A simple multifactor "factor adjustment" for the treatment of credit capital diversification

Abstract

We present a simple adjustment to the single-factor credit capital model, which recognizes the diversification from a multi-factor model. We introduce the concept of a diversification factor at the portfolio level, and show that it can be expressed as a function of two parameters that broadly capture the size (sector) concentration and the average cross-sector correlation. The model further supports an intuitive capital allocation methodology through the definition of marginal diversification factors at the sector or obligor level. We estimate the diversification factor for a family of models, and show that it can be express in parametric form or tabulated for potential regulatory applications and risk management. As a risk management tool, it can be used to understand concentration risk, capital allocation and sensitivities, stress testing, as well as to compute "real-time" marginal risk.

Measuring Sectoral Diversification in an Asymptotic Multi-Factor Framework

“…The material presented here is closely related to work by Pykhtin (2004) andGarcia Cespedes et al (2006). Pykhtin describes an approximation of multi-factor models by single-factor models, thus transferring the computational simplicity of single-factor models to multi-factor models.…”

Diversification, performance and optimal business mix of insurance portfolios

“…The Euler principle of capital allocation has been discussed in Tasche (2004Tasche ( , 2006Tasche ( , 2007, Memmel andWehn (2006) andGarcia Cespedes et al (2006). Let us denote the portfolio of risks under consideration by Ω = {X 1 , ..., X d } with S = d 1 X i as before.…”

“…Among others, the Euler principle by Tasche (1999Tasche ( , 2004Tasche ( , 2007, Hallerbach (2003) and Gourieroux et al (2000) is a notable method that provides an economic basis for measuring line-wise performance using the return on risk adjusted capital. Related to this, the notion of the diversification index for a portfolio under the Euler allocation is introduced and discussed in, e.g., Tasche (2004Tasche ( , 2006Tasche ( , 2007, Memmel and Wehn (2006) and Garcia Cespedes et al (2006), for a given risk measure, Skoglund and Chen (2009) developed an information measure, based on the Kullback information theory, that conveys similar information to the Euler decomposition for non-linear portfolios.…”

Risk factor contributions in portfolio credit risk models

“…It ignores the distributions of all other positions, and as such does not take into account any diversifying or hedging effects resulting from its inclusion in the institution's portfolio. It can be useful in measuring the reduction in risk due to diversification, and in measuring diversification factors for portfolios (see Garcia-Cespedes et al, 2006;Tasche, 2006). It can also be considered as an upper bound on the contribution to the risk for any reasonable allocation rule.…”