1. Worst-case guarantee: the algorithm is universal in the sense that it asymptotically performs almost as well as the best constant rebalanced portfolio determined in hindsight from the realized market prices. Furthermore, it attains the tightest known bounds on the regret, or the log-wealth difference relative to the best constant rebalanced portfolio. We prove that the regret of algorithm is bounded by $$O(\log Q)$$, where $$Q$$ is the quadratic variation of the stock prices. This is the first improvement upon Cover’s [Cover, 1991] seminal work that attains a regret bound of $$O(\log T)$$, where $$T$$ is the number of trading iterations.