Instability of Factor Strength in Asset Returns

We study the problem of detecting structural instability of factor strength in asset pricing models for financial returns with observable factors. We allow for strong and weaker factors, in which the sum of squared betas grows at a rate equal to and slower than the number of test assets, respectively: this growth rate determines the strength of the corresponding factor. We propose LM and Wald statistics for the null hypothesis of stability and derive their asymptotic distribution when the break fraction is known, as well as when it is unknown and has to be estimated. We corroborate our theoretical results through a comprehensive series of Monte Carlo experiments. An extensive empirical analysis uncovers the dynamics of instability of factor strength in financial returns from equity portfolios.