Portfolio selection under model uncertainty: a penalized moment-based optimization approach

Abstract

We present a new approach that enables investors to seek a reasonably robust policy for portfolio selection in the presence of rare but high-impact realization of moment uncertainty. In practice, portfolio managers face diffculty in seeking a balance between relying on their knowledge of a reference financial model and taking into account possible ambiguity of the model. Based on the concept of Distributionally Robust Optimization (DRO), we introduce a new penalty framework that provides investors flexibility to define prior reference models using moment information and accounts for model ambiguity in terms of "extreme" moment uncertainty. We show that in our approach a globally-optimal portfolio can in general be obtained in a computationally tractable manner. We also show that for a wide range of specifications our proposed model can be recast as semidefinite programs. Computational experiments show that our penalized moment-based approach outperforms classical DRO approaches in terms of both average and downside-risk performance using historical data.

Robust Multiarmed Bandit Problems

“…The penalty approach, which we are using, has been widely adopted in the robust control literature (e.g., Jacobson 1973;Whittle 1981Whittle , 1990Whittle , 1991Dai Pra et al 1996;Petersen et al 2000), and has also been used in economics and operations research applications (e.g., Hansen and Sargent 2005, 2007, 2008Lim and Shanthikumar 2007;Lim et al 2012;Li and Kwon 2013). The constraint approach has been widely applied to single-stage optimization problems with parameter or moment uncertainty (e.g., Ben-Tal and Nemirovski 1998, 1999Bertsimas and Sim 2004;El Ghaoui and Lebret 1997), but has also been extended to dynamic problems with uncertainty in the model of state dynamics (e.g., Iyengar 2005, Lim et al 2011, Nilim and El Ghaoui 2005and Wiesemann et al 2013).…”

Robust Control of Partially Observable Failing Systems

“…In the constraint approach, the set of alternative models is represented as a hard constraint, and confidence in the nominal is captured by the size of this uncertainty set (see, e.g., Ben-Tal and Nemirovski 1998, 1999, 2000Bertsimas and Sim 2004;El Ghaoui and Lebret 1997;Iyengar 2005;Li and Kwon 2013;Nilim and El Ghaoui 2005;Wiesemann et al 2013). The penalty approach on the other hand expresses confidence in the nominal by penalizing alternative models that deviate too far from the nominal, and does so via a penalty function (soft constraint) that appears in the objective function (see, e.g., Dai Pra et al 1996, Peterson et al 2000, Hansen and Sargent 2007, Jain et al 2010, Kim and Lim 2015, Lim and Shanthikumar 2007.…”

Robustifying Convex Risk Measures for Linear Portfolios: A Nonparametric Approach

“…1-14, © 2014INFORMS El Ghaoui et al (2003, Goldfarb and Iyengar (2003), Maenhout (2004) and Shapiro and Ahmed (2004). While most approaches make strong assumptions about the nature of the ambiguity, there is also some research that uses nonparametric methods (see Calafiore 2007, Pflug and Wozabal 2007, Delage and Ye 2010, Zymler et al 2011, Wozabal 2012, Li and Kwon 2013.…”