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).
Although our procedure relies on the same @math group norm to encourage diversification, our algorithm differs from that of Johnson and Banerjee in two ways: first, rather than generating portfolios on the stock themselves, we generate a weighted ensemble over investment algorithms. Second, our learning algorithm exploits the exp-concavity of our loss function, allowing the use of online Newton steps as in @cite_16 to guarantee @math regret w.r.t. the best fixed ensemble in hindsight. A direct application of our procedure over the stocks themselves yields exponential improvement in regret relative to the result of JohnsonB2015 . Also worth mentioning is that our implementation utilizes a fixed grouping of the stocks given by the standard GICS industry taxonomy, whereas JohnsonB2015 employ a correlation-based heuristic to group the stocks on the fly. Our numerical examples in Section 3 include a direct comparison with the method of JohnsonB2015 , showing an overwhelming advantage to our method (see, e.g., Figure ).
@cite_16
2068643490
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.