Incorporating uncertainty into the Black–Litterman portfolio selection model

Abstract

We present a robust Black–Litterman (BL) model that takes into account the possibility of model misspecification. In place of a single prior distribution, we utilize multiple priors around the estimated expected excess returns and covariance matrix. The model has two primary advantages over the original BL model: (1) it systematically incorporates model misspecification in the form of Kullback–Leibler (KL) divergence and (2) by explicitly targeting robust allocations, it improves upon traditional bootstrap approaches.

Keywords:

• Black–Litterman
• robust optimization
• Kullback–Leibler divergence

JEL Classification:

• G11
• D80
• C61

Notes

This article contains the current opinions of the authors and not necessarily those of PIMCO (Pacific Investment Management Company LLC). These opinions are subject to change without notice.