The author re-examines the demand-for-money theory in an intertemporal optimization model. The demand for real money balances is derived to be a function of real income and the rates of return of all financial assets traded in the economy. Unlike the traditional money-demand relation, however, where the elasticities are assumed to be constant, the coefficients of the explanatory variables are not constant and depend on the degree of an agent's risk aversion, the volatilities of the price level and income, and the correlation of asset returns. The author shows that the response of households to increased volatilities in the financial markets, economic activity, and prices cannot be predicted, because a rise in general uncertainties has an ambiguous impact on the demand for money. This suggests that increased uncertainty is not very helpful for the planning decisions of households, because the optimal level of money holdings in the period of uncertainty cannot be ascertained.