A common assumption in standard economic models is that agents are risk-averse and prudent, and it is often argued that prudence is necessary to generate precautionary savings. This paper shows that prudence is not necessary to generate precautionary savings in small open economy models with more than two periods. A new class of preferences, which enables the isolation of the effect of risk aversion on precautionary savings, is introduced. The effects of changes in risk aversion, interest rates, and persistence and volatility of shocks on average asset holdings are qualitatively identical to the ones observed for standard constant-elasticity-of-substitution preferences. These results show that the almost universal assertion in the literature - that only prudent consumers can generate positive levels of precautionary savings - is simply incorrect.