Robust Portfolio Control with Stochastic Factor Dynamics

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. However, 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.

Asset Liability Modelling and Pension Schemes: The Application of Robust Optimization to USS

“…It is helpful if the ratio of the number of factors to the number of assets and liabilities is small. In previous robust optimization studies this ratio is 0.080 and 0.233 (Goldfarb & Iyengar, 2003); 0.125 and 0.238 (Ling & Xu, 2012) and 0.200 (Glasserman & Xu, 2013). With four factors and 14 assets and liabilities we have a ratio of 0.286, which is higher than previous studies.…”

“…Finally, the use of factors plays a significant role in making the robust optimization problem computationally tractable (e.g. a second order cone problem -SOCP), see for instance Goldfarb and Iyengar (2003), Glasserman and Xu (2013), and Kim et al (2014). where m is the number of factors.…”

On the relationship between entropy, demand uncertainty, and expected loss

“…References to entropy within both operations management (see for example Andersson, Jörnsten, Nonås, Sandal, & Ubøe, 2013;Maglaras & Eren, 2015;Perakis & Roels, 2008;Shuiabi, Thomson, & Bhuiyan, 2005) and related contexts are increasing. This includes the contexts of pricing models (Lim & Shanthikumar, 2007), portfolio optimization (Glasserman & Xu, 2013), and discrete optimization (Nakagawa, James, Rego, & Edirisinghe, 2013). Of particular interest, Andersson et al (2013) numerically demonstrate promising performance characteristics of using entropy-based demand distributions for ordering decisions; our work complements this insight by theoretically connecting entropy and loss in a similar setting.…”

Stress Testing with Misspecified Models

“…In comparison with existing literature the worst case-type analysis is akin to that discussed in Breuer, Jandacka, Rheinberger, and Summer (2009) and, given our use of entropic measures of plausibility, to Breuer and Csiszr (2013), Glasserman and Xu (2014) and Glasserman and Xu (2013). Breuer and Csiszr (2013), however, concentrates on simplified loan-portfolio/credit-risk applications or employs linear-Gaussian approximations to implement their methods.…”

“…In addition, we explicitly blend the methodology with tilting to impose 'judgment' which will always be an important element of stress testing in practice. Glasserman and Xu (2014) and Glasserman and Xu (2013) also explore robust tilts to forecast distributions, including those that impose expectations constraints as additional restrictions on plausibility. However, their work is again more theoretical and portfolio-oriented (rather than employing a practical example of an extended macro-stress testing model such as CLASS) and does not explore the usefulness of exponential tilting as an approach to introducing judgment in its own right, separate from any worst case analysis.…”