The aim of this paper is to compare the conventional monetary model of the exchange rate with an alternative model, which incorporates a stock price measure and is based on Friedman's money demand function. These models are then compared using data from the UK, Canada and the USA, applying the Autoregressive Distributed Lag (ARDL) Bounds testing approach and the Phillips-Hansen approaches to cointegration. Although the results from the conventional monetary model are poor, the version which includes stock prices produces evidence of a long-run relationship, which has more appropriate long-run coefficients than the conventional model.