Liquidity risk meets economic capital and RAROC: a framework for measuring liquidity risk in banks

Liquidity risk is a crucial and inherent feature of the business model of banks. While banks and regulators use sophisticated mathematical methods to measure a bank's solvency risk, they use relatively simple tools for a bank's liquidity risk such as coverage ratios, sensitivity analyses, and scenario analyses. In this thesis we present a more rigorous framework that allows us to measure a bank's liquidity risk within the standard economic capital and RAROC setting. In particular, we introduce the concept of liquidity cost profiles as a quantification of a bank's illiquidity at balance sheet level, which leads subsequently to the concept of liquidity-adjusted risk measures defined on the vector space of balance sheet positions under liquidity call functions. We study the model-free effects of adding, scaling, and mixing balance sheets. In particular, we show that convexity and positive super-homogeneity of the underlying risk measures is preserved in terms of positions under the liquidity adjustment, given certain moderate conditions are met, while coherence is not, reflecting the common idea that size does matter in the face of liquidity risk.\ud We also show that a liquidity-adjustment of the well-known Euler capital allocation principle is possible without losing the soundness property that justifies the principle. However, it is in general not possible to combine soundness with the total allocation property for both the numerator and the denominator in liquidity-adjusted RAROC. Liquidity-adjusted risk measures could be a useful addition to banking regulation and bank management as they capture essential features of a bank's liquidity risk, can be combined with existing risk management systems, possess reasonable properties under portfolio manipulations, and lead to an intuitive risk ranking of banks