The Joint Dynamics of Equity Market Factors

59 Pages Posted: 10 Sep 2011 Last revised: 17 Mar 2014

See all articles by Peter Christoffersen

Peter Christoffersen

University of Toronto - Rotman School of Management; Copenhagen Business School; Aarhus University - CREATES

Hugues Langlois

HEC Paris - Finance Department

Date Written: April 18, 2012


The four equity market factors from Fama and French (1993) and Carhart (1997) are pervasive 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 strategies 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 find striking evidence 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 benefits of diversification across the factors. We model the nonlinear factor dependence and explore its economic importance in a portfolio allocation experiment which shows that significant economic value is earned when acknowledging the nonlinear dependence.

Keywords: Factors, threshold correlation, copulas, portfolio optimization, asymmetry.

JEL Classification: G11, G12

Suggested Citation

Christoffersen, Peter and Langlois, Hugues, The Joint Dynamics of Equity Market Factors (April 18, 2012). Journal of Financial and Quantitative Analysis (JFQA), 2013, Vol. 48, No. 5, pp. 1371–1404, Available at SSRN: or

Peter Christoffersen (Contact Author)

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5P 3C4
416-946-5511 (Phone)

Copenhagen Business School

Solbjerg Plads 3
Frederiksberg C, DK - 2000

Aarhus University - CREATES

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C

Hugues Langlois

HEC Paris - Finance Department ( email )


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