Using an analytically tractable heterogeneous agent New Keynesian model, we show that whether incomplete markets resolve New Keynesian “paradoxes” depends on the cyclicality of income risk. Incomplete markets reduce the effectiveness of forward guidance and multipliers in a liquidity trap only with procyclical risk. Countercyclical risk amplifies these “puzzles.” Procyclical risk permits determinacy under a peg; countercyclical risk may generate indeterminacy even under the Taylor principle. By affecting the cyclicality of risk, even “passive” fiscal policy influences the effects of monetary policy.