The Joint Dynamics of Equity Market Factors

The four equity market factors from Fama and French (1993) and Carhart (1997) are perva- sive in academic empirical asset pricing studies and in applied portfolio allocation. However, the joint distributional dynamics of the factors are rarely studied. For investors basing strate- gies on the factors or using them to model the returns of a wider set of assets, proper risk management requires knowing the joint factor dynamics which we model. We ?nd striking ev- idence of asymmetric tail dependence across the factors. While the linear factor correlations are small and even negative, the extreme correlations are large and positive, so that the linear correlations drastically overstate the bene?ts of diversi?cation across the factors. We model the nonlinear factor dependence and explore its economic importance in a portfolio allocation experiment which shows that signi?cant economic value is earned when acknowledging the nonlinear dependence.