A common component of Fama and French factor variances

Abstract

This is the first study that explicitly explores the risk of the Fama and French equity factors in terms of their realized variances. Our results show that realized factor variances exhibit strong power-law behavior. A striking commonality is that the power-law exponents are close to α ≈ 2 regardless of which factor variance is analyzed. Notably, our novel joint test designed to test Mandelbrot’s infinite variance hypothesis in the cross-section of realized factor variances shows that the null hypothesis of α = 1.9 cannot be rejected, which further corroborates the evidence that (a) there exist a common component governing factor variance risk, and (b) factor variance risk is statistically undefined. Further evidence derived from co-fractality analysis shows that (c) risk diversification appears to be very limited as factor variances tend to exhibit power-law behavior coincidently. We argue that our study has several theoretical and practical implications—especially due to the fact that factor investing reached $5 trillion in assets under management.