Inverse Optimization: A New Perspective on the Black-Litterman Model

Dimitris Bertsimas (), Vishal Gupta () and Ioannis Ch. Paschalidis ()
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Dimitris Bertsimas: Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Vishal Gupta: Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Ioannis Ch. Paschalidis: Department of Electrical and Computer Engineering, Boston University, Boston, Massachusetts 02215

Operations Research, 2012, vol. 60, issue 6, 1389-1403

Abstract: The Black-Litterman (BL) model is a widely used asset allocation model in the financial industry. In this paper, we provide a new perspective. The key insight is to replace the statistical framework in the original approach with ideas from inverse optimization. This insight allows us to significantly expand the scope and applicability of the BL model. We provide a richer formulation that, unlike the original model, is flexible enough to incorporate investor information on volatility and market dynamics. Equally importantly, our approach allows us to move beyond the traditional mean-variance paradigm of the original model and construct “BL”-type estimators for more general notions of risk such as coherent risk measures. Computationally, we introduce and study two new “BL”-type estimators and their corresponding portfolios: a mean variance inverse optimization (MV-IO) portfolio and a robust mean variance inverse optimization (RMV-IO) portfolio. These two approaches are motivated by ideas from arbitrage pricing theory and volatility uncertainty. Using numerical simulation and historical backtesting, we show that both methods often demonstrate a better risk-reward trade-off than their BL counterparts and are more robust to incorrect investor views.

Keywords: finance; portfolio optimization; programming; inverse optimization; statistics; estimation (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (24)

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