Implications of Sharpe Ratio as a Performance Measure in Multi-Period Settings

We study effects of using Sharpe ratio as a performance measure for compensating money managers in a dynamic and frictionless market setting. First, we demonstrate that with such a performance measure, the manager's focus on the short horizon performance is detrimental to the investor's long horizon performance. Numerical experiments illustrate that when returns are iid, the performance loss is significant, even when the investor's investment horizon is not much longer than the manager's. When expected returns are mean reverting, the performance loss is exacerbated. Second, we show that Sharpe ratio maximization strategies tend to increase (decrease) the risk in the later part of the optimization period after a bad (good) performance in the earlier part of the optimization period. As illustrated by a simulation exercise, this prediction is in agreement with empirical observations, and it presents a rational expectations alternative to the prevalent tournament theory explanation.