Using firm-level weekly closing stock prices of Nigerian firms, this study gives a new insight into the possible asymmetry in exchange rate and stock prices relationship. The Linear ARDL (Pesaran et al., 2001) and Non-Linear ARDL (Shin et al., 2014) framework are adapted into panel data form to explore the responses of stock prices to exchange rate movements. Exchange rate is measured using Naira exchange value to US Dollar for the main analysis while Naira to Britain Pound Sterling is used for robustness check. Findings from the empirical analyses suggest that the relationship between exchange rate and stock prices is largely symmetry for most of the firms, except those in few sectors like conglomerates, consumer goods and financial services. Thus, this result supports empirical arguments that exposure of stock prices of firms in developing countries to exchange rate is identical in the long-run regardless of whether the domestic currency appreciates or depreciates.