The term leverage effect refers to the observed relationship between an asset's volatility to be negatively correlated with the asset's returns. The study intended to find whether the volatility tendency increased when the stock markets experienced a fall and attempted to explore the heteroskedastic behavior of Indian equity market stocks by using the GARCH family models to examine the leverage effect that explained the asymmetric volatility of the automobile stocks listed on the NSE (National Stock Exchange). It attempted to find the effects of good and bad news on volatility in the Indian stock market during the extensive and crucial periods from April 24, 2003 to September 7, 2015, when the equity markets experienced three bull and three bear phases. The study used three different volatility estimators from the return series data of the selected stocks of NSE to account for the robustness in the analysis. The standard GARCH models were applied to study whether there was volatility during the study period ; hence, asymmetric volatility models, that is, EGARCH and TGARCH were employed to find out the leverage effect. The study reported an evidence of volatility, which exhibited the clustering and persistence of stocks. The return series of the stocks selected for the study were found to react on the good and bad news asymmetrically. The negative shocks to these stocks exhibited more volatility than the positive shocks of the same magnitude.