Robust Portfolio Control with Stochastic Factor Dynamics

45 Pages Posted: 17 Nov 2011 Last revised: 29 Oct 2012

See all articles by Paul Glasserman

Paul Glasserman

Columbia Business School

Xingbo Xu

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Date Written: October 27, 2012

Abstract

Portfolio selection is vulnerable to the error-amplifying effects of combining optimization with statistical estimation and model error. For dynamic portfolio control, sources of model error include the evolution of market factors and the influence of these factors on asset returns. We develop portfolio control rules that are robust to this type of uncertainty, applying a stochastic notion of robustness to uncertainty in model dynamics. In this stochastic formulation, robustness reflects uncertainty about the probability law generating market data, and not just uncertainty about model parameters. We analyze both finite- and infinite-horizon problems in a model in which returns are driven by factors that evolve stochastically. The model incorporates transaction costs and leads to simple and tractable optimal robust controls for multiple assets. We illustrate the performance of the controls on historical data. As one would expect, in-sample tests show no evidence of improved performance through robustness -- evaluating performance on the same data used to estimate a model leaves no room to capture model uncertainty. But robustness does improve performance in out-of-sample tests in which the model is estimated on a rolling window of data and then applied over a subsequent time period. By acknowledging uncertainty in the estimated model, the robust rules lead to less aggressive trading and are less sensitive to sharp moves in underlying prices.

Suggested Citation

Glasserman, Paul and Xu, Xingbo, Robust Portfolio Control with Stochastic Factor Dynamics (October 27, 2012). Available at SSRN: https://ssrn.com/abstract=1960723 or http://dx.doi.org/10.2139/ssrn.1960723

Paul Glasserman

Columbia Business School ( email )

3022 Broadway
403 Uris Hall
New York, NY 10027
United States
212-854-4102 (Phone)
212-316-9180 (Fax)

Xingbo Xu (Contact Author)

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

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