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

• 成果类型: Article
• 署名作者: Bertsimas, Dimitris; Gupta, Vishal; Paschalidis, Ioannis Ch.
• 署名单位: Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Boston University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.1120.1115
• 发表日期: 2012
• 页码: 1389-1403
• 关键词: asset pricing-models; RISK; distributions; variance

摘要

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. Subject classifications: finance: portfolio optimization; programming: inverse optimization; statistics: estimation. Area of review: Financial Engineering. History: Received May 2011; revisions received November 2011, January 2012; accepted June 2012. Published online in Articles in Advance November 20, 2012.