This paper shows that the recent trend of separating macroprudential and monetary policies (M&Ms) into two autonomous institutions is undesirable. A strategic (game of chicken type) conflict is likely to occur, whereby each M&M ignores exuberant credit booms, trying to induce the other institution to tighten conditions. This has been observed, for example, in Sweden and Norway after 2010. We postulate a generalised concept of stochastic leadership and argue that greater rigidities give the prudential authority the upper hand strategically on the central bank. We show how this leads to a second type of unpleasant monetarist arithmetic and costly economic fluctuations.