Suppose you are the money manager of a $5.21 million investment fund. The fund consists of four stocks with the following investments and betas: Stock Investment Beta A $ 320,000 1.50 B 780,000 (0.50) C 1,260,000 1.25 D 2,850,000 0.75 If the market's required rate of return is 10% and the risk-free rate is 5%, what is the fund's required rate of return

8.65%

Explanation:

First find the weights of the stocks:

Total = 320,000 + 780,000 + 1,260,000 + 2,850,000

= $‭5,210,000‬

Stock A:

= 320,000 / ‭5,210,000‬

= 6.14%

Stock B:

= 780,000 / ‭5,210,000‬

= 14.97%

Stock C:

= 1,260,000 / ‭5,210,000‬

= 24.18%

Stock D:

= 2,850,000 / ‭5,210,000‬

= 54.70%

Then calculate Portfolio Beta.

Portfolio beta = (6.14% * 1.50) + (14.97% * - 0.5) + (24.18% * 1.25) + (54.72% * 0.75)

= 0.7299

Required rate of return using Capital Asset Pricing Model (CAPM)

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

= 5% + 0.7299 * (10% - 5%)

= 8.65%

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