Antinoise in U.S. equity markets

Abstract

There are many well documented behavioral biases in financial markets. Yet, analyzing U.S. equities reveals that less than 1% of returns are predictable in recent years. Given the high number of biases, why are returns not more predictable? We provide new evidence in support of one possible explanation. In the long-run, low correlations across signals that trigger biases may create sufficient antinoise which mutes more sizable patterns in returns. However, in the short-run, correlation spikes coincide with market volatility indicating that behavioral biases may become more visible during crises.

Keywords:

• Noise traders
• Behavioral economics
• Machine learning
• Asset pricing

JEL Classification:

• G41
• G11
• G14

Acknowledgments

We thank Frank Fabozzi, David-Michael Lincke, Stefan Nagel, Andrei Shleifer, Friedrich Wetterling, Karl Whelan as well as the editor, Jim Gatheral, and two anonymous referees for meaningful feedback that helped us improve our work. Annika Sophia Benecke and Ancil Crayton provided outstanding research assistance.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 In the Appendices, we show how this finding is robust to (A) varying the number of long-positions in the portfolio (B) using an alternative in-sample/out-of-sample split (C) rebalancing and forecasting at a weekly or monthly frequency (D) using different sets of boosting parameters (E) employing an alternative predictor normalization procedure.

2 The reason is that the chance of actions canceling out amid strong correlations between signals is lower. Intuitively, with strong correlations between signals, we would need the negative and positive signals to trigger quantitatively identical opposing bets in order for trades to cancel out in the aggregate—a highly unlikely scenario, which we verify in our Monte-Carlo simulations.

3 There is a large literature that argues that return predictability is caused by predictors representing risk premia. This interpretation would only strengthen our argument, as it would imply that the predictability we discover is the result of biases. The current scientific limitations in this field do not allow us to distinguish between these two sources of predictability. This is why we abstain further from investigating the deeper roots of predictability.

4 Our emphasis is on robustness in this context, as non-parametric methods such as Boosted Trees suffer from high variability when applied to noisy data, as with the relation between predictors and returns in financial markets. We also studied neural networks, but had difficulties obtaining robust results that could be replicated. The results from these networks vastly changed when using different random number seeds. Even averaging the results from hundreds of randomly drawn seeds did not ensure stability of the results.

5 As tree estimations are highly sensitive in noisy environments, we average the estimated models several hundred times. The computations are therefore quite demanding. Hence, we rely on a computationally efficient Boosting procedure from Microsoft called LightGBM in combination with an Amazon Web Services (AWS) cluster with 10 instances of 96 virtual CPUs with 768GB RAM each. The code is a mixture of C, C++, and Python. This combination allows us to complete the computations within a single day. For Boosting we use a set of standard parameters. The results under alternative boosting parameters are reported in Appendix 4.

6 To generate a correlation matrix with a bimodal distribution, we follow a simple three step procedure: (i) generate a symmetric random matrix $\mathbf{A}$, where each column is drawn from a normal distribution and add a fixed constant premultiplied by a random value from a normal distribution which later governs the shape of the distribution, (ii) $\mathbf{B}=\mathbf{A}{\mathbf{A}}^T$, (iii) $\mathbf{C}={\mathbf{D}}^{-0.5}\mathbf{B}{\mathbf{D}}^{-0.5}$, where $\mathbf{D}=\text{diag}\mathbf{B}$.