Question

A mutual fund has earned annual returns of 11%, -5% and 21% over the past three years. If the average risk-free rate during that time was 2% per year, what was this fund's Sharpe Ratio during that time period?

		a) 0.47
		b) 0.51
		c) 0.53
		d) 0.56
		e) 0.58

Answer 1

Answer = c) 0.53

Note:

1. Average Return =Sum of returns / Number of Periods

= (11%-5%+21%)/3

= 9%

2. Computation of standard deviation :

Probable Return	Deviation ( Probable Return- Expected Return)	Deviation Squared
11	2.000	4
-5	-14.000	196
21	12.000	144
	Deviation Squared Total	344.0000000000

standard deviation = [Sum of Deviation Squared / (Number of Periods -1)]^(1/2)

= [344/(3-1)]^(1/2)

Standard Deviation = 13.11487705%

3. Sharpe Ratio = (Average return - risk free return ) / Standard Deviation

= (9%-2%)/13.11487705%

= 0.53

Answer = c) 0.53