Generalized Black-Litterman Portfolio Optimization with Decision Fusion

The Black–Litterman asset allocation model (BLM) provides a framework for combining investors’ views with market (equilibrium) views within a classical Markowitz mean-variance framework. In the BLM, three key inputs are used: the reference portfolio, the investors’ views, and some covariance matrix. However, BLM assumes that the reference portfolio is recovered from the CAPM, and that the covariance matrix is constant over time. Both assumptions are questionable when applied to financial returns. Furthermore, the literature on BLM has so far relied primarily on trading strategies and distributional properties of financial returns to establish the investors’ views. In this paper, we address the weakness of BLM and offer three methodological contributions. We characterize investors’ views as results of decision-making and develop an entropy-based multiple classifiers combination system in the framework of Dempster and Shafer’s Theory of Evidence, to elicit the investors' views. We replace the reference portfolio calibrated using the CAPM with a reference portfolio that is designed using a quantitative model, and blend the prior information consistently with investors' views. We also relax the assumption of constant covariance matrix and propose a diversification-based GLasso-Wishart model to estimate conditional volatility. Our novel, generalized BLM strategy outperforms five well-studied benchmark strategies by a clear margin in terms of the risk-return metrics and realized tail-risks. These results are robust to a range of risk aversion coefficients, asset menus, rebalancing periods, and pre- and post-transaction costs.