Hierarchical allocation method for capital: a general method

Min Wu and Yimin Yang

Abstract

This paper introduces a novel approach for allocating a bank’s risk capital across individual portfolios and transactions. This allocation is pivotal for various capital applications, including risk-adjusted return on capital and lending decisions. Our proposed method, the hierarchy allocation method (HAM), overcomes several limitations inherent in traditional approaches such as the Euler principle. Notably, HAM is versatile enough to be applied to a broad spectrum of risk capital types, including both coherent measures, such as expected shortfall, and noncoherent measures, such as value-at-risk. A unique feature of our approach is its flexibility in accounting for diversification benefits, as it does not assume that combining portfolios will necessarily reduce risk. To provide a comprehensive understanding of risk capital, we also present a general mathematical definition. Empirical validation is conducted through data experiments that underscore the method’s practical advantages and its capacity to handle different levels of correlation and diversification effects.