Nonparametric nearest neighbor based empirical portfolio selection strategies

Abstract

Summary:In recent years optimal portfolio selection strategies for sequential investment have been shown to exist. Although their asymptotical optimality is well established, finite sample properties do need the adjustment of parameters that depend on dimensionality and scale. In this paper we introduce some nearest neighbor based portfolio selectors that solve these problems, and we show that they are also log-optimal for the very general class of stationary and ergodic random processes. The newly proposed algorithm shows very good finite-horizon performance when applied to different markets with different dimensionality or scales without any change: we see it as a very robust strategy.

Moving average reversion strategy for on-line portfolio selection

“…Based on nonparametric prediction [29], this category consists of several pattern-matching based investment strategies [27,31,30,44,28].…”

“…Note that the authors adopted two threshold parameters for theoretical analysis. Nonparametric nearest neighbor-based sample selection [30] searches the price relatives whose preceding market windows are within the nearest neighbor of the latest market window in terms of Euclidean distance, that is,…”

“…Györfi et al [27] presented nonparametric kernel-based log-optimal investment strategy (B K ), which combines the kernel-based sample selection and log-optimal utility function and proved its universality. Györfi et al [30] proposed nonparametric nearest neighbor log-optimal investment strategy (B NN ), which combines the nearest neighbor sample selection and log-optimal utility function and proved its universality. Li et al [44] created correlation-driven nonparametric learning approach (CORN) by combining the correlation driven sample selection and log-optimal utility function and showed its superior empirical performance over previous three combinations.…”

“…Data from other types of markets, such as high frequency intra-day quotes and Forex markets, are either too expensive or hard to obtain and process, and thus may reduce the experimental reproducibility. Summarized in Table 4, we employ six real and diverse datasets from several financial markets 11 The first dataset, "NYSE (O)", is one "standard" dataset pioneered by Cover [14] and followed by others [37,8,1,27,30] indices, which may be potentially applicable to "Fund on Fund" (FOF) 15 . As a remark, although we numerically test the proposed algorithms on stock and ETF markets, we note that the proposed strategy could be generally applied to any types of financial markets.…”

“…B K : Nonparametric kernel-based moving window strategy with W = 5, L = 10 and threshold c = 1.0, which has the best empirical performance according to Györfi et al [27]; 9. B NN : Nonparametric nearest neighbor-based strategy with parameters W = 5, L = 10 and p = 0.02+0.5 −1 L−1as the authors suggested[30];…”