• Doron Avramov, Si Cheng, and Lior Metzker

Machine Learning versus Economic Restrictions: Evidence from Stock Return Predictability


Financial economists have uncovered a plethora of firm characteristics that forecast stock returns in the cross section. However, recent work has challenged the credibility of such predictable patterns. For instance, Hou, Xue, and Zhang (2018) show that 82% of the 452 anomalies turn insignificant (at the 1% level) upon excluding microcap stocks as well as employing value-weighted returns. There is also mounting evidence that anomalies extract the sheer part of their profitability from the short leg of the trade. Notably, the majority of predictable patterns have attenuated following the decimalization in 2001 due to increased market liquidity and arbitrage activity in U.S. equity market.

Counter to this ‘anomaly-challenging’ strand of literature, there has been an emerging body of work that reports outstanding investment profitability by employing various machine learning methods. Machine learning offers a natural way to accommodate high-dimensional predictor set and flexible functional forms and employs “regularization” methods to select models, mitigate overfitting biases, and uncover complex patterns and hidden relationships (Gu, Kelly, and Xiu 2019) (GKX). Thus, while individual predictive signals tend to attenuate over time, machine learning techniques can still combine multiple, possibly weak, sources of information into a meaningful composite signal.

Our recent paper,"Machine Learning versus Economic Restrictions: Evidence from Stock Return Predictability," comprehensively analyzes the relatively unexplored territory of whether machine learning methods clear sensible economic restrictions in empirical finance, as well as the economic grounds of investment decisions advocated by the seemingly opaque machine learning methods. We first implement neural network with three hidden layers as in GKX, and then follow Chen, Pelger, and Zhu (2019) (CPZ) to incorporate no-arbitrage conditions into multiple connected neural networks. Both deep learning methods account for a large number of firm characteristics and macroeconomic predictors as well as non-linear interaction terms, and deliver superior performance comparing with competing machine learning methods and benchmark predictive models.

We analyze a large sample of U.S. stocks between 1987 and 2017. We find that machine learning methods often fail to clear standard economic restrictions in empirical finance, such as value-weighting returns and excluding microcaps or distressed firms. In the full sample, the value-weighted portfolio payoff declines by 47% (43%) across all performance measures for GKX (CPZ) method comparing with equal-weighted payoff. Once imposing further economic restrictions, the value-weighted portfolio payoff based on GKX (CPZ) signal is 48% (62%) lower once excluding microcaps, 46% (72%) lower once excluding non-rated firms, and 70% (64%) lower once excluding distressed firms around credit rating downgrades. Similar evidence applies to machine learning method based on ridge regression, advocated by Kozak, Nagel, and Santosh (2019). Notably, machine learning methods require high turnover and taking extreme stock positions, therefore would struggle to leave alpha on the table in the presence of transaction costs.

To the extent that deep learning signals predict cross-sectional stock returns, the trading strategy is more profitable during periods of increasing limits to arbitrage, such as high investor sentiment, high market volatility, and low market liquidity. Focusing on the most restrictive subsample that excludes credit rating downgrades, deep learning signals fail to deliver meaningful risk-adjusted return.

We also examine the economic grounds for the two machine learning methods. We find that both deep learning signals identify stocks in line with most anomaly-based trading strategies. Specifically, stocks in the long position of a machine learning-based trading strategy are also small, value, illiquid and old stocks with low price, low beta, low past one-month return, high past 11-month return, low asset growth, low equity issuance, high operating performance, low credit rating coverage, low analyst coverage, and high earnings surprise. In addition, machine learning methods are more likely to specialize in stock picking than industry rotation.

Finally, our findings should not be taken as evidence against applying machine learning techniques in quantitative investing. Machine learning-based trading strategies display less downside risk and continue to generate positive payoff during the crisis period. Although the profitability of individual anomalies is primarily driven by short positions and often disappears in recent years, deep learning signals yield considerable profit in the long positions and remain viable in the post-2001 period. This could be particularly valuable for real-time trading, risk management, and long-only institutions.

The collective evidence shows that machine learning techniques face the usual challenge of cross-sectional return predictability, and the anomalous return patterns are concentrated in difficult-to-arbitrage stocks and in times of high limits to arbitrage. Therefore, even though machine learning offers unprecedented opportunities to improve investment outcomes, it is important to consider the common economic restrictions in assessing the success of a newly developed machine learning method.

Doron Avramov - IDC Herzliya

Si Cheng - Department of Finance, The Chinese University of Hong Kong

Lior Metzker - The Hebrew University of Jerusalem


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