Title: A Separation Principle for Dynamic Trading and Portfolio Optimization

Abstract: We consider multi-period optimal trading or portfolio optimization problems in the presence of
predictable returns (“alpha”). The setting is general in that it allows essentially arbitrary
dynamics for returns and return predictions, but requires restrictive assumptions on transaction
costs, risk preferences, and trading constraints. When restricted to this setting, we establish
that that the term structure of future conditional mean returns is a sufficient statistic for
optimal decision making. This provides a separation principle that partitions optimal trading into
two natural steps: at each time, (1) conditionally forecast the term structure of future expected
returns; and (2) given the forecast term structure, compute the optimal trading decision by
solving a single-period, deterministic Markowitz-style mean-variance optimization problem, but
with an endogenously determined effective time horizon. The method is tractable for realistic
problems with a large number of assets and many predictive variables over multiple time horizons.

Implications of results for alpha research and the optimal combination of alphas will be discussed.

Joint work with Benjamin Van Roy (Stanford).

About the speaker:
Ciamac C. Moallemi is an Associate Professor of Business in the Decision, Risk, and Operations Division of the Graduate School of Business at Columbia University, where he has been since 2007. He also develops quantitative trading strategies at Bourbaki LLC, a quantitative investment advisor. He holds editorial positions at the journals Operations Research and Management Science. His research interests are in the area of the optimization and control of large-scale stochastic systems and decision-making under uncertainty, with an emphasis on applications in financial engineering.