Question

You are assessing a new trading strategy for inclusion in your hedge fund. The trading strategy has a 10 year backtest. The mean monthly return is 1.2%, and the standard deviation of monthly returns is 3.1%. The annual risk free rate is 1.2%.

1. a) Calculate the annualised Sharpe Ratio of the strategy. You should use simple compounding for returns. What assumptions have you made?

   b) Calculate a 95% confidence interval for the annualised Sharpe Ratio. Your calculation should use monthly returns, and you should use the normal distribution when calculating your confidence intervals.

Answer 1

a. To calculate the yearly returns, we use compounding formula.

1.012^12 - 1 = 15.389%. Similarly, the yearly s.d. of returns = 3.1 x sqrt(12) = 10.73%.

Hence, Sharpe ratio = (Mean- riskfree rate)/s.d. = (15.389 - 1.2)/10.73 = 1.322.

We have made the assumption of compounding i.e. every month we make this return of 1.2% and we put all the capital made into this strategy again.

b. Our 95% confidence level will depend on the monthly return's confidence intervals. Hence, the 95% confidence level of monthly returns will be within 1.96 sigma. Hence, the value will be = 1.2 - 1.96 x 3.1 = -4.876% and 1.2 + 1.96 x 3.1 = 7.276%. Annualizing these we have: (1-0.04876)^12 -1 = -45.11% and (1.07276)^12 - 1 = 132.29%. Hence, the interval for Sharpe ratio will be (-45.11 - 1.2)/10.73 = -4.3159 and (132.29 - 1.2)/10.73 = 12.21