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A mutual fund has earned an annual average return of 15% over the last 5 years....

A mutual fund has earned an annual average return of 15% over the last 5 years. During that time, the average risk-free rate was 2% and the average market return was 12% per year. The correlation coefficient between the mutual fund’s and market’s returns was 0.7. The standard deviation of returns was 45% for the mutual fund and 22% for the market. What was the fund’s CAPM alpha?

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Answer #1

CAPM Alpha = Annual Average Return - Required Return as per CAPM

CAPM Alpha = 15% - 16.30% = -1.30%

As per CAPM, Required return on equity = Risk free Rate + Beta x Market Risk Premium

Required return on equity = Risk free Rate + Beta x (Market Return - Risk free Rate)

Required return on equity = 2% + Beta x (12% -2%)

Required return on equity = 2% +1.43 x (12% -2%) =16.30%

Calculation of Beta of fund = Covariance between fund and market / variance of market

Beta of fund = 693 / (22 x 22 ) = 1.43

covariance = correlation between fund and market x standard deviation of fund x standard deviation of market

covariance = 0.7 x 45 x 22 = 693

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