Suppose you are the money manager of a $5.04 million investment fund. The fund consists of four stocks with the following investments and betas: Stock Investment Beta A $ 220,000 1.50 B 600,000 (0.50 ) C 1,420,000 1.25 D 2,800,000 0.75 If the market's required rate of return is 10% and the risk-free rate is 4%, what is the fund's required rate of return

r (P) = 0.086488 or 8.6488% rounded off to 8.65%

Explanation:

To calculate the required rate of return for the fund, we will use the weighted average of the required rate of returns of each of the stock contained in the fund. The formula for the required rate of return of a portfolio will be used which is,

r (P) = wA * rA  +  wB * rB  +  ...  +  wN * rN

Where,

We will first calculate the required rate of return of each stock using the CAPM equation.

r = rRF + Beta * (rM - rRF)

Where,

Required rate or return

A = 0.04 + 1.5 * (0.1 - 0.04)   =  0.13

B = 0.04 - 0.5  * (0.1 - 0.04)   =  0.01

C = 0.04 + 1.25 * (0.1 - 0.04)   =  0.115

D = 0.04 + 0.75 * (0.1 - 0.04)   =  0.085

r (P) = 220000/5040000  *  0.13  +  600000/5040000  *  0.01  +  

1420000/5040000  *  0.115   +  2800000/5040000  *  0.085

r (P) = 0.086488 or 8.6488% rounded off to 8.65%

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