Static marginal expected shortfall: Systemic risk measurement under dependence uncertainty

Abstract

Measuring the contribution of a bank or an insurance company to overall systemic risk is a key concern, particularly in the aftermath of the 2007--2009 financial crisis and the 2020 downturn. In this paper, we derive worst-case and best-case bounds for the marginal expected shortfall (MES) -- a key measure of systemic risk contribution -- under the assumption that individual firms' risk distributions are known but their dependence structure is not. We further derive tighter MES bounds when partial information on companies' risk exposures, and thus their dependence, is available. To represent this partial information, we employ three standard factor models: additive, minimum-based, and multiplicative background risk models. Additionally, we propose an alternative set of improved MES bounds based on a linear relationship between firm-specific and market-wide risks, consistent with the Capital Asset Pricing Model in finance and the Weighted Insurance Pricing Model in insurance. Finally, empirical analyses demonstrate the practical relevance of the theoretical bounds for industry practitioners and policymakers.