Systemic and Systematic Risks-Driven Marginal Expected Side-effect

System-wide stress events (SWSE) can occur in social, economic, financial, environmental, medical, and many other systems. An SWSE can cause severe damage to some or all members in the system. Understanding and measuring the marginal expected side-effect (MES) for each member caused by an SWSE can lead to better risk management and decision-making. This paper defines an SWSE as a scenario in which either a representative systematic index or the index of the worst-performing member (systemic index) in a system exceeds its respective prescribed threshold. This broadened SWSE definition introduces an innovative systemic and systematic risks-driven marginal expected side-effect (SYS2MES) index. We construct estimators for SYS2MES and establish their asymptotic theories within the multivariate extreme value theory framework, including tail dependent and tail independent scenarios, thereby enhancing its applicability to a wide range of models. The finite sample performance of the estimators is investigated in a simulation study. The advantages of SYS2MES are demonstrated by studying its application to Dow Jones’ 30 stocks and COVID-19 data in the United States, yielding more meaningful results than existing approaches.