Question

.  Problem 8.07

Click here to read the eBook: Risk in a Portfolio Context: The CAPM Problem Walk-Through PORTFOLIO REQUIRED RETURN Suppose you are the money manager of a $3.79 million investment fund. The fund consists of four stocks with the following investments and betas: Stock Investment Beta A $   200,000                                 1.50 B 560,000                                 (0.50) C 1,180,000                                 1.25 D 1,850,000                                 0.75 If the market's required rate of return is 9% and the risk-free rate is 5%, what is the fund's required rate of return? Do not round intermediate calculations. Round your answer to two decimal places. %

Answer 1

First we will calculate the weights of each stock in the portfolio. This is done to calculate the weighted average beta of the portfolio.

Weight of each stock = Stock's value / Total portfolio value

Total portfolio value = $3.79 million or $3790000

Stock A's weight = $200000 / $3790000 = 0.05277

Stock B's weight = $560000 / $3790000 = 0.14775

Stock C's weight = $1180000 / $3790000 = 0.31134

Stock D's weight = $1850000 / $3079000 = 0.488126

In the next step, we will multiply the weights calculated above with the respective betas of stocks as per below:

Stock A = 0.05277 * 1.5 = 0.079155

Stock B = 0.14775 * (-0.5) = - 0.073878

Stock C = 0.31134 * 1.25 = 0.389182

Stock D = 0.488126 * 0.75 = 0.36609

In the next step, we will calculate the portfolio beta by adding the weighted average beta calculated in the above step:

Portfolio beta = 0.079155 + (-0.073878) + 0.389182 + 0.36609

Portfolio beta = 0.76

Now, we will use the CAPM equation to find the expected or required rate of return of the fund. As per CAPM equation,

Required rate of return = Risk free rate + Beta * ( Market rate - Risk free rate)

Given: Risk free rate = 5%, Market rate = 9%, Beta of the portfolio = 0.76

Now, putting these values in the above equation ,we get,

Required rate of return = 5% + 0.76 * (9% - 5%)

Required rate of return = 5% + (0.76 * 4%)

Required rate of return = 5% + 3.04%

Required rate of return = 8.04%