We study the effects of central bank balance sheet policies—namely, quantitative easing and foreign exchange interventions—in a model where people form expectations through an iterative level-k thinking process. We emphasize two main theoretical results. First, under a broad set of conditions, central bank interventions are effective under level-k thinking, while they are neutral in the rational expectations equilibrium. Second, when preferences exhibit constant relative risk aversion, asset purchases increase aggregate output if they target assets with pro-cyclical returns but reduce it if asset returns are counter-cyclical. Finally, we empirically show that forecast errors about future asset prices are predictable by balance sheet interventions, a property that differentiates our channel from popular alternatives, such as portfolio-balance and signaling channels.