Empirical Asset Pricing with Many Test Assets

We formulate the problem of estimating risk prices in a stochastic discount factor (SDF) model as an instrumental variables regression. The IV estimator allows efficient estimation for models with non-traded factors and many test assets. Optimal instruments are constructed using a regularized sparse first stage regression. In a simulation study, the IV estimator is close to the infeasible GMM estimator in a setting with many assets. In an empirical application, the tracking portfolio for consumption growth appears strongly correlated with consumption news. It implies that consumption is a priced factor for the cross-section of excess equity returns. A similar regularized regression, projecting the SDF on test assets, leads to an estimate of the Hansen-Jagannathan distance, and identifies portfolios that maximally violate the pricing implications of the model.