Portfolio constraints and the fundamental law of active management

Active portfolio management is typically conducted within constraints that do not allow managers to fully exploit their ability to forecast returns. Constraints on short positions and turnover, for example, are fairly common and materially restrictive. Other constraints, such as market-capitalization and value-growth neutrality with respect to the benchmark or economic-sector constraints, can further restrict an active portfolio's composition. We derive ex ante and ex post correlation relationships that facilitate the performance analysis of constrained portfolios. The ex ante relationship is a generalized version of a previously developed "fundamental law of active management" and provides an important strategic perspective on the potential for active management to add value. The ex post correlation relationship represents a practical decomposition of performance into the success of the return-prediction process and the "noise" associated with portfolio constraints. We verify the accuracy of these relationships with a Monte Carlo simulation and illustrate their application with equity portfolio examples based on the S&P 500 Index as the benchmark.