Statistical Arbitrage Risk Premium by Machine Learning

TL;DR

This paper introduces a machine learning approach to estimate the statistical arbitrage risk premium (SARP) by constructing peer portfolios without knowing specific factors, revealing that unique stocks have higher SARP and excess returns.

Contribution

It develops a novel method using elastic-net to estimate SARP, linking peer-based residual risk to expected returns, and demonstrates its empirical significance.

Findings

High SAR stocks have 1.101% higher monthly SARP than low SAR stocks.

High SAR stocks have 0.710% higher monthly excess returns.

Average SAR is countercyclical across the market.

Abstract

How to hedge factor risks without knowing the identities of the factors? We first prove a general theoretical result: even if the exact set of factors cannot be identified, any risky asset can use some portfolio of similar peer assets to hedge against its own factor exposures. A long position of a risky asset and a short position of a "replicate portfolio" of its peers represent that asset's factor residual risk. We coin the expected return of an asset's factor residual risk as its Statistical Arbitrage Risk Premium (SARP). The challenge in empirically estimating SARP is finding the peers for each asset and constructing the replicate portfolios. We use the elastic-net, a machine learning method, to project each stock's past returns onto that of every other stock. The resulting high-dimensional but sparse projection vector serves as investment weights in constructing the stocks' replicate portfolios. We say a stock has high (low) Statistical Arbitrage Risk (SAR) if it has low (high) R-squared with its peers. The key finding is that "unique" stocks have both a higher SARP and higher excess returns than "ubiquitous" stocks: in the cross-section, high SAR stocks have a monthly SARP (monthly excess returns) that is 1.101% (0.710%) greater than low SAR stocks. The average SAR across all stocks is countercyclical. Our results are robust to controlling for various known priced factors and characteristics.