Developing a stress testing framework based on …

1 Developing a stress testing framework based on market risk modelsqCarol Alexander, Elizabeth Sheedy*ICMA Centre, University of Reading, Box 242, Reading RG6 6BA, UKMacquarie Applied Finance Centre, Macquarie University, Sydney, AustraliaReceived 29 May 2007; accepted 31 December 2007 Available online 15 January 2008 AbstractThe Basel 2 Accord requires regulatory capital to cover stress tests, yet no coherent and objective framework for stress testing port-folios exists. We propose a new methodology for stress testing in the context of market risk models that can incorporate both volatilityclustering and heavy tails. Empirical results compare the performance of eight risk models with four possible conditional and uncondi-tional return distributions over different rolling estimation periods.

2 When applied to major currency pairs using daily data spanning morethan 20 years we find that stress test results should have little impact on current levels of foreign exchange regulatory capital. 2008 Elsevier All rights classification:G18; G19; G21 Keywords:Value-at-Risk models; stress testing ; market risk; Exchange rates; GARCH1. IntroductionA stress test is a risk management tool used to evaluatethe potential impact on portfolio values of unlikely,although plausible, events or movements in a set of finan-cial variables (Lopez, 2005). They are designed to explorethe tails of the distribution of losses beyond the threshold(typically 99%) used in Value-at-Risk (VaR) analysis. Sincethe end of 1997 financial institutions using internal VaRmodels to assess capital adequacy have been required toimplement stress testing (seeBasel Committee on BankingSupervision, 1996).

3 They provide an input to decisions con-cerning, amongst other things, hedging, limit setting, port-folio allocations and capital Basel 2 Accord recommends a more direct linkbetween stress tests and risk capital, A bank mustensure that it has sufficient capital the resultsof its stress testing (Basel Committee on Banking Supervi-sion, 2006, at paragraph 778 (iii), p. 218, emphasis added).As a result leading industry practitioners have called for are-examination of stress testing methodologies, seeRowe(2005).A recent survey of stress testing practice (Committee onthe Global Financial System, 2005) shows that most stresstests are currently designed around a series of scenariosbased either on historical events, hypothetical events, orsome combination of the two. These methods have beencriticised byBerkowitz (2000) and Greenspan (2000)fortheir lack of rigour.

4 They are typically conducted withouta risk model so the probability of each scenario isunknown, making its importance difficult to is also a distinct possibility that many extreme yetplausible scenarios are not even tests conducted in the context of a risk model canprovide a useful alternative or complement to the currentad hoc methods of stress testing . Several authors haveattempted to build such a bridge between stress tests andrisk models includingKupiec (1998)who examines cross- market effects resulting from a market shock andAragones0378-4266/$ - see front matter 2008 Elsevier All rights paper was accepted by Prof. Giorgio Szego while he was theManaging Editor of The Journal of Banking and Finance, and by the pastEditorial Board.*Corresponding author. Tel.: +61 2 9850 7755; fax: +61 2 9850 Sheedy).

5 Online at of Banking & Finance 32 (2008) 2220 2236et al. (2001)who incorporate hypothetical stress events intoan Extreme Value Theory (EVT) research begins by asking a more fundamentalquestion: What is the most suitable risk model in whichto conduct a stress test? If the model is misspecified, thenour approach is vulnerable to a considerable degree ofmodel risk. Hence a significant part of this paper performsextremely thorough backtests, which are designed to reducethe model risk in risk models that are used for risk model used for stress testing need not necessar-ily have the same features as that used for daily VaR mod-els; indeed it could be argued that there are advantages inusing different models for cross-checking purposes. Theempirical performance of VaR models used at commercialbanks has been analysed byBerkowitz and O Brien (2002)and Berkowitz et al.

6 (2006). These studies suggest thatbanks VaR models may be misspecified since they donot fluctuate much while actual volatility of trading reve-nues is clearly time-varying. This is almost certainlybecause many banks use simple unconditional models toestimate VaR. The possibility that bank VaR models aremisspecified creates further incentive to ensure that anappropriate model is selected for stress testing therefore backtest eight risk models including bothconditional and unconditional models and four possiblereturn distributions. We include in our analysis risk modelsthat are already popular in the industry and those that arerelatively accessible to financial institutions. Our backtest-ing methodology is designed with stress testing applicationsin mind, that is, we assess the ability of risk models to fore-cast extreme percentiles (up to ) of returns distribu-tions over relatively short multi-day horizons.

7 We alsouse assessment criteria based on expected tail loss (ETL)as well as Value-at-Risk (VaR) to ensure that the modelperforms well for extreme outcomes beyond VaR. Ourfindings support the use of conditional risk models withnon-normal innovations such as the empirical distributionand Student choose major exchange rates as the context for anal-ysis due to their importance in the portfolios of financialinstitutions in many countries, and because of the availabil-ity of high quality data over a lengthy historical period. Weinvestigate daily returns for three of the most traded cur-rency pairs1: the USD/JPY, GBP/USD and the AUD/USD. The importance of these three currencies for the riskof financial institutions is highlighted in a recent paper oncarry trade activity (seeGalati et al., 2007).

8 Having identified our preferred risk models, we thendevelop and illustrate a model- based stress testing method-ology. The methodology includes specification of an initialshock event and analyses the subsequent market responseto that shock using simulation. Alternatively analysts canspecify hypothetical shock events and use the risk modelsonly to assess its after effects as volatility increases inresponse to the shock. The methodology can readily beextended to handle multiple assets/risk factors and toincorporate changing liquidity conditions. market partici-pants may also use this framework to assess their ownresponse to a market crisis, immediate versus gradualhedging. The methodology is evaluated by comparing itto current stress testing techniques and outline of the paper is as follows: Section2explainsthe risk models that will be examined in this study, and thereasons for their selection.

9 Section3presents an empiricalanalysis of these models in currency markets. Section4takes the best-performing models and shows how theymay be adapted for stress testing purposes. Section5eval-uates the stress tests and Section6summarises Risk modelsWhat guidance can the market risk capital assessmentliterature provide regarding the selection of appropriaterisk models for stress testing ? Previous research, which typ-ically explores the 99th percentile of outcomes at 1-dayhorizons, suggests that accurate risk models will capturetwo key characteristics: volatility clustering and stress testing requires exploration of moreextreme outcomes and, since immediate hedging may notbe practical in a market crisis, longer De Vries (2000)make the point that the most extrememarket moves tend to exhibit reduced dependency betweensuccessive daily returns.

10 This suggests that unconditionalrisk models may be sufficient for our application, providedthey have sufficiently heavy tails. We therefore examine arange of unconditional risk modelling approaches, eachwith its conditional counterpart, to give a total of eight uni-variate risk (2000)has argued that the distribution of anasset or risk factor during periods of market stress is verydifferent from its usual distribution. Therefore, we haveincluded a two-component normal mixture distribution asa candidate return distribution; here the two componentdistributions can be interpreted as corresponding to nor-1 According to Bank for InternationalSettlements Bank for Interna-tional (2005); Triennial Central Bank Survey: Foreign exchange andderivatives market activity in 2004 (Bank for International Settlements,Basel) these were the three most actively traded currency pairs after theEuro/USD in 2004, and the Euro/USD could not be included in theanalysis due to lack of historical RiskMetrics Group popularised the Exponentially WeightedMoving Average method for estimating volatility.