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Abstract:
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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.
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