The paper studies the compliance of the CZK - EUR exchange rate with the uncovered parity of returns on assets denominated in the two named currencies. A comparison with the same property for the euro-dollar rate is made. An uncovered total return parity (UTRP) formula is derived from the equilibrium in a portfolio optimization model with liquidity constraints. It is shown that the uncovered parity of total returns, and not of short-term money market rates, is a natural outcome of stochastic equilibrium asset pricing models that generalize the International Consumption-based Capital Asset Pricing Model. Accordingly, the traditional uncovered interest rate parity should be replaced by UTRP in empirical analysis. UTRP tests for the CZK/EUR and the USD/EMU currency pairs are conducted using yields of long-term government bond yields. UTRP typically holds, although the time horizons and measures of exchange rate movements, for which it becomes visible, may vary.