Kalman Filtering and Online Learning Algorithms for Portfolio Selection

Abstract

This paper proposes a new online learning algorithms for portfolio selection based on alternative measure of price relative called the Cyclically Adjusted Price Relative (CAPR). The CAPR is derived from a simple state-space model of stock prices and we prove that the CAPR, unlike the standard raw price relative widely used in the machine literature, has well deÂ…ned and desirable statistical properties that makes it better suited for nonparametric mean reversion strategies. We find that the statistical evidence of out-of-sample predictability of stock returns is stronger once stock price trends are adjusted for high persistence. To demonstrate the robustness of our approach we perform extensive historical simulations using previously untested real market datasets. On all datasets considered, our proposed algorithms significantly outperform their comparative benchmark allocation techniques without any additional computational demand or modeling complexity.

Online Learning, Portfolio Selection, Kalman Filter, Price Relative