Portfolio-Invariant Capital Allocation Scheme Accounting for Concentration Risk Based on Response Surface Methodology

Abstract

The Euler allocation scheme is a well-suited risk management tool that meets the three axioms of capital allocation: diversification, continuity, and RORAC compatible. However, the Euler allocation scheme of the risk measure VaR meets the desirable property of portfolio-invariance only under the asymptotically single-risk-factor model (ASRF) framework. Without portfolio-invariance, the marginal capital contribution of a sector can be different when the composition of other sectors in the portfolio varies. This study proposes an approximated portfolio-invariant Euler allocation scheme of VaR in an asymptotically fine-grained portfolio under the Merton-type multi-factor (multi-sector) framework by adopting the response surface methodology (RSM). In the proposed scheme, to account for the concentration risk, a second-order canonical polynomial that approximates the risk measure VaR over the entire region where the sectors’ exposure weights are defined is estimated. Comparisons are made between the proposed RSM approach to two other approximated Euler allocation schemes in a seven-sector environment. It is hoped the proposed RSM can provide a sound capital allocation scheme under a multi-systemic-risk-factor environment to overcome the general critique of the revised Basel II based on the single-risk-factor framework.