Knowledge-based Black-Litterman Asset Allocation with High-Dimensional Realized Covariance

Abstract

This paper introduces a knowledge-based Black-Litterman (KBL) asset allocation framework. Experts’ views are generated using a distributed modeling framework fusing several types of uncertain and incomplete knowledge from experts to derive optimal decisions rationally. We use Shannon’s information measure to develop aggregation rules integrating multiple experts’ predictions while calibrating their reliability. The fusion parameters are adaptively learned by minimizing the decision error of the induced combination, which we formulate as a constrained optimization problem. We further enhance covariance estimation by modeling realized covariances from high-frequency data using the Conditional Threshold Autoregressive Wishart (CTAW) model, providing the first analytical framework for addressing its high-dimensional estimation challenges. We derive explicit gradient expressions and solve the optimization using the method of moving asymptotes. Empirical analysis on a U.S. equity universe shows that the proposed approach achieves superior risk-adjusted returns, outperforming six established allocation strategies with statistically significant improvements over the   1/N benchmark in the presence of transaction costs. In addition, we show that incorporating our parameter estimation methods enhances the performance of existing benchmark strategies. Results remain robust to sensitivity tests.

Keywords: Risk Management, Investment Analysis, Black-Litterman, Parameter Uncertainty, Knowledge Fusion