Using data for the major currencies from 1973 to 1994, we apply recent tests of asset price volatility to re-examine whether exchange rates have been excessively volatile with respect to the predictions of the monetary model of the exchange rate and of standard extensions that allow for sticky prices, sluggish money adjustment, and time-varying risk premia. Consistent with previous evidence from regression-based tests, most of the models that we examine are rejected by our volatility-based tests. In general, however, we find that exchange rates have not been excessively volatile relative to movements of their determinants, with respect to the predictions of even the most restrictive version of the monetary model. Alternative measures of “volatility”, however, may disguise the cause of rejection as excessive exchange rate volatility. This a Working Paper and the author(s) would welcome any comments on the present text. Citations should refer to a Working Paper of the International Monetary Fund, mentioning the author(s), and the date of issuance. The views expressed are those of the author(s) and do not necessarily represent those of the Fund.