Robust Asset Allocation

Abstract

This article addresses the problem of finding an optimal allocation of funds among different asset classes in a robust manner when the estimates of the structure of returns are unreliable. Instead of point estimates used in classical mean-variance optimization, moments of returns are described using uncertainty sets that contain all, or most, of their possible realizations. The approach presented here takes a conservative viewpoint and identifies asset mixes that have the best worst-case behavior. Techniques for generating uncertainty sets from historical data are discussed and numerical results that illustrate the stability of robust optimal asset mixes are reported.

Robust portfolios: contributions from operations research and finance

“…A few different methods for modeling uncertainty in the covariance matrix are used in practice. Some are superimposed on top of factor models for returns (Goldfarb and Iyengar 2003b), while others consider confidence intervals for the individual covariance matrix entries (Tütüncü and Koenig 2004). Benefits for portfolio performance have been observed even when the uncertainty set is defined simply as a collection of several possible scenarios for the covariance matrix (Rustem et al 2000;Costa and Paiva 2002).…”

“…Instead of using uncertain sets based on estimates from a factor model, Tütüncü and Koenig (2004) directly specify intervals for the individual elements of the covariance matrix:…”

“…This robust technique has obtained prodigious success since the late 1990s, especially in the field of optimization and control with uncertainty parameters Nemirovski 1998, 1999;El Ghaoui and Lebret 1997;Goldfarb and Iyengar 2003a). With respect to portfolio selection, the major contributions have come in the 21st century (see, for example, Rustem et al 2000;Costa and Paiva 2002;Ben-Tal et al 2002;Goldfarb and Iyengar 2003b;El Ghaoui et al 2003;Tütüncü and Koenig 2004;Pinar and Tütüncü 2005;Lutgens and Schotman 2006;Natarajan et al 2009;Garlappi et al 2007;Pinar 2007;Calafiore 2007;Huang et al 2008;Natarajan et al 2008a;Brown and Sim 2008;Natarajan et al 2008b;Shen and Zhang 2008;Elliott and Siu 2008;Zhu and Fukushima 2008). For a complete discussion of robust portfolio management and the associated solution methods, see Fabozzi et al (2007), Föllmer et al (2008), and the references therein.…”

Combining RMT-based filtering with time-stamped resampling for robust portfolio optimization

“…We also find many authors who focus on a second way, handling the uncertainty in parameters during the optimization process 17,18,19,20 . Other efforts regarding the second line were made to introduce robustness in multiobjective optimization 21 . For instance Deb et al 22 launched a robust adaptation for NSGA-II algorithm to optimize portfolios and then Garcia et al 23 dealt with the problem of robustness but using resampling and a third objective as a time-stamp.…”

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

“…Most DRO approaches are developed with the purpose of achieving a computational tractable model so that they are applicable to real world large-scale problems. Aside from the moment-based DRO approaches, several other facets of constructing a robust portfolio based on limited statistical information can also be found in Goldfarb and Iyengar [16], Tütüncü and Koenig [30], Calafiore [9], and Zhu and Fukushima [34].…”