This paper develops a framework for measuring, allocating and managing systemic risk. SystRisk, our measure of total systemic risk captures the a priori cost to society for providing tail-risk insurance to the financial system. Our allocation principle distributes the total systemic risk among individual institutions according to their size-shifted marginal contributions. To describe economic shocks and systemic feedback effects we propose a reduced form stochastic model that can be calibrated to historical data. We also discuss systemic risk limits, systemic risk charges and a cap and trade system for systemic risk.