Implications of the 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 market. We demonstrate that the manager's focus on the short horizon is detrimental to the long-horizon investor. When the returns are iid, the performance loss is significant, even when horizons are not very different. When the returns are mean reverting, the performance loss is exacerbated. We show that the manager's strategy tends to increase (decrease) the risk in the latter part of the optimization period after a bad (good) performance in the earlier part of the period, in agreement with empirical observations.