Abstract Online portfolio selection, one of the major fundamental problems in finance, has been explored quite extensively in recent years by machine learning and artificial intelligence communities. Recent state-of-the-art methods have focused on Mean Reversion significantly and have demonstrated outstanding performance. Another version of the same phenomenon, Median Reversion, has also performed well and demonstrated its ability to be robust against noises and outliers. Another important characteristic is Momentum. In this paper, a Bayesian ensembling approach to extract knowledge from both Mean Reversion and Median Reversion simultaneously based on the momentum associated with each one is proposed for the online portfolio selection task. The proposed method demonstrates its effectiveness by outperforming current state-of-the-art algorithms on several datasets.