We introduce the technique of worst case search to macro stress testing. Among the macroeconomic scenarios satisfying some plausibility constraint we determine the worst case scenario which causes the most harmful loss in loan portfolios. This method has three advantages over traditional macro stress testing: First, it ensures that no harmful scenarios are missed and therefore prevents a false illusion of safety which may result when considering only standard stress scenarios. Second, it does not analyse scenarios which are too implausible and would therefore jeopardize the credibility of stress analysis. Third, it allows for a portfolio specific identification of key risk factors. Another lesson from this paper relates to the use of partial stress scenarios specifying the values of some but not all risk factors: The plausibility of partial scenarios is maximised if we set the remaining risk factors to their conditional expected values.
Macro stress testing has become an important method of risk analysis for lending acitivities. This paper introduces the technique of worst case analysis to macro stress testing. Among the macroeconomic scenarios satisfying some plausibility constraint we determine the worst case scenario which causes the most harmful loss. In this way one can be sure not to miss out any harmful but plausible scenarios, which is a serious danger when considering only standard stress scenarios.
This kind of systematic worst case analysis with plausibility constraints was developed for market risk stress testing, see ? and ??. The loss in the worst case scenario can also be regarded as risk measure. As such it was originally introduced under the name Maximum Loss by ??. Maximum Loss is a coherent risk measure in the sense of ?. Actually, it is the prototype of a coherent risk measure because by a duality argument every coherent risk measure can be represented as Maximum Loss over some set of generalised scenarios, see ? and ?. As a risk measure Maximum Loss has two advantages over Value at Risk. First, it is coherent and therefore can be the basis of economic capital allocation to subportfolios. Secondly, it provides information about which economic situations are really harmful and suggests possible counteraction to reduce risk in case it is considered unacceptable, see ?
Stress testing started in market risk analysis but in recent years it has been applied to macro analysis as well. A brief introduction into macro stress testing as well as an overview of EU country-level macro stress testing practices is given in a special feature of the Financial Stability Report of the ?. According to the ECB, macro stress testing is a way of quantifying the link between macroeconomic variables and the health of either a single financial institution or the financial sector as a whole. A detailed introduction into the topic and an overview of related literature is given in ?. In many countries, central banks’ endeavour with macro stress testing was boosted by the IMF running a Financial Sector Assessment Program (FSAP). For details see ? and ?. A stress analysis of sector concentration risk in credit portfolios is given in ?. Our paper adds to this literature by introducing the technique of worst case search to macro stress testing. However, we perform macro stress tests only of loan portfolios but not of a whole banking system.
The rest of the paper is structured as follows. First, in Section 2 we develop a methodology of macro stress testing and worst case analysis. In Section 3 we develop a model describing both macro and credit risk as well as their interaction in loan portfolios. On the basis of this model in Section 4 we apply the general methodology to loan portfolios and derive implications for their risk structure.
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Macro Stress and Worst Case Analysis of Loan Portfolios
