7) Suppose you are the money manager of a $4.09 million investment fund. The fun

Question

7)

Suppose you are the money manager of a $4.09 million investment fund. The fund consists of four stocks with the following investments and betas:

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? Do not round intermediate calculations. Round your answer to two decimal places.

______%

Stock Investment Beta A $   340,000                                 1.50 B 360,000                                 (0.50) C 1,340,000                                 1.25 D 2,050,000                                 0.75

Explanation / Answer

This question requires application of the CAPM equation:

Required return on stock = Risk free rate + Beta * (Market required rate - Risk free Rate)

But, we first need to calculate beta for the stock portfolio. Beta for a portfolio is weighted average of its constitutents. So betah for portfolio in question:

Total Investment = $4,090,000

Weight of Stock A = 340,000/4090000 = 8.31%

Weight of Stock B = 360,000/4090000 = 8.80%

Weight of Stock C = 1340000/4090000 = 32.76%

Weight of Stock D = 2050000/4090000 = 50.12%

Beta of portfolio = (8.31% * 1.50) + (8.80% * -0.50) + (32.76% * 1.25) + (50.12% * 0.75) = 0.8661

Required return on portfolio = 4% + 0.8661 * (13% - 4%) = 4% + 7.80% = 11.80%

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