Question

We have the following historical returns on a portfolio. Assume the monthly risk-free rate in the same time period was 3%. Estimate the Sharpe ratio of this portfolio.

Round your answer to 4 decimal places. For example if your answer is 3.205%, then please write down 0.0321.

month	return
1	10%
2	5%
3	-2%
4	3%
5	15%

Answer 1

Expected Return = [0.10 + 0.05 + (-0.02) + 0.03 + 0.15] / 5
Expected Return = 0.31 / 5
Expected Return = 0.062 or 6.20%

Variance = [(0.10-0.062)^2 + (0.05-0.062)^2 + (-0.02-0.062)^2 + (0.03-0.062)^2 + (0.15-0.062)^2] / 4
Variance = 0.01708 / 4
Variance = 0.00427

Standard Deviation = (0.00427)^(1/2)
Standard Deviation = 0.0653 or 6.53%

Sharpe Ratio = [Expected Return - Risk-free Rate] / Standard Deviation
Sharpe Ratio = (0.062 - 0.03) / 0.0653
Sharpe Ratio = 0.4900