund's required rate of return calculation would involve determining the fund's overall weighted average beta. This when used with the market's required return rate and the risk-free rate in a CAPM model will give the fund's required rate of return.

Stock	Investment Value	Beta
A	$ 240000	1.5
B	$ 380000	0.5
C	$ 1420000	1.25
D	$ 2900000	0.75

Total Fund Value = V = 240000 + 380000 + 1420000 + 2900000 = $ 4940000

Weighted Average Fund Beta = B(f) = (240000 / 4940000) x 1.5 + (380000/4940000) x (-0.5) + (1420000/4940000) x 1.25 + (2900000/4940000) x 0.75 = 0.83 approximately.

Market Rate of Return = 12 % and Risk-Free Rate = 4 %

Using CAPM, the fund's required rate of return = 4 + B(f) x [12 - 4] = 4 + 0.83 x (12 - 4) = 10.64 %