Behaviouralizing Black-Litterman: Expert Opinions and Behavioural Biases in a Diffusion Setting

Abstract

This paper proposes a continuous time version of the Black-Litterman model that accounts for, and corrects, some of the main behavioural biases that analysts may exhibit. We formulate the model as a stochastic control problem under partial observations, and derive the optimal investment strategy and value function in closed form. We implement this model with three partially observable state variables corresponding to the three factors of the Fama-French model, and fourteen sources of observations: market data from eleven ETFs, views from two analysts, and one stress test scenario. With this example, we show concretely how to calibrate analyst views and mitigate the impact of behavioural biases. To explore the effect that views and biases have on the asset allocation, we compare the results of six dynamic investment models. We find that the views have a modest impact on the Kelly portfolio, but the confidence intervals around the views have a large impact on the intertemporal hedging portfolio.