Meta Algorithms for Portfolio Selection

We consider the problem of sequential portfolio selection in the stock market. There are theoretically well grounded algorithms for the problem, such as Universal Portfolio (UP), Exponentiated Gradient (EG) and Online Newton Step (ONS). Such algorithms enjoy the property of being universal, i.e., having low regret with the best constant rebalanced portfolio. However, the practical performance of such popular algorithms is sobering compared to heuristics such as Anticor, which have no theoretical guarantees but perform surprisingly well in practice. Motivated by such discrepancies, in this paper we focus on designing meta algorithms for portfolio selection which can leverage the best of both worlds. Such algorithms work with a pool of base algorithms and use online learning to redistribute wealth among the base algorithms. We develop two meta-algorithms: MAEG which uses online gradient descent following EG and MAONS which uses online Newton step following ONS. If one of the base algorithms is universal, it follows that the meta-algorithm is universal. Through extensive experiments on two real stock market datasets, we show that the meta-algorithms are competitive and often better than the best base algorithm, including heuristics, while maintaining the guarantee of being an universal algorithm.