Quantile Regression Analysis of the Asymmetric Return-Volatility Relation

Abstract

We use quantile regression to investigate the short-term return-volatility relation between stock index returns and changes in implied volatility index. Neither the leverage hypothesis nor the volatility feedback hypothesis effectively explains the asymmetric return-volatility relation. Instead, behavioral explanations, such as the affect and representativeness heuristics, are supported by our results, particularly in the short-term; the affect heuristic plays an important role. Moreover, in the context of an extreme volatility change distribution, the affect heuristic and time-pressure dominate. Thus, we observe strong negative and asymmetric relations between each volatility index and its corresponding stock market index. The asymmetry increases monotonically from the median quantile to the uppermost quantile (i.e., 95%); therefore, OLS regression underestimates this relation at upper quantiles. Additionally, the VIX presents the highest asymmetric return-volatility relation, followed by the VSTOXX, VDAX and VXN. Finally, the observed asymmetry is more pronounced with the new volatility index measure than with the old, at-the-money volatility index measure.

Keywords: Asymmetric return-volatility relation, implied volatility, index options, quantile regression, volatility index

JEL Classification: C21, G12, G13