Abstract: Since downside risk measures such as VaR and CVaR have flaws in characterizing the variance of tail data and measuring extreme financial risk, the tail conditional variance, the variance of loss beyond VaR, motivated by tail conditional expectation is studied in this paper. The explicit solution of the tail conditional variance of portfolio under a mixture of multivariate elliptically distributions and an important heavy tail distribution in modeling financial data are obtained. Some numerical examples and empirical application on the optimal portfolio selection are finally provided to illustrate the proposed method. The results can help investors to better control extreme portfolio risk.

Key words: portfolio, risk measure, tail conditional variance, mixture elliptically distribution