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The relationship between idiosyncratic risk and stock return has been debated for decades; this study reexamined this relationship in the Pakistani stock market by using the quantile regression approach along with the prospect theory.

The present study is quantitative, and secondary data obtained from an emerging market are used. The quantile regression method allows the estimates of idiosyncratic risk to vary across the entire distribution of stock returns, i.e. the dependent variable. In this study, the standard deviation of regression residuals from the Fama and French three-factor model was used to measure idiosyncratic risk. Convenience sampling is employed; the sample consists of 82 firms listed on the KSE-100 index, with 820 annual observations for the ten years from 2011 to 2020. After computing results by using quantile regression, the study's findings, ordinary least squares (OLS) and least sum of absolute deviation (LAD) regression techniques are also compared.

The quantile regression estimation results indicate that idiosyncratic risk is positively correlated with stock returns and that this relationship is contingent on whether prices are rising or falling. Consistent with the prospect theory, the finding suggests that stock investors tend to avoid risk when they anticipate a loss but are more willing to take risks when they anticipate a profit. The results of the OLS and LAD regressions indicate that the method typically employed in previous studies does not adequately describe the relationship between idiosyncratic risk and stock return at extreme points or across the entire distribution of stock return.

These empirical findings shed new light on the relationship between idiosyncratic risk and stock return in Pakistani stock market literature.