This paper proposes that computational complexity generates noise. The same asset is often held for completely different reasons by many funds following a wide variety of threshold-based trading rules. Under these conditions, we show it can be computationally infeasible to predict how these various trading rules will interact with one another, turning the net demand from these funds into unpredictable noise. This noise-generating mechanism can operate in a wide range of markets and also predicts how noise volatility will vary across assets. We confirm this prediction empirically using data on exchange-traded funds. (JEL G00, G02, G14). Received May 28 2019; editorial decision December 16 2020 by Editor Thierry Foucault.

The anomaly zoo has caused many to question whether researchers are using the right tests of statistical significance. But even if researchers are using the right tests, they will still draw the wrong conclusions from their econometric analyses if they start out with the wrong priors (i.e., if they start out with incorrect beliefs about the ex ante probability of encountering a tradable anomaly, the “anomaly base rate”). We propose a way to estimate it by combining two key insights: Empirical Bayes methods capture the implicit process by which researchers form priors about the likelihood that a new variable is a tradable anomaly based on their past experience, and under certain conditions, a one-to-one mapping exists between these prior beliefs and the best-fit tuning parameter in a penalized regression. The anomaly base rate varies substantially over time, and we study trading-strategy performance to verify our estimation results.