PORTFOLIO REQUIRED RETURN Suppose you are the money manager of a $5.05 million i

Question

PORTFOLIO REQUIRED RETURN

Suppose you are the money manager of a $5.05 million investment fund. The fund consists of four stocks with the following investments and betas:

If the market's required rate of return is 9% and the risk-free rate is 6%, 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 $   420,000                                 1.50 B 680,000                                 (0.50) C 1,300,000                                 1.25 D 2,650,000                                 0.75

Explanation / Answer

By CAPM Equation,

Expected return on a portfolio/stock = Risk free rate + Beta * (Expected Market Return - Risk free rate)

We first need to calculate Beta of the portfolio. Beta of the portfolio is weighted average of beta of individual constituents.

Hence, Weight of A, Wa = 420,000/5,050,000 = 8.32%

Wb = 680,000/5,050,000 = 13.47%

Wc = 1,300,000/5,050,000 = 25.74%

Wd = 2,650,000/5,050,000 = 52.48%

Portfolio Beta = (8.32% * 1.50) + (13.47% * -0.5) + (25.74% * 1.25) + (52.48% * 0.75) = 0.7728

Now, by applying CAPM equation,

Required rate of return on fund = 6% + 0.7728 * (9% - 6%) = 8.32% --> Answer

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