We provide an accurate closed-form expression for the expected shortfall of linear portfolios with elliptically distributed risk factors. Our results aim to correct inaccuracies that originate in and are present also in at least thirty other papers referencing it, including the recent survey on...

We provide an accurate closed-form expression for the expected shortfall of linear portfolios with elliptically distributed risk factors. Our results aim to correct inaccuracies that originate in Kamdem (2005) and are present also in at least thirty other papers referencing it, including the...

Correct specification of a conditional quantile model implies that a particular conditional moment is equal to zero. We nonparametrically estimate the conditional moment function via series regression and test whether it is identically zero using uniform functional inference. Our approach is...