An approach to capital allocation based on mean conditional value-at-risk

It is well known that the convergence rate of classic nonparametric estimators for Euler capital allocation based on value-at-risk is lower than the standard rate. In this paper, we propose an alternative approach to Euler capital allocation, based on mean conditional value-at-risk (MCVaR), that involves adjusting the probability level so the total capital remains equal to the reference quantile-based capital level. The optimistic coefficient of the model incorporates the risk preferences of investors into the MCVaR-based allocation. We apply the nonparametric estimation for the new probability level and the new allocation, which could converge at the standard rate. Then, we derive the asymptotic normality of the proposed nonparametric estimator. In order to assess the performance of the method, we discuss the nonoverlapping block bootstrap and moving block bootstrap methods to real-world data and compare the estimates based on the MCVaR of various optimistic coefficients for the new level with those based on value-at-risk.