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, assets have cash flows that are linear in characteristics, with unknown coefficients. Risk-neutral Bayesian investors learn these coefficients and determine market prices. If and 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