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Activity Number: 59 - Nonparametric Modeling
Type: Contributed
Date/Time: Monday, August 3, 2020 : 10:00 AM to 2:00 PM
Sponsor: Section on Nonparametric Statistics
Abstract #312256
Title: A Regression Approach to Expected Shortfall
Author(s): Yuanzhi Li* and Xuming He
Companies: University of Michigan and University of Michigan
Keywords: two-step regression; conditional value-at-risk; super-quantile; risk quantification; covariate effect

Expected shortfall (ES), also known as the conditional value-at-risk (CVaR), is a popular measure of risk in finance and other decision-making processes. The ES measures the average value of a response, knowing that it exceeds a given quantile level. Despite its popularity, there have been few attempts to model and estimate the effect of covariates on the ES through what is often called super-quantile regression. In this talk, we present a two-step approach for super-quantile regression. We first estimate the conditional quantile function, followed by the second step of fitting the least-squares regression to the data above the quantile function. We show that this approach consistently estimates the super-regression coefficients in heteroscedastic linear models. We further develop a statistical inference procedure for the super-quantile regression. Compared with the existing approaches in the literature, this method is remarkably easy to implement, and yet performs favorably in a wide variety of settings.

Authors who are presenting talks have a * after their name.

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