Strategy design and the fallacies of breadth

Abstract

High return correlations between assets have widely and plausibly been said to detract from active performance. The concept of Breadth supports this view. Buckle, however, reported that these correlations improve active performance. Based on three approaches, we report that Buckle is correct. First, we introduce a model of active investing that includes return correlations between assets. Design formulae give the time averages of active risk and return and other portfolio characteristics. Next, we show that Monte Carlo simulations confirm the conclusions of the model. Finally, we provide the investment intuition behind the conclusions. All else equal, active managers should be more aggressive when return correlations are expected to be high, not low. A related widely held belief is that return forecasts with lower correlations between assets provide better performance. The model also includes these correlations. The same approaches show that this consensus too is incorrect: all else equal, correlations of return forecasts between assets improve performance. The design formulae can be used for operational strategy design aimed at performance improvements. As examples, we use it to exploit differences in predictive power between sectors and to efficiently incorporate Environmental, Social and Governance controls into active security selection.