  This paper proposes analytic forms of portfolio CoVaR and CoCVaR on the
normal tempered stable market model. Since CoCVaR captures the relative risk of
the portfolio with respect to a benchmark return, we apply it to the relative
portfolio optimization. Moreover, we derive analytic forms for the marginal
contribution to CoVaR and the marginal contribution to CoCVaR. We discuss the
Monte-Carlo simulation method to calculate CoCVaR and the marginal
contributions of CoVaR and CoCVaR. As the empirical illustration, we show
relative portfolio optimization with thirty stocks under the distress condition
of the Dow Jones Industrial Average. Finally, we perform the risk budgeting
method to reduce the CoVaR and CoCVaR of the portfolio based on the marginal
contributions to CoVaR and CoCVaR.
