  Systemic risk refers to the risk that the financial system is susceptible to
failures due to the characteristics of the system itself. The tremendous cost
of systemic risk requires the design and implementation of tools for the
efficient macroprudential regulation of financial institutions. The current
paper proposes a novel approach to measuring systemic risk.
  Key to our construction is a rigorous derivation of systemic risk measures
from the structure of the underlying system and the objectives of a financial
regulator. The suggested systemic risk measures express systemic risk in terms
of capital endowments of the financial firms. Their definition requires two
ingredients: a cash flow or value model that assigns to the capital allocations
of the entities in the system a relevant stochastic outcome; and an
acceptability criterion, i.e. a set of random outcomes that are acceptable to a
regulatory authority. Systemic risk is measured by the set of allocations of
additional capital that lead to acceptable outcomes. We explain the conceptual
framework and the definition of systemic risk measures, provide an algorithm
for their computation, and illustrate their application in numerical case
studies.
  Many systemic risk measures in the literature can be viewed as the minimal
amount of capital that is needed to make the system acceptable after
aggregating individual risks, hence quantify the costs of a bail-out. In
contrast, our approach emphasizes operational systemic risk measures that
include both ex post bailout costs as well as ex ante capital requirements and
may be used to prevent systemic crises.
