Null hypothesis

Big data

Bayesian probability

Efficient-market hypothesis

Biology

Statistics

Contrast (vision)

Chromatography

Predictability

Stock market

Market efficiency

Economics

Data mining

Computer science

Business

Paleontology

Mathematics

Econometrics

Horse

Artificial intelligence

Financial economics

Chemistry

Sample (material)

Journal of Financial Economics

Modern investors face a high-dimensional prediction problem: thousands of observable variables are potentially relevant for forecasting. We reassess the conventional wisdom on market efficiency in light of this fact. In our equilibrium model, N assets have cash flows that are linear in J characteristics, with unknown coefficients. Risk-neutral Bayesian investors learn these coefficients and determine market prices. If J and N are comparable in size, returns are cross-sectionally predictable ex post. In-sample tests of market efficiency reject the no-predictability null with high probability, even though investors use information optimally in real time. In contrast, out-of-sample tests retain their economic meaning.

Market efficiency in the age of big data