It [Black and Litterman, 1992], [He and Litterman, 1999].Statistics 157 Black-Litterman Model This paper introduces the Black -Litterman model and its applications.
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 tradeoff than their BL counterparts and are more robust to incorrect investor views.
In this paper we have used techniques from inverse optimization to create a novel, richer, reformulation of the Black-Litterman (BL) framework. The major advantage of this approach is the increased flexibility for specifying views and the ability to consider more general notions of risk than the traditional mean-variance approach. We have exploited this flexibility to introduce two new BL-type estimators and their corresponding portfolios, a Mean-Variance Inverse Optimization (MV-IO) approach and a Robust Mean-Variance Inverse Optimization (RMV-IO) approach. The major distinction between the approaches is that the first allows investors to capitalize upon any private information they may have on volatility, while the second seeks to insulate investors from volatility uncertainty when they have no such information. Computational evidence suggests that these approaches provide certain benefits over the traditional BL model, especially in scenarios where views are not known precisely.