This study investigates the relationship between idiosyncratic risk and return based on the model (GARCH)-in-mean for individual by individual securities in Tehran Stock Exchange during the period from 2001 to 2015. The evidence suggests that, on average, 27% of stocks experienced a significant relationship between idiosyncratic risk and return. This is the way that companies with a negative relationship comprise a far greater proportion than those with a positive relationship in changes with the proportion of all securities (19%). The results of investigating the effect of characteristics on the probability of a significant relationship between returns and idiosyncratic risk indicate that some characteristics influence the probability of a...