A new method for statistical arbitrage using eigendecomposition and deep learning

Abstract

This study proposes a new method for constructing statistical arbitrage strategies. Statistical arbitrage is an investment strategy derived from arbitrage. Both strategies exploit distorted relationships between asset prices. However, they differ in that arbitrage assumes a deterministic adjustment of distortions between asset prices, whereas statistical arbitrage assumes a stochastic adjustment of distortions. Therefore, the critical issue for trading strategies that target statistical arbitrage is whether we can stably operate the statistical arbitrage strategy. However, methods based on cointegration tests, which have often been used in previous studies of statistical arbitrage, do not necessarily construct stable portfolios. The main objective of this study is to overcome such problems. Specifically, we attempt to find stable portfolio components with the help of eigenvalue decomposition and improve the profitability and stability of portfolios using standard deep learning architectures such as GRUs and CNNs. Through numerical simulations using a dataset of stocks listed in the S&P 500, we first demonstrate the superiority of our method over conventional methods based on cointegration tests. Then, we verify that the method's performance can be improved with the help of deep learning.