A Tale of Six Factors: An Empirical Analysis on the Tail Distributions of Factor Returns

Abstract

This thesis uses extreme value theory to analyze the tail distributions for each of the factors in the Fama-French five factor model and Carhart’s momentum factor. The analysis is conducted on the unconditional return distributions for each factor and the conditional return distributions after a GARCH(1,1) model is applied to control for the clustering of volatility for each factor. With asset returns, empirical studies reported in the literature indicate that the main cause of fat tails is attributable to volatility clustering. Performing the same analysis on factor returns in this study, I find the same to be true of factor returns. That is, the main cause of fat tails in factor returns is attributable to the clustering of volatility. After volatility clustering is controlled for using the GARCH technique, the tail distributions for all factors, except the market factor, can be fit by a generalized Pareto distribution that assumes exponential tail decay. However, after controlling for the clustering of volatility, the market factor exhibits normal tails, which is inconsistent with the literature that has focused on the tail distribution of stock returns. This study has implications for financial risk management and for portfolio selection theory.