Optimal Active Share

Active Share is a widely used measure of an active portfolio´s deviation from the benchmark holdings. Initial research by M. Cremers and A. Petajisto [1] indicated that managers with a high Active Share value tend to outperform others. That observation promoted Active Share value as a predictor of fund performance. However, in an unrelated study, S. Johnson, R. Kahn and D. Petrich [2] showed that alpha, risk and gearing can not be selected independently. They also showed that imposing enhanced gearing value through a penalty can result in a significant deterioration in investment strategy performance. These results can be immediately translated into an active space where the gearing target becomes an Active Share target. In this paper, we analyzed the impact of directly setting an Active Share target by a constraint. Our results show that constraining Active Share to a higher value than the one consistent with the selected risk target has only negative impact on investment strategy performance. While we agree that achieving a higher unconstrained value of an Active Share measure may be a good sign of “activeness”, our results illustrate that reaching this objective by adding a binding constraint is neither a good investment practice nor one that will translate into a better performance.