Question

Suppose you are the money manager of a $4.58 million investment fund. The fund consists of four stocks with the following investments and betas:

Stock Investment Beta
A $ 260,000 1.5
B 420,000 (0.5)
C 1,100,000 1.25
D 2,800,000 0.75
If the market's required rate of return is 13% and the risk-free rate is 7%, what is the fund's required rate of return?

Answer 1

The required rate of return for the fund is 12.325%.

Step-by-step explanation:

To calculate the required rate of return for the fund, we need to determine the weighted average beta of the stocks. The weighted average beta is calculated by multiplying each stock's beta by its investment amount, and then dividing the sum by the total investment amount.

(1.5 * 260,000 + (-0.5) * 420,000 + 1.25 * 1,100,000 + 0.75 * 2,800,000) / 4,580,000 = 0.8875

The required rate of return for the fund can be calculated using the following formula:

Required Rate of Return = Risk-Free Rate + Beta * (Market Required Rate of Return - Risk-Free Rate)

Using the given values:

Required Rate of Return = 7% + 0.8875 * (13% - 7%) = 7% + 0.8875 * 6% = 7% + 5.325% = 12.325%