Using security-level holdings of bond and equity mutual fund shares, we study how different investor types respond to inflation shocks. We distinguish between cost-push (“bad”) inflation and demand-driven (“good”) inflation. Using expectations from the Survey of Professional Forecasters as a proxy for sophisticated investors’ beliefs, we show that bad inflation shocks induce stagflationary expectations, whereas good inflation shocks raise expected inflation while also improving expected economic activity. Household expectations move in a remarkably similar way. We then show that portfolio rebalancing is broadly consistent with these shifts in expectations, although investors differ in both the speed and the intensity of their responses. Our identification compares flows across fund shares held by different investors within the same fund, holding the underlying portfolio risk fixed. Investment funds rebalance rapidly and strongly following inflation shocks. Insurance companies behave as steady-hand investors, with overall more muted responses. Household rebalancing responses are smaller in magnitude but more persistent. These findings shed light on how inflation shocks are transmitted to stock and bond prices.