Measurement of Factor Strenght: Theory and Practice

This paper proposes an estimator of factor strength and establishes its consistency and asymptotic distribution. The estimator is based on the number of statistically significant factor loadings, taking multiple testing into account. Both cases of observed, and unobserved factors are considered. The small sample properties of the proposed estimator are investigated using Monte Carlo experiments. It is shown that the proposed estimation and inference procedures perform well, and have excellent power properties, especially when the factor strength is sufficiently high. Empirical applications to factor models for asset returns show that out of 146 factors recently considered in the literature, only the market factor is truly strong, while all other factors are at best semi-strong, with their strength varying considerably over time. Similarly, we only find evidence of semi-strong factors using a large number of U.S. macroeconomic indicators.