Question

# 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 30% for the mutual fund and 22% for the market. What was the fund’s CAPM alpha?

actual return Ra = 15%

Standard deviation SDa = 30%

Expected return on market Rm = 12%

Standard deviation of market SDm = 22%

Correlation of mutual fund with market p = 0.7

=> So, beta of mutual fund is calculates using formula

Beta of mutual fund = p * SDa/SDm = 0.7*30/22 = 0.9545

Risk free rate = 2%

So, using CAPM, expected return on mutual fund E(r) = Rf + Beta*(Rm - Rf)

=> E(r) = 2 + 0.9545*(12 - 2) = 11.54%

CAPM alpha on mutual fund = actual return - expected return = 15 - 11.54 = 3.45%

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