In light of recent events, there have been proposals to establish a theory of financial system risk management analogous to portfolio risk management. One important aspect of portfolio risk management is risk attribution, the process of decomposing a risk measure into components that are attributed to individual assets or activities. The theory of portfolio risk attribution has limited applicability to systemic risk because systems can have richer structure than portfolios. We take a first step towards a theory of systemic risk attribution and illuminate the design process for systemic risk attribution by developing some schemes for attributing systemic risk in an application to deposit insurance.