A portfolio-invariant capital allocation scheme penalizing concentration risk

- A portfolio-invariant capital allocation scheme is proposed, in which the marginal capital contribution of a sector in the portfolio will not be affected by other sectors' exposure weights.
- The proposed capital allocation scheme penalizes the concentration risk in that marginal capital contribution is increasing in the exposure weight.
- Response surface methodology is adopted to construct the proposed capital allocation scheme.
- Portfolio-invariance and penalizing concentration risk are the unique features of the proposed capital allocation scheme compared to three other capital allocation schemes.

In the internal ratings-based (IRB) approach under the revised Basel II, a well-suited risk capital scheme should meet the desirable property of portfolio-invariance, without which a sector's marginal capital contribution can be different when the composition of other sectors in the portfolio varies. However, an allocation scheme of the risk measure VaR can be portfolio-invariant only under the asymptotically single-risk factor (ASRF) framework, which understates the economic capital of a highly concentrated portfolio in a multi-risk factor environment. This study proposes a portfolio-invariant capital allocation scheme of VaR of an asymptotically fine-grained portfolio in a multi-risk factor environment. To penalize the concentration risk, the strategy for the proposed capital allocation scheme is to estimate the second-order polynomial that approximates the risk measure VaR using the response surface methodology (RSM). Comparisons are made between the proposed capital allocation scheme to three other capital allocation schemes including the approximated Euler capital allocation scheme, and the schemes based on the approximated single-risk factor approach and the diversification factor approach, respectively. The results indicate that the proposed RSM allocation scheme is the only scheme among the four that is portfolio-invariant and penalizes the sectors with concentrated exposures.