The goal of this paper is to explain a recent regularity observed in economies in which central banks have moved from using a money aggregate as the instrument for the conduction of monetary policy towards a short-term interest rate (for example Peru in 2002). In particular, in those economies we observe that, after the change in the policy instrument, there is a decrease in the macroeconomic volatility accompanied by a reduction in the average level of both inflation and interest rates vis-à-vis an increase in the average level of money aggregates (an increase in the money demand). In order to explain the previous stylized fact, a second order solution of a general equilibrium model for a small open economy is evaluated. By analyzing the second order solution we relax the assumption of certainty equivalence which permits consider the role of uncertainty (risk) in the equilibrium solution of the economy. The previous solution takes into account the reduction of macroeconomic uncertainty (risk) as a consequence of changing the instrument (from money aggregates to interest rate rules), helping to explain the stylized fact. Our findings show that the use of the interest rate as the instrument for the conduction of monetary policy induces a reduction of macroeconomic risks. In turn, the previous reduction has driven a decrease in the average level of interest rates and inflation which is consistent with the increase in the demand for money observed in Peru in the 2000s. Hence, the recent increase in the growth rate of money aggregates should not be linked, whatsoever, to higher inflation rates.