Analyzing Idiosyncratic Risk and Returns Relationship based on Quantile Regression and Bayesian Approach

Financial researchers use different techniques to asses risk and explore its relationship with returns. Different results are why the relationship is known as “returns-idiosyncratic risk puzzle.” Statistical population consists of firms which are active in Tehran stock exchange. Time duration starts from 3 August 2013 and ends in 1 January 2017 This research uses panel-GARCH model to estimate idiosyncratic risk and then risk-returns relationship is studied based on quantile regression and Bayesian approach. The study shows that the relationship in lower quantiles is negative, in upper quantiles is positive and in median no relation observed. Therefore, results show that the relationship is nonlinear and based on returns distribution. This findings show that information that exists in distribution boundaries are important for financial data .Also, it is necessary to be captured by modeling and to be considered in interpreting the results. In addition, returns-idiosyncratic risk puzzle is solved.