The U.S. dollar price of the U.K. pound sterling is tested for a speculative bubble, defined as a period with a nonzero median in excess returns. A nonparametric procedure is developed which controls for data mining over the period of flexible exchange rates and finds a negative bubble in the excess return to holding sterling rather than dollar assets during 1981-84. Possible interpretations are boot-strap equilibria (rational bubbles), asymmetric fundamentals, and nonrational expectations.