Relationship between the S&P 500 index and its constituents: A regime-switching copula approach and a model-free asymmetry test

Abstract

This paper examines the relationship between the returns of the S&P 500 index and its constituents, utilizing a regime-switching copula approach and a model-free asymmetry test. The asymmetry test reveals that, while the unconditional relationship between the raw returns of the index and each constituent is generally not asymmetric, asymmetry exists in the conditional relationship between their filtered returns. From the regime-switching copula approach, we find that such asymmetric conditional dependence is not consistently present over time; symmetric copulas, rather than asymmetric ones, are typically selected for the low dependence regime. It is also found that the asymmetric and high dependence regime tends to occur during periods of high market volatility. Finally, cross-sectional regressions show that the degree of asymmetric correlation is stronger for stocks with lower dividend yields and higher return volatilities.

Keywords: Copula, Regime-switching, Asymmetry test, Asymmetric correlation

JEL Classification: C32, C58, G19