Market efficiency in the age of big data

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.