Question

Question 15

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?

		a) -2.9%
		b) -1.3%
		c) 0.3%
		d) 1.9%
		e) 3.5%

Answer 1

Given about mutual fund,

actual return Ra = 15%

Standard deviation SDa = 45%

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*45/22 = 1.4318

Risk free rate = 2%

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

=> E(r) = 2 + 1.4318*(12 - 2) = 16.3%

CAPM alpha on mutual fund = actual return - expected return = 15 - 16.3= -1.3%

Option b is correct.