The time is central to much of financial economics, forming the basis of option-pricing theory (Black and Scholes 1973; Merton 1973b) and a number of intertemporal valuation models (Merton 1973a; Breeden 1979). The continuous time model involves two sets of assumptions. The first concerns the characteristics of the market (absence of frictions, continuous trading opportunities, and so forth); the second concerns the stochastic process governing prices. These assumptions are usually introduced as if they were independent; that is, as if the characteristics of the market did not constrain the nature of the stochastic process. In this paper we ask the following question: If trading is continuous and frictionless, what classes of stochastic processes may be chosen to describe prices which also admit equilibrium? Attention will be restricted to processes whose sample paths are continuous. The most frequently employed continuous processes are diffusions, all intimately related to Brownian motion. Among the characteristics of such processes is that their sample paths display unbounded variation. (Variation, to be defined rigorously in Sec. III, represents the cumulative upward and downward displacement of the function in question.) This property makes the asThe time in finance makes assumptions both about the characteristics of the market (absence of frictions, continuous trading opportunities, and so forth) and about the stochastic process that governs prices. Usually, these assumptions are introduced as if they were independent, that is, as if the characteristics of the market did not constrain the choice of stochastic process. In this paper we ask the following question: If trading is continuous and frictionless, what classes of stochastic process may be chosen that also admit equilibrium? We restrict our attention to processes whose sample paths are continuous. Our conclusion is given by the title of the paper.