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

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,

w is the weight of each stock in the portfolio as a percentage of total investment in the portfolio
r is the required rate of return of each stock

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

r = rRF + Beta * (rM - rRF)

Where,

rRF is the risk free rate
rM is the required rate of return on market

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%