Sharpening Shapley Allocation: from Basel 2.5 to FRTB

TL;DR

This paper reviews and compares risk allocation strategies in finance, introduces novel solutions for negative and multi-level allocations, and finds Shapley allocation offers an optimal balance of properties and computational efficiency.

Contribution

It systematically evaluates risk allocation methods, proposes new practical solutions, and assesses their performance under Basel 2.5 and FRTB regulations.

Findings

Shapley allocation balances simplicity, properties, and computational cost.

Monte Carlo simulation enhances scalability and convergence.

Framework applicable to various financial risk types.

Abstract

Risk allocation, the decomposition of a portfolio-wide risk measure into component contributions, is a fundamental problem in financial risk management due to the non-additive nature of risk measures, the layered organizational structures of financial institutions, and the range of possible allocation strategies characterized by different rationales and properties. In this work, we conduct a systematic review of the major risk allocation strategies typically used in finance, comparing their theoretical properties, practical advantages, and limitations. To this scope we set up a specific testing framework, including both simplified settings, designed to highlight basic intrinsic behaviours, and realistic financial portfolios under different risk regulations, i.e. Basel 2.5 and FRTB. Furthermore, we develop and test novel practical solutions to manage the issue of negative risk allocations and of multi-level risk allocation in the layered organizational structure of financial institutions, while preserving the additivity property. Finally, we devote particular attention to the computational aspects of risk allocation. Our results show that, in this context, the Shapley allocation strategy offers the best compromise between simplicity, mathematical properties, risk representation and computational cost. The latter is still acceptable even in the challenging case of many business units, provided that an efficient Monte Carlo simulation is employed, which offers excellent scaling and convergence properties. While our empirical applications focus on market risk, our methodological framework is fully general and applicable to other financial context such as valuation risk, liquidity risk, credit risk, and counterparty credit risk.