Detecting Anomalies: The Relevance and Power of Standard Asset Pricing Tests

The two standard approaches for identifying capital market anomalies are cross-sectional coefficient tests, in the spirit of Fama and MacBeth (1973), and time-series intercept tests, in the spirit of Jensen (1968). A new signal can pass the first test, which we label a “score anomaly,” it can pass the second test as a “factor anomaly,” or it can pass both. We demonstrate the relevance of each to a mean-variance optimizing investor facing simple transaction costs that are constant across stocks. For a risk-neutral investor facing transaction costs, only score anomalies are relevant. For a risk-averse investor facing no transaction costs, only factor anomalies are relevant. In the more general case of risk aversion and transaction costs, both tests matter. In extensions, we derive modified versions of the basic tests that net out anomaly execution costs for situations where the investor faces capital constraints, a multi-period portfolio choice problem, or transaction costs that vary across stocks. Next, we measure the econometric power of the two tests. Time-series factor tests have uniformly lower power than equivalent cross-sectional score tests, with the gap increasing in the in-sample Sharpe ratio of the incumbent factor model. New factor anomalies are successively harder to detect. There is a lower natural limit on the number of anomalies, after which new factors can no longer be verified. Meanwhile, for an investor facing transaction costs, where score anomalies are also applicable, there is a higher natural limit on the number of anomalies that can be statistically validated as relevant.