Tests of Asset Pricing Models with A Large Number of Assets

We propose both statistical and economic asset pricing tests that extend the well-known Gibbons, Ross, and Shanken (1989) test to allow for many assets whose dimensionality exceeds sample size. Empirically, we find that the tests reject six well-known asset pricing models at the stock level. In particular, the economic test provides a real time profitable trading strategy that exploits mispricing, and the mispricing patterns are similar across all the models. The significant profitability is unexplained by limits-to-arbitrage, prospect theory, and expectation extrapolation, suggesting that new factors are needed to better understand the cross section of stock returns.