Asymmetric relationship between implied volatility, index returns and trading volume: an application of quantile regression model

The study explored a vital issue on market microstructure that is the relationship between volatility, index returns and trading volume within the Indian stock market. The daily closing prices of select indices, from 2 March 2009 to 31 July 2018, were taken. The investor’s fear index India Volatility Index (VIX) was used as an implied volatility measure popularly the investor’s fear index, whereas Nifty50 daily returns and trading volume were considered. Toda–Yamamoto causality test provided limited information about the causal relationship among the variables. The results of the Toda–Yamamoto test captured only the central values of the dependent variable’s distribution; therefore, quantile regression models (QRM) were estimated. Through QRM, the asymmetric impact of returns was estimated on volume and volatility changes. The asymmetric relationship of stock returns with changes in volatility and volume distribution was found significant. It was found to be stronger at extreme ends of the dependent variable’s distribution. The study supports the behavioural justification for a contemporaneous negative return–volatility relationship but conditionally. Evidence of investor’s heterogenous beliefs is found. The evidence of leverage effect was also significant for the lagged period. The contemporaneous negative relationship was found between volatility and volume changes highlighting that the investors in Indian markets are risk-averse. But the positive lagged effect of changes in volatility on trading volume supports sequential arrival of information hypothesis and affirmed the presence of noise traders. They make the information arrival sequential and allow the slow diffusion of information. India VIX potentially can be used for portfolio hedging purposes.