Characterizing the Tail-Risk of Factor Mimicking Portfolios

Abstract

By assuming that short-run returns are independent and identically distributed, it is straightforward to extrapolate short-run risks to longer horizons. However, by generalizing the variance-ratio test to include higher co-moments, we establish a significant and sizable intertemporal dependency in all higher moments of equity returns. The intertemporal dependency is strong enough to prevent the convergence to normally distributed returns, at least up to a five-year holding period. We also demonstrate that the intertemporal dependency is both horizon \emph{and} portfolio-specific. Consequently, the common practice of extrapolating the short-run risk by assuming independent and identically distributed returns will severely bias the expected long-run risk.

Keywords: intertemporal dependency, risk factors, skewness, kurtosis, bootstrap

JEL Classification: G11, G12, C22, C12, C15, C58