In an influential paper, Engel and West (2005) claim that the near random-walk behavior of nominal exchange rates is an equilibrium outcome of a variant of present-value models when economic fundamentals follow exogenous first-order integrated processes and the discount factor approaches one. Subsequent empirical studies further confirm this proposition by estimating a discount factor that is close to one under distinct identification schemes. In this paper, I argue that the unit market discount factor implies the counterfactual joint equilibrium dynamics of random-walk exchange rates and economic fundamentals within a canonical, two-country, incomplete market model. Bayesian posterior simulation exercises of a two-country model based on post-Bretton Woods data from Canada and the United States reveal difficulties in reconciling the equilibrium random-walk proposition within the two-country model; in particular, the market discount factor is identified as being much lower than one.