Spectral Capital Allocation

Ludger Overbeck

Portfolio modelling has two main objectives: the quantification of portfolio risk, which is usually expressed as the economic capital of the portfolio, and its allocation to subportfolios and individual transactions. The standard approach in credit portfolio modelling is to define the economic capital in terms of a quantile of the portfolio loss distribution. The capital charge of an individual transaction is usually based on a covariance technique and called volatility contribution.¹¹We refer to Bluhm et al (2002) and Crouhy et al (2000) for a survey on credit portfolio modelling and capital allocation.

Since the work by Artzner et al (1997) coherent risk measures are discussed intensively in finance and risk management. More recent is the question of a more coherent capital allocation. Especially the use of expected shortfall allocation as an allocation rule that is recommend in Overbeck (1999), Denault (2001), Bluhm, Overbeck and Wagner (2002), Kurth and Tasche (2003), Kalkbrener, Lotter and Overbeck (2004).

Expected shortfall measures are the building blocks of more general coherent risk measures, the spectral risk measure. These are convex mixtures of expected shortfall