We consider online learning of ensembles of portfolio selection algorithms and aim to regularize risk by encouraging diversification with r espect to a predefined risk-driven grouping of stocks. Our procedure uses online convex optimization to control capital allocation to underlying investment alg orithms while encouraging non-sparsity over the given grouping. We prove a logarithmic regret for this procedure with respect to the best-in-hindsight ensemble. We applied the procedure with known mean-reversion portfolio selection algorithms using the standard GICS industry sector grouping. Empirical Experimental results showed an impressive percentage increase of risk-adjusted return (Sharpe r atio).
We experimentally study on-line investment algorithms first proposed by Agarwal and Hazan and extended by which achieve almost the same wealth as the best constant-rebalanced portfolio determined in hindsight. These algorithms are the first to combine optimal logarithmic regret bounds with efficient deterministic computability. They are based on the Newton method for offline optimization which, unlike previous approaches, exploits second order information. After analyzing the algorithm using the potential function introduced by Agarwal and Hazan, we present extensive experiments on actual financial data. These experiments confirm the theoretical advantage of our algorithms, which yield higher returns and run considerably faster than previous algorithms with optimal regret. Additionally, we perform financial analysis using mean-variance calculations and the Sharpe ratio.