Question

Suppose you are the money manager of a $4.08 million investment fund. The fund consists of four stocks with the following investments and betas: Stock Investment Beta A $ 320,000 1.50 B 540,000 (0.50) C 1,420,000 1.25 D 1,800,000 0.75 If the market's required rate of return is 13% and the risk-free rate is 4%, what is the fund's required rate of return

Answer 1

r fund = 0.11356617647 or 11.356617647% rounded off to 11.36

Step-by-step explanation:

The required rate of return on the fund can be calculated using the CAPM equation. The equation is as follows,

r fund = rRF + beta * (rM - rRF)

Where,

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

To calculate the required rate of return of the fund, we first need to calculate the fund beta. The beta on fund can be calculated using the formula for portfolio beta which is,

Portfolio Beta = wA * Beta of A + wB * Beta of B + ... + wN * Beta of N

Where,

• w represents the weight of each stock in the portfolio

Portfolio or fund beta = 320000/4080000 * 1.5 + 540000/4080000 * -0.5 + 1420000/4080000 * 1.25 + 1800000/4080000 * 0.75

Portfolio or fund beta = 0.81740196078 rounded off to 0.82

The required rate of return on fund will be,

r fund = 4% + 0.81740196078 * (13% - 4%)

r fund = 0.11356617647 or 11.356617647% rounded off to 11.36