Converting Tail-VaR to VaR: An econometric study

This paper studies the link between two popular measures of risk, that are the Value-at-Risk (VaR) and the Tail-VaR (TVaR). We study how the TVaR and VaR are related through their risk levels and characterize the underlying distributions under which this relationship is linear. A large portion of this paper is devoted to the related econometric analysis, such as the estimation and test of this relationship. We apply the results to currency portfolios and observe that this linearity relationship between the TVaR and VaR is a surprisingly common phenomenon for the portfolios considered for both historical and conditional risk measures.