On the Evaluation of Marginal Expected Shortfall

Abstract

In the analysis of systemic risk, Marginal Expected Shortfall may be considered to evaluate the marginal impact of a single stock on the market Expected Shortfall. These quantities are generally computed using log-returns, in particular when there is also a focus on returns conditional distribution. In this case, the market log-return is only approximately equal to the weighed sum of equities log-returns. We show that the approximation error is large during turbulent market phases, with a subsequent impact on Marginal Expected Shortfall. We then suggest how to improve the evaluation of Marginal Expected Shortfall by means of a second order approximation.

Keywords: Marginal Expected Shortfall, Log-Returns, Systemic Risk

JEL Classification: C18, C58, G10