Algorithms for Portfolio Management Based on the Newton Method

Abstract

We experimentally study on-line investment algorithms first proposed by Agarwal and Hazan and extended by Hazan et al. 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.