Abstract <p>Universal portfolio, is recursively constructive portfolio. Though different initially, eventually the portfolio average return remains close to that of best constantly rebalanced portfolio. For that purpose, recursive update of weights was obtained by Cover. The main problem with universal portfolios is the required computational power. In this paper we provide different look on the portfolio construction. We argue that some sort of Bayesian process may be enough to converge to same results. We show, both empirically and theoretically, that Bayesian update process, without regard to particular distribution of stocks’ prices processes, will replicate the same behavior as universal portfolio. We also show empirically that universal portfolios with constraints maybe also treated by this mechanism.</p>