Tail value of a distribution is important for investors and risk managers as tail events could have a devastating effect on investment returns. Most studies on risk and return relationship are based on ordinary least squares (OLS) regression. OLS regression is mainly based on the mean values of the covariates and is not efficient in evaluating tailed distributions. To capture such tailed events, this study used quantile regression. In contrast to OLS regression, quantile regression estimates the conditional median or the conditional quantile of the dependable variables for the given independent variables. The present study compares the Fama-French three factor coefficients estimates obtained from both OLS and quantile regression for 25 size-value sorted portfolios of BSE 500. The two techniques used, OLS and quantile regression, have provided significantly different insights for the coefficients of RM (market), SMB (size) and LMH (value). Further, the study plots coefficient of RM, SMB and LMH obtained from quantile regression across the quantiles and finds that the coefficients for RM, SMB and LMH vary significantly across the quantiles (0.05 to 0.95). The estimates obtained from both the OLS and quantile regression results in most of the cases clearly indicate the inefficiency of OLS over quantile regression in capturing the tailed distribution relationship between the dependent and independent variables. The study finds that the quantile regression estimates give much more information about the varying effect of predictor variables such as RM, SMB and LMH on the investment returns. Hence, the present study would help analysts and investors by providing more significant insights about the varying effects of the predictor variables over different quantiles in making investment decision and maximising returns.
