A note on empirical Sharpe ratio dynamics

Generating a high positive excess return in a prospective period does not necessarily increase the empirical Sharpe ratio of an investment fund. Therefore, we derive a critical range in which prospective excess returns must lie in order to increase its empirical Sharpe ratio. We also give a formal statement of an excess return value within this critical range that leads to the maximum possible empirical Sharpe ratio in the prospective period.

► High prospective excess returns can lower the empirical Sharpe ratio. ► We derive a range for excess return values that increase the empirical Sharpe ratio. ► We also derive an excess return value that maximizes the empirical Sharpe ratio.