Estimating Statistical Arbitrage Risk Premiums with Elastic Net Peer Portfolios

Summary

This study proposes a way to estimate the return associated with an individual stock’s risk that is not shared with similar stocks, even when the underlying risk factors are unknown. It constructs a peer replication portfolio by projecting each stock’s historical returns onto the returns of other stocks. Elastic net produces sparse portfolio weights, and the gap between a stock and its peer portfolio represents its factor residual risk. The expected return on that residual is called the Statistical Arbitrage Risk Premium.

Stocks with lower peer-fit R-squared are classified as having greater statistical arbitrage risk. In the reported cross-sectional results, high-risk stocks have higher monthly residual premiums and excess returns than low-risk stocks; average risk across stocks is countercyclical. The authors say the results persist after controlling for known factors and firm characteristics. The excerpt does not describe implementation costs, portfolio turnover, or out-of-sample performance, so it does not show whether the measured premium is directly capturable after trading frictions.

Key ideas

• Peer portfolios can help hedge a stock’s factor exposure when the factors themselves are unknown.
• Elastic net projects each stock’s past returns onto other stocks to create sparse peer portfolio weights.
• A low peer-fit R-squared indicates greater stock-specific statistical arbitrage risk.
• The study reports higher residual premiums and excess returns for high-risk stocks.
• The reported relationships are robust to controls, but trading costs and out-of-sample results are not described.

Tags

# Statistical Arbitrage Risk Premium by Machine Learning


# Statistical Arbitrage Risk Premium by Machine Learning









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.