This paper asks whether the 'leverage effect -as defined by Black (1976) for stock markets- is also a characteristic of foreign exchange markets. The study focuses on five Latin American emerging markets which have adopted a floating exchange regime. It finds that the response of exchange rates to volatility shocks is characterized by long memory and symmetry in most countries. The response is asymmetric only in Brazil and Peru. A possible explanation for this asymmetry is the fear of floating' that induces side-effects on interest rates and inflation, which the market considers 'bad news'. The opposite direction of the asymmetry may be explained by the particular characteristics of each economy.