The effect of unexpected volatility shocks on intertemporal risk-return relation

Abstract

We suggest that an unexpected volatility shock is an important risk factor toinduce the intertemporal relation, and the conflicting findings on the relationcould be attributable to an omitting variable bias resulting from ignoring the effect of an unexpected volatility shock on the relation. With the effect of an unexpected volatility shock incorporated in estimation, we find a strong positive intertemporal relation for the US monthly excess returns for 1926:12–2008:12. We reexamine the relation for the sample period studied by Glosten, Jagannathan, and Runkle (Journal of Finance 48, 1779–1801, 1993) and find that their sample period is indeed characterized by a positive (negative) relation under a positive (negative) volatility shock with the effect of a volatility shock incorporated in estimation.We also find a significant link between the asymmetric mean reversion and the intertemporal relation in that the quicker reversion of negative returns is attributed to the negative intertemporal relation under a prior negative return shock. For estimations we employ the ANST-GARCH model that is capable of capturing the asymmetric volatility effect of a positive and negative return shock. The key feature of the model is the regime-shift mechanism that allows a smooth, flexible transition of the conditional volatility between different states of volatility persistence. The regime-switching mechanism is governed by a logistic transition function that changes values depending on the level of the previous return shock. With a negative (positive) return shock, the conditional variance process is described as a high (low)-persistence-in-volatility regime. The ANST-GARCH model describes the heteroskedastic return dynamics more accurately and generates better volatility forecasts.​