icml - Algorithms for Portfolio Management based on the...

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Unformatted text preview: Algorithms for Portfolio Management based on the Newton Method Amit Agarwal aagarwal@cs.princeton.edu Elad Hazan ehazan@cs.princeton.edu Satyen Kale satyen@cs.princeton.edu Robert E. Schapire schapire@cs.princeton.edu Princeton University, Department of Computer Science, 35 Olden Street, Princeton, NJ 08540 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 of- fline optimization which, unlike previous ap- proaches, exploits second order information. After analyzing the algorithm using the po- tential function introduced by Agarwal and Hazan, we present extensive experiments on actual financial data. These experiments confirm the theoretical advantage of our al- gorithms, which yield higher returns and run considerably faster than previous algorithms with optimal regret. Additionally, we per- form financial analysis using mean-variance calculations and the Sharpe ratio. 1. Introduction In the universal portfolio management problem, we seek online wealth investment strategies which enable an investor to maximize his wealth by distributing it on a set of available financial instruments without knowing the market outcome in advance. The under- lying model of the problem makes no statistical as- sumptions on the behavior of the market (such as ran- dom walks or Brownian motion of stock prices (Lu- enberger, 1998)). In fact, the market is even allowed to be adversarial. The simplicity of the model per- mits the formulation of the centuries-old problem of wealth maximization as an online learning problem, Appearing in Proceedings of the 23 rd International Con- ference on Machine Learning , Pittsburgh, PA, 2006. Copy- right 2006 by the author(s)/owner(s). and the application of machine learning algorithms. The study of such a model was started in the 1950s by Kelly (1956) followed by Bell and Cover (1980; 1988), Algoet and Cover (1988). Absolute wealth maximization in an adversarial mar- ket is of course a hopeless task; we therefore aim to maximize our wealth relative to that achieved by a reasonably sophisticated investment strategy, the constant-rebalanced portfolio (Cover, 1991), abbrevi- ated CRP. A CRP strategy rebalances the wealth each trading period to have a fixed proportion in every stock in the portfolio. We measure the performance of an online investment strategy by its regret , which is the relative difference between the logarithmic growth ra- tio it achieves over the entire trading period, and that achieved by a prescient investor one who knows all the market outcomes in advance, but who is con- strained to use a CRP. An investment strategy is said to be universal if it achieves sublinear regret....
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This note was uploaded on 12/08/2011 for the course CIS 625 taught by Professor Michaelkearns during the Spring '12 term at Pennsylvania State University, University Park.

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icml - Algorithms for Portfolio Management based on the...

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