An Approach to Capital Allocation Based on Mean-Conditional-Value-At-Risk

In this paper, we propose an approach based on mean-conditional-value-at-risk (MCVaR) to Euler capital allocation via adjusting the probability level, which takes into account the different attitudes of investors towards risk by considering the optimistic coefficient. We obtain a new probability level so that the measure of MCVaR under the new probability level is equivalent to the measure of value-at-risk (VaR). We give nonparametric estimators for the new probability level and allocation, derive the asymptotic normality, and show that the estimators can converge at the standard rate. Finally, bootstrapping method is applied to the real data, and we compare the estimation results based on MCVaR with those based on VaR, which shows the effectiveness of our method