Nonparametric Kernel‐based Sequential Investment Strategies

Abstract

The purpose of this paper is to introduce sequential investment strategies that guarantee an optimal rate of growth of the capital, under minimal assumptions on the behavior of the market. The new strategies are analyzed both theoretically and empirically. The theoretical results show that the asymptotic rate of growth matches the optimal one that one could achieve with a full knowledge of the statistical properties of the underlying process generating the market, under the only assumption that the market is stationary and ergodic. The empirical results show that the performance of the proposed investment strategies measured on past NYSE and currency exchange data is solid, and sometimes even spectacular.

PAMR: Passive aggressive mean reversion strategy for portfolio selection

“…The first one is NYSE dataset, one "standard" dataset pioneered by Cover (1991) and followed by several other researchers (Singer 1997;Helmbold et al 1996;Borodin et al 2004;Agarwal et al 2006;Györfi et al 2006. This dataset contains 5651 daily price relatives of 36 stocks 5 in New York Stock Exchange (NYSE) for a 22-year period from Jul.…”

“…In addition, Györfi et al (2006) recently introduced a framework of Nonparametric Kernel-based Moving Window (B K ) learning strategies for portfolio selection based on nonparametric prediction techniques (Györfi and Schäfer 2003). Their algorithm first identifies a list of similar historical price relative sequences whose Euclidean distances with recent market windows are smaller than a threshold, then optimizes the portfolio with respect to the list of similar sequences.…”

“…Rather than trading with a single stock using computational intelligence techniques, learning to select portfolio approach focuses on a portfolio, which consists of multiple assets/stocks. Several approaches for online portfolio selection, often characterized by machine learning formulations and effective optimization solutions, have been proposed in literature (Kelly 1956;Breiman 1961;Cover 1991;Ordentlich and Cover 1996;Helmbold et al 1996;Borodin and El-Yaniv 1998;Borodin et al 2000Borodin et al , 2004Stoltz and Lugosi 2005;Hazan 2006; Györfi et al 2006;Blum and Mansour 2007;Levina and Shafer 2008;. Despite being studied extensively, most approaches are limited in some aspects or the other.…”

An asymptotic analysis of the mean-variance portfolio selection

“…These strategies are universal with respect to the class of all stationary and ergodic processes as it was proved by Algoet [1]. Györfi and Schäfer [11], Györfi, Lugosi, Udina [10] constructed a practical kernel based algorithm for the same problem.…”

“…We also present an experimental performance analysis for the data sets of New York Stock Exchange (NYSE) spanning a twenty-two-year period with thirty six stocks included, which set was presented in [10].…”