Dynamic, Correlated Active Management : A Closed Form Solution

We present a closed-form solution for the steady state investment properties of actively managed strategies. Our goal is to provide clear, practical predictions to guide the design of active strategies and improve their performance. The solution includes cost control, correlated assets, correlated signals, and multi-horizon predictive power. It yields explicit predictions for active return, active risk, turnover, signal exposure, before- and after-cost Information Ratios and other quantities. In addition we provide a dynamic generalization of the Fundamental Law that includes turnover control, correlations, and other practical features of active management. Examples illustrate the predictions, show how to use them to improve performance, and reveal some unexpected findings. The predictions prove to be reliable guides to investment decision-making in a wide range of scenarios