Algorithms for portfolio management based on the Newton methodAlgorithms for portfolio management based on the Newton methodAgarwal, Amit and Hazan, Elad and Kale, Satyen and Schapire, Robert E.2006

Paper summarycdmurray80The authors present an algorithm for investment (picking which stocks to buy). This online algorithm chooses an investment in N stocks (a point on the N-dimensional simplex) every period. It works by optimizing, every period, some approximation to the current lossdefining a portfolio loss minus the two-norm of the investment vector. This algorithm can be easily implemented and the authors claim is has optimal regret with respect to the best CRP (constantly rebalanced portfolio) chosen in hindsight (I leave technical details of the algorithm to those who want to read the paper). The authors have experiments indicating that the algorithms does better than buy-and-hold on randomly selected S&P stocks. My personal experiments with this algorithm (using code from one of the authors) indicated that the regret bounds, though optimal, are far too weak to be economically meaningful (the terminal wealth of ONS may lag the best CRP by a factor exponential in $22 \cdot N \cdot \sqrt{T}$, where $N$ is the number of stocks and T the number of periods) and the algorithm performed roughly as well as buy-and-hold on monthly data.

The authors present an algorithm for investment (picking which stocks to buy). This online algorithm chooses an investment in N stocks (a point on the N-dimensional simplex) every period. It works by optimizing, every period, some approximation to the current lossdefining a portfolio loss minus the two-norm of the investment vector. This algorithm can be easily implemented and the authors claim is has optimal regret with respect to the best CRP (constantly rebalanced portfolio) chosen in hindsight (I leave technical details of the algorithm to those who want to read the paper). The authors have experiments indicating that the algorithms does better than buy-and-hold on randomly selected S&P stocks. My personal experiments with this algorithm (using code from one of the authors) indicated that the regret bounds, though optimal, are far too weak to be economically meaningful (the terminal wealth of ONS may lag the best CRP by a factor exponential in $22 \cdot N \cdot \sqrt{T}$, where $N$ is the number of stocks and T the number of periods) and the algorithm performed roughly as well as buy-and-hold on monthly data.

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