A large-dimensional test for cross-sectional anomalies: Efficient sorting revisited

Many researchers seek factors that predict the cross-section of stock returns. In finance, the key is to replicate anomalies by long-short portfolios based on their firm characteristics, with microcap biases alleviated via New York Stock Exchange (NYSE) breakpoints and value-weighted returns. In econometrics, the key is to include a covariance matrix estimator of stock returns for (mimicking) the portfolio construction. This paper marries these two strands of literature in order to test the zoo of cross-sectional anomalies by injecting size controls, basically NYSE breakpoints and value-weighted returns, into efficient sorting. We propose to use a covariance matrix estimator for ultra-high dimensions (up to 5,000) taking into account large, small and microcap stocks. We demonstrate that using a nonlinear shrinkage estimator of the covariance matrix substantially enhances the power of tests for cross-sectional anomalies: On average,..-statistics more than double. Furthermore, the proposed revisited efficient sorting method computes even highly significant factor portfolios net of transaction costs.