Kernel-Based Semi-Log-Optimal Empirical Portfolio Selection Strategies

Abstract

The purpose of this paper is to introduce an approximation of the kernel-based logoptimal investment strategy that guarantees an almost optimal rate of growth of the capital under minimal assumptions on the behavior of the market. The new strategy uses much less knowledge on the distribution of the market process. It is analyzed both theoretically and empirically. The theoretical results show that the asymptotic rate of growth well approximates 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 proposed semi-log-optimal and the log-optimal strategies have essentially the same performance measured on past nyse data.

Empirical Log-Optimal Portfolio Selections: A Survey

“…More precisely, the data set contains the daily price relatives, that was calculated from the nominal values of the closing prices corrected by the dividends and the splits for all trading day. This data set has been used for testing portfolio selection in Cover [12], in Singer [48], in Györfi, Lugosi, Udina [21], in Györfi, Udina, Walk [23] and in Györfi, Urbán, Vajda [24].…”

“…Györfi, Urbán, Vajda [24]). In this section we present some numerical results obtained by applying the kernel based semilog-optimal algorithm to the 19 large assets of the second NYSE data set.…”

PAMR: Passive aggressive mean reversion strategy for portfolio selection

“…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. Under the same framework, Györfi et al (2007) proposed another variant called Nonparametric Kernel-based Semi-log-optimal strategy, which is actually an approximation of the B K strategy, mainly to improve the computational efficiency. Replacing log utility function by Markowitz-type utility function, Ottucsák and Vajda (2007) proposed Nonparametric Kernel-based Markowitz-type strategy, which connects return and risk (or mean and variance) with the online portfolio selection strategy.…”

An asymptotic analysis of the mean-variance portfolio selection

“…As the main tool we apply the semi-log function introduced by Györfi, Urbán and Vajda [12]. The semi-log function is the second order Taylor expansion of log z at z = 1…”

“…The relationship between the log-optimal and semi-log optimal approach was examined in [12]. We present formal, rigorous analysis for the comparison of the investment strategies in the subsequent sections.…”