Dealing with Drift Uncertainty : A Bayesian Learning Approach

One of the main challenges investors have to face is model uncertainty. Typically, the dynamic of the assets is modeled using two parameters: the drift vector and the covariance matrix, which are both uncertain. Since the variance/covariance parameter is assumed to be estimated with a certain level of confidence, we focus on drift uncertainty in this paper. Building on filtering techniques and learning methods, we use a Bayesian learning approach to solve the Markowitz problem and provide a simple and practical procedure to implement optimal strategy. To illustrate the value added of using the optimal Bayesian learning strategy, we compare it with an optimal non-learning strategy that keeps the drift constant at all times. In order to emphasize the prevalence of the Bayesian learning strategy above the non-learning one in different situations, we experiment three different investment universes: indices of various asset classes, currencies and smart beta strategies