Capital Allocation to Business Units and Sub-Portfolios: the Euler Principle

TL;DR

This paper provides a comprehensive overview of the Euler allocation principle, detailing its theoretical foundation, practical estimation methods, and applications to risk measures and non-linear portfolios in financial risk management.

Contribution

It offers a detailed description of Euler risk contributions, including estimation techniques and applications to CDO tranches and non-linear portfolios, filling a gap in existing literature.

Findings

Euler risk contributions can be estimated for key risk measures.

Euler's theorem can analyze CDO tranche expected losses.

A new approach measures risk factor impacts on non-linear portfolios.

Abstract

Despite the fact that the Euler allocation principle has been adopted by many financial institutions for their internal capital allocation process, a comprehensive description of Euler allocation seems still to be missing. We try to fill this gap by presenting the theoretical background as well as practical aspects. In particular, we discuss how Euler risk contributions can be estimated for some important risk measures. We furthermore investigate the analysis of CDO tranche expected losses by means of Euler's theorem and suggest an approach to measure the impact of risk factors on non-linear portfolios.