This paper aims at investigating first, the (possibly time-varying) empirical relationship between price and financial stability, and second, the effects of some macro and policy variables on this relationship in the United States and the Eurozone. Three empirical methods are used to examine the relevance of A.J. Schwartz's “conventional wisdom” that price stability would yield financial stability. Using simple correlations and VAR and Dynamic Conditional Correlations, we reject the hypotheses that price stability is positively correlated with financial stability and that the correlation is stable over time. The latter result and the analysis of the determinants of the link between price stability and financial stability cast some doubt on the appropriateness of the “leaning against the wind” monetary policy approach.