Calculating Incremental Risk Charges: The effect of the liquidity horizon

by Jimmy Skoglund of SAS Institute Inc., and
Wei Chen of SAS Institute Inc.

June 30, 2010

Abstract: The recent incremental risk charge addition to the Basel (1996) market risk amendment requires banks to estimate, separately, the default and migration risk of their trading portfolios that are exposed to credit risk. The new regulation requires the total regulatory charges for trading books to be computed as the sum of the market risk capital and the incremental risk charge for credit risk. In contrast to Basel II models for the banking book no model is prescribed and banks can use internal models for calculating the incremental risk charge. In the calculation of incremental risk charges a key component is the choice of the liquidity horizon for traded credits. In this paper we explore the effect of the liquidity horizon on the incremental risk charge. Specifically we consider a sample of 28 bonds with different rating and liquidity horizons to evaluate the impact of the choice of the liquidity horizon for a certain rating class of credits. We ?find that choosing the liquidity horizon for a particular credit there are two important effects that needs to be considered. Firstly, for bonds with short liquidity horizons there is a mitigation effect of preventing the bond from further downgrades by trading it frequently. Secondly, there is the possibility of multiple defaults. Of these two effects the multiple default effect will generally be more pronounced for non investment grade credits as the probability of default is severe even for short liquidity periods. For medium investment grade credits these two effects will in general o¤set and the incremental risk charge will be approximately the same across liquidity horizons. For high quality investment grade credits the effect of the multiple defaults is low for short liquidity horizons as the frequent trading effectively prevents severe downgrades.

JEL Classification: C00.

Keywords: credit risk, incremental risk charge, liquidity horizon, Basel III

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