Open AccessIt has been viewed as an unsolved puzzle that for only a small number of firms a significant impact of foreign exchange rate risk on firm value could be detected empirically even though the financial theory strongly supports that a change in the exchange rate should affect the value of the firm. We explain it by the facts that (i) previous studies mostly investigated mature and non-open economies and (ii) they mostly concentrated on one part of the relationship between exchange exposure and firm value. Our empirical results are based on a sample of 107 Taiwanese non-financial firms from 6th June 1990 to 14th July 2010 and the bilateral exchange rate USD / TWD. We use an orthogonalized model with conventional augmented CAPM specifications and asymmetric variables. Because the exposure cannot be viewed as a single coefficient, we also add GJR GARCH specifications to measure the asymmetric profile of the firms and the existence of asymmetric volatility of returns. Our findings show a strong exposure for most of our sample with exclusively a negative exposure (Taiwanese firms benefit from an appreciation of the domestic currency). We also find that exposure is non-linear. Moreover, the asymmetric profiles of the firms modify significantly their exposure. Finally, a high percentage of our monthly sample is affected by a positive coefficient of volatility of the stock returns associated with exchange rates changes but conversely for our daily sample. It means that the leverage of positive and negative shocks changes with the time horizon.