Oesterrechsche Natonalbank Gudelnes on Market Rsk Volume 5 Stress Testng
Gudelnes on Market Rsk Volume 1: General Market Rsk of Debt Instruments nd revsed and extended edton Volume : Standardzed Approach Audts Volume 3: Evaluaton of Value-at-Rsk Models Volume 4: Provsons for Opton Rsks Volume 5: Stress Testng Volume 6: Other Rsks Assocated wth the Tradng Book
Publshed and produced by: Oesterrechsche Natonalbank Edtor n chef: Wolfdetrch Grau Author: Fnancal Markets Analyss and Survellance Dvson Translated by: Foregn Research Dvson Layout, desgn, set, prnt and producton: Prntng Offce Internet: http://www.oenb.at Paper: Salzer Demeter, 100% woodpulp paper, bleached wthout chlorne, acd-free, wthout optcal whteners. DVR 0031577
The second major amendment to the Austran Bankng Act, whch entered nto force on January 1, 1998, faced the Austran credt nsttutons and bankng supervsory authortes wth an unparalleled challenge, as t entaled far-reachng statutory modfcatons and adjustments to comply wth nternatonal standards. The successful mplementaton of the adjustments clearly marks a quantum leap n the way banks enganged n substantal securtes tradng manage the assocated rsks. It also puts the spotlght on the mportance of the competent staff's tranng and sklls, whch requres szeable nvestments. All of ths s certan to enhance professonal practce and, feedng through to the nterplay of market forces, wll ultmately beneft all market partcpants. The Oesterrechsche Natonalbank, whch serves both as a partner of the Austran bankng ndustry and an authorty charged wth bankng supervsory tasks, has ncreasngly postoned tself as an agent that provdes all market players wth servces of the hghest standard, guaranteeng a level playng feld. Two volumes of the sx-volume seres of gudelnes centerng on the varous facets of market rsk provde nformaton on how the Oesterrechsche Natonalbank apprases value-at-rsk models and on how t audts the standardzed approach. The remanng four volumes dscuss n depth stress testng for securtes portfolos, the calculaton of regulatory captal requrements to cover opton rsks, the general nterest rate rsk of debt nstruments and other rsks assocated wth the tradng book ncludng default and settlement rsk. These publcatons not only serve as a rsk management tool for the fnancal sector, but are also desgned to ncrease transparency and to enhance the objectvty of the audt procedures. The Oesterrechsche Natonalbank selected ths approach wth a vew to renforcng confdence n the Austran fnancal market and aganst the backdrop of the global lberalzaton trend to boostng the market s compettveness and buttressng ts stablty. Gertrude Tumpel-Gugerell Vce Governor Oesterrechsche Natonalbank
Today, the fnancal sector s the most dynamc busness sector, save perhaps the telecommuncatons ndustry. Buoyant growth n dervatve fnancal products, both n terms of volume and of dversty and complexty, bears ample testmony to ths. Gven these developments, the requrement to offer optmum securty for clents' nvestments represents a contnual challenge for the fnancal sector. It s the mandate of bankng supervsors to ensure complance wth the provsons set up to meet ths very requrement. To ths end, the competent authortes must have flexble tools at ther dsposal to swftly cover new fnancal products and new types of rsks. Novel EU Drectves, ther amendments and the ensung amendments to the Austran Bankng Act bear wtness to the dauntng pace of dervatves developments. Just when t seems that large projects, such as the lmtaton of market rsks va the EU's captal adequacy Drectves CAD I and CAD II, are about to draw to a close, regulators fnd themselves facng the nnovatons ntroduced by the much-dscussed New Captal Accord of the Basle Commttee on Bankng Supervson. The latter document wll not only make t necessary to adjust the regulatory captal requrements, but also requre the supervsory authortes to develop a new, more comprehensve coverage of a credt nsttuton's rsk postons. Many of the approaches and strateges for managng market rsk whch were ncorporated n the Oesterrechsche Natonalbank s Gudelnes on Market Rsk should n lne wth the Basle Commttee s standpont not be seen as merely confned to the tradng book. Interest rate, foregn exchange and optons rsks also play a role n conventonal bankng busness, albet n a less conspcuous manner. The revoluton n fnance has made t mperatve for credt nsttutons to conform to changng supervsory standards. These gudelnes should be of relevance not only to banks nvolved n large-scale tradng, but also to nsttutons wth less volumnous tradng books. Prudence dctates that rsk ncludng the "market rsks" nherent n the bank book be thoroughly analyzed; banks should have a vested nterest n effectve rsk management. As the gudelnes ssued by the Oesterrechsche Natonalbank are desgned to support banks n ths effort, banks should turn to them for frequent reference. Last, but not least, ths seres of publcatons, a key contrbuton n a hghly specalzed area, also testfes to the cooperaton between the Austran Federal Mnstry of Fnance and the Oesterrechsche Natonalbank n the realm of bankng supervson. Alfred Lejsek Drector General Federal Mnstry of Fnance
Preface Stress testng s ganng sgnfcance as a rsk management tool. Independent of supervsory requrements, banks' top executves have been payng ever greater attenton to stress testng over the past two years. The mountng mportance credt nsttutons attach to ths mode of testng has rased the qualty of stress testng schemes. Interestngly enough, there s as yet no unform, generally accepted standard n place. Ths gudelne sheds lght on the varous developments reflected n stress testng programs and presents mmnum requrements applcable to Austran credt nsttutons usng nternal models for measurng ther exposure. A reference tool desgned to prme nsttutons on how to ncorporate stress tests n ther rsk management system, t clearly revolves around market rsk, but also touches upon lqudty and credt rsk. The dea for ths publcaton may be traced to the Oesterrechsche Natonalbank's nvolvement n evaluatng propretary models used by banks to lmt market rsk. Gven the OeNB's experence n ths area, two aspects have come to the fore n partcular, whch also underscored the potental need for such a gudelne. For one, gven ther desgn, stress tests may serve as a farly smple tool for managng rsk. In addton, lttle has thus far been wrtten on the topc. Apart from the banks whch employ nternal models and are therefore requred by the Austran Bankng Act to perform stress testng, such testng methods also lend themselves to any credt nsttuton or enterprse wth a treasury department. After all, stress testng may be mplemented for n-house rsk management purposes n a quck manner. It goes wthout sayng that there s no lmt to refnng the methods used. Ths s where the scentfc communty comes n: It s desrable to nvestgate stress testng further, whch should best be acheved va an nterdscplnary approach brngng together fnance, macroeconomcs, statstcs and econometrcs, to name just the key dscplnes. The authors would lke to extend thanks to Alan Cathcart and Nck Palmer of the Fnancal Servces Authorty, London; Benjamn Cohen of the Basle Commttee on the Global Fnancal System; Zahra El-Mekkawy of the Basle Commttee on Bankng Supervson as well as Stefan Walter and Kevn Clarke of the Federal Reserve Bank of New York for frutful dscussons about nternatonal stress testng practces. Credt also goes to Mchael Boss and Ronald Laszlo for ther comments and valuable suggestons. Specal thanks are due to the head of the dvson, Helga Mramor, who promoted the producton of ths seres of gudelnes on market rsk. Venna, September 1999 Thomas Breuer Gerald Krenn
Table of Contents 1 Introducton... 1 1.1 Legal Framework... 1 1. Why Use Stress Tests... 1.3 Stress Tests and Value-at-Rsk Models... 3 1.4 Weaknesses of Value at Rsk and Strenghts of Stress Tests: a Case Study... 5 1.5 Scope of ths Gudelne... 7 General Aspects of Stress Testng... 9.1 What s a Stress Test... 9. Portfolo Valuaton: Lnear Approxmaton or Complete Revaluaton...10.3 Lqudty Crses...1.4 Credt Rsk...14.5 How Tough Should Stress Scenaros Be...15.6 Standardzed Stress Tests...16.7 Interpretaton of the Results of Stress Tests, Reportng and Contngency Plannng...17 3 Constructon of Stress Scenaros Usng Hstorcal Data... 1 3.1 Why Use Hstorcal Scenaros...1 3. Analyss of Tme Seres of One Factor...3 3..1 Identfyng Maxmum Movements of Indvdual Factors...3 3.. Integratng the Movements of Indvdual Factors nto a Scenaro...5 3..3 Tables of Maxmum Changes of Indvdual Rsk Factors...7 3..3.1 Maxmum Changes of Stock Prce Indeces...7 3..3. Maxmum Changes of Exchange Rates...8 3..3.3 Maxmum Changes of Interest Rates...30 3.3 Analyss of Tme Seres of Several Factors...3 3.3.1 Smple Scenaro Constructon Usng Tme Seres of Several Rsk Factors...3 3.3. Measurng Smultaneous Changes of Several Rsk Factors...33 3.3..1 Senstvtes...34 3.3.. Maxmum Portfolo Value Changes...36 3.3.3 Table of Maxmum Changes of Several Rsk Factors...37
4 Identfyng Portfolo-Specfc Worst-Case Scenaros... 39 4.1 Legal Bass of the Search for Worst-Case Scenaros...39 4. Worst-Case Scenaros versus Hstorcal Scenaros...39 4.3 Subjectve Search for Worst-Case Scenaros...40 4.4 Systematc Search for Worst-Case Scenaros...41 4.4.1 Why Search Systematcally for Worst-Case Scenaros...41 4.4. Reportng on the Systematc Search for Portfolo-Specfc Worst-Case Scenaros...4 4.5 Emergency Plans for Worst-Case Scenaros...44 5 Summary of Stress Testng Requrements for Banks Usng Internal Models... 47 5.1 Reportng and Organzaton...47 5. Scenaro Selecton...48 5.3 Computaton...49 Techncal Annex... 51 A.1 Admsson Crtera for Scenaros n the Systematc Search for Worst-Case Scenaros.51 A.1.1 Admsson Crtera whch Ignore Correlatons...51 A.1. Admsson Crtera whch Take nto Account Correlatons...5 A. Methods for the Systematc Search for Worst-Case Scenaros...55 A..1 Factor Push Method...55 A.. Monte Carlo and Quas-Monte Carlo Methods...56 A..3 Other Loss Maxmzaton Algorthms...58 Bblography... 61
Stress Testng Introducton 1 Introducton 1.1 Legal Framework The second major amendment to the Austran Bankng Act ntroduced the term stress testng nto the legal rsk management provsons applcable to Austran credt nsttutons. Ths amendment, whch ncorporated the captal adequacy Drectve (CAD) nto Austran law, entaled a change n the computaton of the regulatory captal requrement credt nsttutons and groups of credt nsttutons need to hold. Credt nsttutons that keep a large-volume tradng book are now requred to calculate the regulatory captal requrement for tradng book postons n lne wth the CAD standardzed approach. Or, nsttutons may mplement nternal models for lmtng the market rsk, also referred to as value-at-rsk (VaR) models, to determne the requred captal for backng both the general and the specfc poston rsk nherent n debt nstruments and stocks contaned n the tradng book as well as n commodtes postons and open currency postons. The use of such propretary models for market rsk management purposes was recommended by the Basle Commttee on Bankng Supervson n ts January 1996 publcaton enttled "Amendment to the Captal Accord to Incorporate Market Rsks." In the meantme, these recommendatons have essentally been ntegrated nto a Drectve amendng the CAD. Both the Basle market rsk paper of January 1996 and the EU Drectve stpulate that the use of an nternal model be subject to approval by the competent bankng supervsory authorty. What s more, both papers spell out stress testng as one of the prerequstes for model approval. In other words, bank regulators consder stress tests to be an effectve and necessary tool that complements statstcal models for quantfyng and montorng rsk. Gven ther role as a control mechansm, stress tests are lsted n the Austran Bankng Act among the qualtatve standards. Stress testng does, however, also set hgh quanttatve standards for rsk management. In summary, any credt nsttuton usng an nternal model to calculate the regulatory captal requrement s bound by law to carry out stress tests. Lkewse, all other credt nsttutons and fnancal nsttutons may n general beneft from ntegratng stress testng nto ther rsk control. The methods underlyng stress tests are easy to comprehend, and the requrements for performng stress tests are farly low. Ths gudelne therefore targets not just those credt nsttutons that use nternal models, but rather all credt nsttutons; besdes, ths publcaton may prove useful to other nsttutonal nvestors. 1
Introducton Stress Testng 1. Why Use Stress Tests The need for stress testng s justfed by the Basle Commttee on Bankng Supervson (1995) as follows: "Banks that use the nternal models approach for meetng market rsk captal requrements must have n place a rgorous and comprehensve stress testng program. Stress testng to dentfy events or nfluences that could greatly mpact banks are a key component of a bank's assessment of ts captal poston. Understandng and protectng aganst the vulnerabltes of a fnancal company's rsk-takng actvtes s of course one of the major responsbltes of ts board of drectors and senor management. Banks' stress scenaros need to cover a range of factors that can create extraordnary losses or gans n tradng portfolos, or make the control of rsk n those portfolos very dffcult. These factors nclude lowprobablty events n all major types of rsks, ncludng the varous components of market, credt, and operatonal rsks. Stress scenaros need to shed lght on the mpact of such events on postons that dsplay both lnear and non-lnear prce characterstcs (.e. optons and nstruments that have optons-lke characterstcs). Banks' stress tests should be both of a quanttatve and qualtatve nature. Quanttatve crtera should dentfy plausble stress scenaros to whch banks could be exposed. Qualtatve crtera should emphasse that two major goals of stress testng are to evaluate the capacty of the bank's captal to absorb potental large losses and to dentfy steps the bank can take to reduce ts rsk and conserve captal. Ths assessment s ntegral to settng and evaluatng the bank's management strategy and the results of stress testng should be routnely communcated to senor management and, perodcally, to the bank's board of drectors." As far as the consequences of stress tests go, the Commttee states: "Stress testng alone s of lmted value unless the bank s ready to respond to ts results. At a mnmum, the results should be revewed perodcally by senor management and should be reflected n the polces and lmts set by management and the board of drectors. Moreover, f the testng reveals partcular vulnerablty to a gven set of crcumstances, the natonal supervsors would expect the bank to take prompt steps to manage those rsks approprately (e.g. by hedgng aganst that outcome or reducng the sze of ts exposures).
Stress Testng Introducton Stress tests should, thus, provde credt nsttutons wth answers to these three questons: 1. What wll the loss be n the event of scenaro X?. What are our nsttuton's worst-case scenaros? 3. What can we do to lmt the losses ncurred n the worst-case scenaros? Stress tests do not, however, provde an answer n quanttatve terms to the queston of how probable any gven scenaro s. Stll, the plausblty of scenaros does play a certan role n nterpretng stress testng results. Sectons.5 and 4.4. dscuss these ponts at greater length. 1.3 Stress Tests and Value-at-Rsk Models The ssue of stress testng often crops up n connecton wth VaR models. As mentoned above, the executon of stress tests s stpulated by law for credt nsttutons that employ VaR models to compute ther regulatory captal requrements. Bascally, stress testng s to complement the nternal models approach. Why do VaR models call for such complementary measures, and how come stress tests ft the bll? The VaR methodology s farly well-known: A holdng perod of t days and a confdence level of p% are gven. The VaR s a statstcal measure of the loss of a portfolo as measured n monetary unts whch wll not be exceeded wth a probablty of p% gven the portfolo remans constant throughout the holdng perod. Losses n excess of the VaR only occur wth a low probablty [(1-p)%]. A VaR model does not shed lght on the dmenson of such "heavy" losses. Ths s the frst reason why stress testng s requred as a complementary measure: stress tests serve to estmate potental extreme losses. The second mportant reason why VaR calculatons shall be combned wth stress tests les n the somewhat skeptcal atttude towards the assumptons on whch most VaR calculatons are based. In the same ven, the multplcaton factor appled to the value at rsk n computng the regulatory captal requrement helps absorb the remanng uncertanty about the accuracy of the model. There are frst and foremost two assumptons whose valdty s debatable. For one, the markets are assumed to reman constant over a gven tme horzon. Only n the event that future market movements mrror those of the past can models produce relable results. Yet, there have always been breaks n market movements. They may be attrbutable to varous causes, for nstance, to full-blown crses, such as wars or envronmental catastrophes, changes n the nterest rate or exchange rate polces pursued by central banks, speculatve attacks on currences and the lke. A stress stuaton shall therefore mean a break n the temporal constancy of a market. The 3
Introducton Stress Testng objectve of stress tests s, among other thngs, to assess the potental loss resultng from such breaks. Furthermore numerous VaR models assume that changes n rsk factors are normally dstrbuted. However, changes n fnancal tme seres are, as a rule, not normally dstrbuted. Instead, such tme seres are marked by fat tals. It follows that extreme changes n the rsk factors are consderably more lkely than s accounted for under the assumpton of a normal dstrbuton. The slump n stock prces trggered by the equty crash of 1987, for example, was reflected by 10 to 0 standard devatons. The table below shows that such a fall n prces should not be possble under the assumpton of a normal dstrbuton. Probabltes of extreme changes under the assumpton of a normal dstrbuton k Probablty of a prce slump of k standard devatons or more 5 6 10-7 6 10-9 7 3 10-1 Table 1 Stress tests are not based on statstcal assumptons on how the changes n rsk factors are dstrbuted. Ths s why the results of stress tests are not dstorted by fat tals. As stress tests do not quantfy the probablty of occurrence of the ndvdual scenaros, they lend themselves to verfyng and complementng statstcal rsk measures such as the value at rsk. As a montorng tool, stress tests prmarly serve to verfy statstcal assumptons unerlyng the model. The prcng model of an nternal model may not or only be partally verfed va stress testng, snce the portfolo valuaton to be carred out durng stress testng tself rests on a prcng model. Whle stress tests do not put exact fgures on the probablty of scenaros, scenaros stll need to be somewhat plausble. The evaluaton of scenaro plausblty calls for, at least, a rough dea of the probablty wth whch gven scenaros wll occur. 4
Stress Testng Introducton 1.4 Weaknesses of Value at Rsk and Strenghts of Stress Tests: a Case Study A case study presented n Gay et al. (1999) llustrates the fact that stress tests should, n partcular n addton to VaR calculatons, be used to measure the rsk of fnancal transactons. In late January 1998, the Korean nvestment house SK Securtes Co. suffered a loss of USD 189 mllon traceable to a total return swap transacton. The swap was entered nto at the end of January 1997 wth a maturty of one year. A payment was to be effected at the end of the maturty the amount of whch would depend on the exchange rates of the currences of Thaland (baht, THB), Indonesa (rupah, IDR) and Japan (yen, JPY) vs-à-vs the USD. Bascally, t had been agreed that SK Securtes would receve the followng amount once the swap came due B N 5 ( B 0 1) + Max (0, 3 R 0 R R 1 R ) + Y Max (0, 1 Y 0 ) 0.97 (1.1) or that t would pay that amount f t happened to be negatve. In the formula above, N desgnates the prncpal of USD 53 mllon, B 0 (B ), R 0 (R ) and Y 0 (Y ) denote the USD rates of the baht, rupah and yen at the begnnng (end) of the lfe of the swap, and R 1 gves the USD rate of the rupah after sx months followng the transacton date (all rates are gven per USD 1). Had the rates remaned constant durng the lfe of the swap transacton, SK Securtes would have receved a payment n the order of N 0.03 = USD 1.59 mllon. Expresson (1.1) shows that a deprecaton of the baht relatve to the USD ( B > B0 ) would have had unfavorable consequences for SK Securtes. A deprecaton of the rupah would lkewse not have benefted SK Securtes, whle the nvestment house would have profted from an apprecaton of the baht or rupah or a deprecaton of the yen. The decson of SK Securtes to enter nto the swap was based on hstorcal rate movements and volatltes of the currences nvolved. The hstorcal data mpled that the rsk was relatvely low. When the swap was transacted and n the years pror to that transacton, Thaland's central bank kept the baht strctly pegged to a currency basket the composton of whch was never made publc but whch allegedly conssted of the USD (80%), JPY (1%) and DEM (8%). The Indonesan central bank targeted a lmtaton of the rupah's loss n value relatve to the USD to a maxmum of 5% per annum. By contrast, the Japanese central bank largely refraned from ntervenng for the yen. The dfferng rate targets of the central banks are reflected n the hstorcal volatltes of the exchange rates vs-à-vs the USD: the closer the peg to the USD, the smaller the volatlty. Ths pont s also llustrated by table showng annualzed hstorcal volatltes based on an observaton perod of 6 weeks pror to January 9, 1997. 5
Introducton Stress Testng Annualzed hstorcal volatltes relatve to the USD; Observaton perod: August 6, 1996 to January 8, 1997; source: Gay et al. (1999) Currency THB IDR JPY Volatlty 1.3%.0% 6.88% Table Followng the swap transacton, the central banks concerned contnued to pursue ther respectve monetary polces. However, once Thaland's central bank had exhausted a large porton of ts offcal reserves to sheld the baht from speculatve attacks, t decded on July, 1999 to dscontnue those nterventons n favor of mprovng Thaland's export opportuntes. The baht promptly deprecated relatve to the USD by 16%. Consequently, the currences of other countres n the regon lost on the USD as well. On August 14, 1997, Indonesa's central bank dropped ts rate target. Table 3 demonstrates the losses on the USD of the currences nvolved n the swap transacton n the perod from end-january 1997 to end-january 1998. Deprecaton relatve to the USD from January 9, 1997 to January 9, 1998; source: Datastream Currency THB IDR JPY Deprecaton relatve to USD 51.8% 77.9%.9% Table 3 The VaR measures computed for the baht and rupah postons n USD at the tme when the swap was transacted and usng a confdence level of 99% and a holdng perod of one year under the assumpton of a normal dstrbuton of the relatve exchange rate fluctuatons would have underestmated based on the volatltes stated n table the actual losses 18fold and 15fold, respectvely (e.g. VaR for USD 100 n baht: VaR = USD 100 0.013.36 = USD.86; actual loss: USD 51.8). Gay et al. (1999) demonstrate that even VaR calculatons coverng the entre swap at the transacton tme would have drastcally underestmated the actual loss ncurred. A Monte Carlo smulaton performed by the authors produces a VaR of USD 16 mllon, at a confdence level of 99%. The actual loss (USD 189 mllon) was 1 tmes as large. In the case descrbed above, stress testng could have been used as a smple method for analyzng the rsk nherent n the transacton or for gettng a feel for the rsk mpled. The deprecatons shown n table 3 represent a scenaro,.e. precsely the scenaro that then actually unfolded. Stress tests essentally revolve around defnng scenaros and determnng the changes n the 6
Stress Testng Introducton value of a gven fnancal nstrument or a portfolo of fnancal nstruments n the event of any one scenaro. 1 Heavy-loss-producng scenaros are partcularly relevant. Selectng adequate scenaros s ntegral to stress testng programs. Chapters 3 and 4 deal exclusvely wth how to dentfy scenaros. Based on consderatons about whch changes n the exchange rates could have adverse effects on the cash flow (1.1) of SK Securtes, for nstance three scenaros correspondng to a mnor, mdsze and major crss (table 4) could have been defned, and t would have been farly easy to calculate the resultng losses. The percentages shown n table 4 gve the assumed deprecatons of the currences relatve to the USD durng the one-year lfe of the swap. The percentages n parentheses ndcate the assumed IDR deprecatons at a sx-month cutoff. Loss on the cash flow (1.1) n three dfferent scenaros THB IDR JPY Loss Scenaro 1: mnor crss -15% -15% (-8%) 0% USD 58.0 mllon Scenaro : mdsze crss -30% -30% (-15%) 0% USD 116.3 mllon Scenaro 3: major crss -50% -50% (-30%) 0% USD 183.9 mllon Table 4 The results provde a consderably more drastc pcture of the loss potental of the gven transacton than the VaR measure of USD 16 mllon mentoned before. What s more, compared to the VaR fgure, they are much easer to compute. Of course, the problem arses whether one beleves a pror n the possble occurrence of the scenaros. A posteror even scenaro 3 seems perfectly realstc, yet the queston remans whether the above scenaros would have been plausble n the eyes of SK Securtes decsonmakers n early 1997. In ths case study, consderng the macroeconomc context would, no doubt, have put the assumpton of constant exchange rate fluctuatons n perspectve. 1.5 Scope of ths Gudelne Ths gudelne s more or less confned to explanng stress testng as related to measurng and managng market rsk. In how far such tests may account for or mplctly cover lqudty crses s descrbed n secton.3. Credt rsk s touched upon n secton.4. Compared to the wealth of publcatons on value at rsk, the lterature on stress testng s scarce. Ths wll, however, most lkely change n the future, not least because crtcsm of VaR models s mountng and stress testng s called for as an alternatve or complementary measure to the nternal models approach. 1 For detals, see sectons.1 and.. 7
Introducton Stress Testng From the bankng supervsors' perspectve, no concrete, nternatonal standards for stress testng are as yet n place, but varous natonal supervsory authortes have started to pay more and more attenton to ths topc. At the current juncture, ths gudelne s desgned to provde a rather general overvew so as not to preclude future nternatonal developments. Chapter 5 outlnes concrete requrements for Austran credt nsttutons employng VaR models. Materal new fndngs about the executon of stress tests as well as more concrete supervsory standards, once they evolve, wll be consdered n future edtons. There should always reman suffcent flexblty n carryng out stress testng though. A creatve approach towards stress testng that bulds on certan mnmum requrements may only be conducve to rsk management. In partcular, the defnton of stress scenaros s an ongong, dynamc process that should nvolve experts of dverse felds. The Basle Commttee on Bankng Supervson (1996) clearly champons the dea of gvng credt nsttutons adequate leeway n performng stress tests. Ths s why chapter 5 only lsts the mnmum requrements applcable to Austran credt nsttutons. These requrements are n lne wth nternatonal standards. 8
Stress Testng General Aspects General Aspects of Stress Testng.1 What s a Stress Test The concept of stress testng s based on the noton that the value of a portfolo depends on market rsk factors (rsk factors). Let us call the rsk factors wth an mpact on the portfolo r,..., factors are gven, P. The values of the rsk factors r 1, r,..., rn characterze the market stuaton as far as t s of relevance to the portfolo. The rsk factors may be combned nto one sngle vector r = ( r, r,..., r ) descrbng the market stuaton. In a market stuaton r, the value of 1, r r n and the functon determnng the value of the portfolo when the values of all rsk : 1 n the portfolo s P (r). Below, r MM wll stand for the vector representng the current values of the rsk factors,.e. the current market stuaton. MM stands for the "current market stuaton", P r ) therefore represents the current value of the portfolo. ( MM A bank's portfolo may be consdered to consst of ts entre tradng book. In such a case, stress testng may be sad to be bank-wde. Under the Austran Regulaton on Internal Models for the Lmtaton of Market Rsks, model users have to conduct stress tests quarterly and whenever a need arses. In practce, addtonal stress tests are frequently carred out for subportfolos at dvson, tradng unt or dealer level or n respect of specfc nstruments (as n the case study n secton 1.4). Lower-level stress tests are usually performed n response to specfc needs and requested by the management responsble for the area concerned. The scenaros employed n such tests are customzed to meet specfc needs. The choce of rsk factors depends on the portfolo. Not all portfolos are nfluenced by the same rsk factors. The number of rsk factors must be chosen so as to nclude all parameters lkely to have an mpact on the value of the portfolo. One may, however, decde to use an even larger number, whch may be wse as t allows the user to restructure hs portfolo later wthout havng to add more rsk factors. The procedure for selectng rsk factors s not clearly defned. The value of the portfolo may be understood as the functon of several sets of rsk factors. Where nterest s concerned, for example, dscount factors or nterest rates may be chosen as rsk factors. The functon P depends on the portfolo: a dfferent portfolo has a dfferent valuaton functon. P s frequently not an explct functon of the rsk factors. Partcularly the values of portfolos of exotc optons are usually determned n a valuaton process rather than by means of a valuaton functon. One such valuaton process would be the valuaton of a portfolo or of sngle postons by means of a Monte Carlo smulaton. Stress tests answer the queston of "What would happen f a market stuaton r suddenly occurred?" The scenaro n ths case s the sudden emergence of a market stuaton r. Scenaros may therefore be dentfed wth market stuatons and represented by vectors r. In general 9
General Aspects Stress Testng language, a "scenaro" s a potental future development. In connecton wth stress testng, a scenaro s a possble future market stuaton. In ths context, the term scenaro therefore does not stand for a process but only for ts outcome. Ths change n meanng s derved from the smulaton of dsturbances n fnancal markets. Such dsturbances are characterzed by a sudden confrontaton of market partcpants wth a changed market stuaton. Ths may have been caused, for example, by a dramatc rse n volatltes: when prces move so rapdly that market partcpants are unable to restructure ther portfolos wthn the reacton tme avalable, the portfolos have to be revalued on the bass of changed market condtons. The same effect occurs n lqudty crses: to a market partcpant, only those prces are of relevance at whch he can rebalance hs postons to the extent desred. In llqud markets, tradng close to quoted market prces s mpossble. Therefore, a portfolo can be restructured only at a later tme and at dramatcally dfferent prces. Even f quoted market prces fluctuate contnuously, the prces relevant to market partcpants may stll change dramatcally n a lqudty crss. For stress testng, scenaros r 1,..., rk are selected accordng to specfc crtera and calculatons are made to determne the value of the current portfolo under these scenaros. These portfolo values are represented by P( r 1 ),..., P( r k ). By comparng them wth the current value of the portfolo P( r MM ) one can assess the losses that would be ncurred f the market suddenly moved from rmm to r 1,..., rk wthout allowng a chance for rebalancng the portfolo.. Portfolo Valuaton: Lnear Approxmaton or Complete Revaluaton Analyzng scenaros means frst of all to determne the value of a gven portfolo on the assumpton that the rsk factors, nstead of ther real values r MM = ( rmm, 1, rmm,,..., rmm, n ), have the values r = ( r1, r,..., rn ) reflected by the scenaro. In a complete revaluaton of the portfolo, the valuaton functon s appled drect to the new values r of the rsk factors. The value of the portfolo n a scenaro r s then P (r). Lnear approxmaton apples the senstvtes δ of the portfolo value relatve to the ndvdual rsk factors. Senstvtes are numbers ndcatng for a specfc rsk factor how senstve the value of a gven portfolo s to changes n that rsk factor. The hgher the senstvty, the heaver the mpact of ths factor on the value of the portfolo. Senstvtes are determned as follows: n a frst step, "typcal" changes 1,,..., n are selected for all rsk factors. Then the senstvty δ s calculated for each rsk factor: P( r1,..., r,..., rn ) P( r1,..., r +,..., rn ) δ =. 10
Stress Testng General Aspects The senstvtes δ reflect the mean slope of the valuaton functon P across the dstance They depend on the Δ selected f the valuaton functon P s non-lnear n the -th rsk factor. Δ. Dfferent slopes for dfferent Δ P Slope δ Slope δ Fgure 1 r From the senstvtes an approxmated portfolo value P s calculated by the followng formula: P( r n 1, r,..., rn ) P( rmm,1, rmm,,..., rmm, n ) + = 1 = ( r r ) δ. P s the lnear approxmaton of the valuaton functon around r MM. When s t permssble then to use a lnear approxmaton of the portfolo value nstead of a complete revaluaton of the portfolo and when s such an approach effcent? Frstly, regardng the queston of effcency: calculaton of the senstvtes requres n complete revaluatons of the portfolo. If only a few scenaros have to be analyzed, complete revaluaton s therefore more effcent and more precse than lnear approxmaton. Approxmaton s more effcent only f a complete revaluaton of the portfolo would requre a large amount of calculatons and f, beyond that, senstvtes have ether been calculated before for other purposes and are therefore avalable wthout any extra effort or f the number of scenaros to be analyzed s much greater than the number n of rsk factors. MM, 11
General Aspects Stress Testng Regardng the permssblty of lnear approxmaton: the general rule s that lnear approxmaton P (r) wll not supply the correct value P (r) of the portfolo n scenaro r f the valuaton functon P s non-lnear n those rsk factors n whch scenaro r dffers from the current stuaton r MM. The error n lnear approxmaton wll usually be small f for those rsk factors n whch the valuaton functon P s non-lnear, the dstance r r MM, s approxmately equal to the typcal dstance used n calculatng senstvty δ. If senstvtes are calculated specfcally for lnear approxmaton, t s therefore best to choose for ths purpose such that rmm +, s close to r of the scenaros to be analyzed. Lnear approxmaton can be used wth confdence only n scenaros n whch changes from the current stuaton r MM occur only n those rsk factors on whch the value of the portfolo depends lnearly. Whether the value of the portfolo depends lnearly on the rsk factors s determned not only by the portfolo but also by the choce of rsk factors. The value of a portfolo understood as a functon of specfc rsk factors may ndeed be lnear n these factors whereas f understood as a functon of another set of rsk factors t s non-lnear n that other set. There exsts no portfolo that would be lnear by nature. Example: The value of a bond depends lnearly on the dscount factors, but non-lnearly on the underlyng nterest rates. If the dscount factors are regarded as a rsk factor, a bond portfolo s lnear; f nterest rates are chosen as rsk factors, the bond portfolo s nonlnear..3 Lqudty Crses Both the Basle Commttee on Bankng Supervson (1996; secton B.5 no 3) and the Austran Regulaton on Internal Models for the Lmtaton of Market Rsks ( 7 para ) requre that lqudty crses be taken nto account: "Stress tests should [...] ncorporate both market rsk and lqudty aspects of market dsturbances." Bascally, one can dstngush between two types of lqudty rsk: frstly, a bank may suddenly lack the fnancal lqudty allowng t to keep holdng certan postons. Due to a changed market stuaton, t may, for example, suddenly be faced wth the need to make margn payments or to provde addtonal securty. Avodance of ths type of lqudty crss s the responsblty of asset/lablty management and wll not be dscussed any further n ths context. Secondly, a shortfall n market lqudty may suddenly occur, preventng the bank from closng certan 1
Stress Testng General Aspects postons. When that happens, t becomes mpossble to fnd a party wllng to take up the poston at the quoted market prce. In such a stuaton the poston cannot be closed at all or only wth an extremely hgh bd-ask spread. Here we want to dscuss only the second type of lqudty rsk, namely the lack of market lqudty. A lack of market lqudty may be attrbutable to several causes: some markets are tradtonally llqud. Other, normally lqud markets, may occasonally suffer lqudty shocks trggered, for example, by unexpected economc or poltcal news. Fnally, a market partcpant's exposure n a specfc market may be so substantal that closng of hs postons destroys the lqudty of the market. Whatever the reason for nadequate market lqudty may be, llqud markets do not allow any tradng close to quoted market prces. Any restructurng of the portfolo ether now or later wll therefore be possble only at dramatcally dfferent prces. The only prces relevant to a portfolo manager are those at whch he s able to restructure hs postons to the desred extent. Even f quoted market prces are movng contnuously, the prces relevant to the portfolo manager may change dramatcally n a lqudty crss. In a market rsk crss, the stuaton facng a portfolo manager s exactly the same: a dramatc rse n volatlty causes prces to change so rapdly that, gven hs lmted reacton speed, he can rebalance hs postons to the desred extent only at dramatcally dfferent prces. In stress stuatons, both lqudty rsk and market rsk have the same negatve consequences, namely dramatc changes n the market that make contnuous restructurng of the portfolo mpossble. To the portfolo manager, t does not make any dfference whether the market suddenly changes overnght and he can rebalance hs postons only the next day or whether, n a stuaton of creepng market changes, he can rebalance hs postons only much later because of nsuffcent market lqudty. Both stuatons lqudty crss and market rsk crss are smulated n stress tests by revalung a gven portfolo aganst a background of radcally changed market condtons. Lqudty stress tests therefore do not requre any specal methodology. Nevertheless, the smulaton of lqudty crses may call for dfferent scenaros than the smulaton of market rsk crses. If, for example, n smulatng a market rsk crss, hstorcal data are used to assess the magntude of moves n sngle rsk factors, one wll probably choose the greatest day-to-day changes or, even better, the greatest changes that occurred wthn the bank's response tme. In smulatng lqudty crses one wll tend to select the scenaro wth the greatest change wthn a perod of tme equvalent to the duraton of the lqudty crss. The n-day drawdown defned n secton 3. s an upper lmt for moves n rsk factors durng a lqudty crss of a maxmum duraton of n days. 13
General Aspects Stress Testng.4 Credt Rsk The Basle Commttee on Bankng Supervson (1996; secton B.5 no ) calls for the consderaton of credt rsks n stress testng: "Banks' stress scenaros need to cover a range of factors that can create extraordnary losses or gans n tradng portfolos or make the control of rsk n those portfolos very dffcult. These factors nclude low-probablty events n all major types of rsk, ncludng the varous components of market, credt and operatonal rsks." Why should rsk types, such as credt rsk, that are not captured by the value-at-rsk model used for market rsk control be ncluded n stress tests? Takng the combned acton of market and credt rsks nto account s very mportant, as a separate consderaton of market and credt rsks may fal to dentfy some materal dangers. Value-at-rsk models ncludng such a capablty are stll n the process of development. Hopes are therefore pnned on stress testng. The combned acton of market and credt rsks can be llustrated by an example: n the frst half of 1998, a number of western banks entered nto ruble forward deals wth Russan banks under whch they agreed to buy from the Russan banks, on a specfed settlement date, dollars aganst rubles at a specfed forward exchange rate. Most of these deals were fully hedged by offsettng transactons wth other western banks. The market rsk of such deals gnorng the default rsk was therefore practcally zero. The default rsk n respect of the Russan banks was lmted to the dfference between the agreed ruble exchange rate at whch dollars were to be delvered to the western banks and the replacement cost n rubles (.e. the spot rate on the settlement date) of dollars not delvered by the Russan banks. The agreed forward rate was usually very close to the spot rate prevalng at the tme the deal was closed as exchange rates had remaned unchanged for a long tme and were therefore not expected to fluctuate n the future ether. As long as there was no change n the ruble exchange rate, the default rsk n respect of the Russan banks was close to zero as any dollars not delvered by the Russan banks could be bought n the market at very smlar prces. Therefore, the default rsk of these deals gnorng the market rsk was also practcally zero. Separate measurements of market rsk and default rsk show both rsks to be practcally zero. A look at the combned acton of market rsk and default rsk, however, reveals the followng stuaton: f the ruble exchange rate declnes and a Russan bank defaults at the same tme, dollars have to be bought n the market at the hgh ruble spot rate and delvered to the western banks at the low forward rate. A market rsk was therefore created only through the default of the Russan banks. Postons that had been closed were suddenly reopened. The combned acton of market and default rsks may lead to enormous losses. Ths example shows the great mportance of an ntegrated assessment of market and credt rsks. 14
Stress Testng General Aspects The example shows a well-known nteracton between credt and market rsk at work: changes n market rsk factors result n changes n the values of assets and labltes held by counterpartes and thus to changes n the losses ncurred n the event of default. On the other hand, the default of a large market player may also trgger strong fluctuatons n market rsk factors. How can the default rsk be ncorporated nto stress testng? For ths purpose, an assessment s needed of how credt losses are nfluenced by market rsk factors. Ths would n fact requre an ntegrated credt and market rsk model. A number of credt rsk models, ncludng McKnsey's CredtPortfoloVew TM and KMV's PortfoloManager TM, take the current state of the economy and a varety of market rsk factors nto account. Even these models, however, are not ntegrated credt and market rsk models. A relatvely smple way of coverng default rsk n stress testng s the followng: for worst-case scenaros, t s justfed to use the smplfyng assumpton that the loss due to a counterparty's default s equal to the full market value of all assets,.e. that nothng can be recovered from a defaultng counterparty. In selectng a credt stress scenaro, two parameters have to be specfed: (1) the values of the market rsk factors and () the defaultng counterpartes. The loss n such a scenaro s then calculated as follows: frstly, the tradng book subportfolo affected by the default s determned. For counterpartes wth whch nettng arrangements are n effect, such a subportfolo conssts of all postons transacted wth the respectve counterparty. For counterpartes wth whom no nettng agreements have been entered nto, the subportfolo comprses all postons transacted wth the counterparty concerned and havng a postve market value. In a second step, the subportfolo affected by the default s valued, usng the rsk factor values chosen n (1)..5 How Tough Should Stress Scenaros Be On the one hand, t s of course n the nature of stress tests to ask what would happen n stuatons that nobody expects to occur. On the other hand, test results from scenaros that are regarded as hghly unlkely are not taken serously by those to whom test reports are addressed. Wth ths n mnd, t may be helpful to run several scenaros of dfferent degrees of severty. For the rsk management of the credt nsttuton concerned t s mportant to apply clear crtera n specfyng scenaros and to account for these crtera n nterpretng the outcome of stress testng. The recpent of a report should not be gven just the mere loss fgures but should also be alerted to the severty of the underlyng scenaros. Where possble, senor management should partcpate n defnng the severty of the scenaros. 15
General Aspects Stress Testng.6 Standardzed Stress Tests Many banks conduct perodc stress tests nvolvng a revaluaton of ther current portfolo aganst certan standard scenaros. These are often standard scenaros n a dual sense: the choce of the scenaros depends nether on the bank nor on the tmng of the stress test. Thus, stress testng wth standard scenaros has the advantage of guaranteeng comparablty n two respects. Frstly: when several banks look at the same scenaros one can compare the outcome of stress tests of dfferent banks. Ths allows the supervsor to assess the banks' exposure to those rsk categores whose rsk factors are changed n the standard scenaros. Secondly: when a bank always looks at the same scenaros, t can compare the results of stress tests conducted at dfferent ponts n tme. Ths enables t to montor how ts exposure to the rsk categores n the standard scenaros changes over tme (exposure montorng). Many banks use standard scenaros smlar to the stress scenaros proposed by the Dervatves Polcy Group (DPG). The DPG s an nformal body of representatves of major Amercan banks and nvestment frms. It was set up n August 1994, at the suggeston of the Securtes and Exchange Commsson, to formulate a code of conduct for tradng n dervatves. Its rules were publshed n the "Framework for Voluntary Oversght." The DPG recommends the performance of stress tests to measure the exposure of a portfolo to certan core rsk factors. The DPG lsts among these core rsk factors. parallel yeld curve shfts,. changes n the steepness of yeld curves,. parallel yeld curve shfts combned wth changes n the steepness of yeld curves, v. changes n yeld volatltes, v. changes n the value of equty ndces, v. changes n equty ndex volatltes, v. changes n the value of key currences (relatve to the USD), v. changes n foregn exchange rate volatltes and x. changes n swap spreads n at least the G-7 countres plus Swtzerland. For an assessment of exposure towards the core rsk factors, the DPG (1995; secton 4 no 4) recommends use of the followng standard scenaros n regular stress testng: a) parallel yeld curve shfts of 100 bass ponts up and down, b) steepenng and flattenng of the yeld curves (for maturtes of to 10 years) by 5 bass ponts, 16
Stress Testng General Aspects c) each of the four permutatons of a parallel yeld curve shft of 100 bass ponts concurrent wth a tltng of the yeld curve (for maturtes of to 10 years) by 5 bass ponts, d) ncrease and decrease n all 3-month yeld volatltes by 0 percent of prevalng levels, e) ncrease and decrease n equty ndex values by 10 percent, f) ncrease and decrease n equty ndex volatltes by 0 percent of prevalng levels, g) ncrease and decrease n the exchange value (relatve to the USD) of foregn currences by 6 percent, n the case of major currences, and 0 percent, n the case of other currences, h) ncrease and decrease n foregn exchange rate volatltes by 0 percent of prevalng levels and ) ncrease and decrease n swap spreads by 0 bass ponts. A comparson of these DPG standard scenaros wth the tables n chapter 3 lstng actual maxmum changes shows that some of the DPG scenaros are far removed from the maxmum changes observed n the past. Therefore, they should not be regarded as reconstructons of hstorcal crses or as worst-case scenaros. Nether the Basle Commttee on Bankng Supervson nor the Austran Regulaton on Internal Models for the Lmtaton of Market Rsks requre banks to perform stress tests at regular ntervals wth standards scenaros lke the DPG's. Nevertheless perodc stress tests wth unchanged scenaros may serve as a useful nstrument n montorng exposures on an ongong bass. The same can be sad of stress test lmts. Such lmts specfy, for a certan unchangng set of scenaros, the maxmum loss acceptable wth each scenaro and what acton to take n case the lmt s exceeded. To date, the Austran bank supervsory authorty has not specfed any standard scenaros for stress testng. However, the authors would recommend credt nsttutons to develop ther own scenaros for contnuous montorng of exposure n ther respectve key markets..7 Interpretaton of the Results of Stress Tests, Reportng and Contngency Plannng Stress tests are used prmarly for the assessment of a bank's captal stuaton and the dentfcaton of measures desgned to mnmze rsk. The Basle Commttee on Bankng Supervson (1996; secton B.5 no 3) notes the followng n ths context: 17
General Aspects Stress Testng "Qualtatve crtera should emphasse that two major goals of stress testng are to evaluate the capacty of the bank's captal to absorb potental large losses and to dentfy steps the bank can take to reduce ts rsk and conserve captal. Ths assessment s ntegral to settng and evaluatng the bank's management strategy and the results of stress testng should be routnely communcated to senor management and, perodcally, to the bank's board of drectors." In nterpretng the results of stress tests the frst queston wll therefore be whether the bank would be able to cope wth the losses ncurred n a stress scenaro. A comparson of the outcome of the stress test wth the bank's own captal resources may n some crcumstances be msleadng, however, as these funds also need to cover rsks other than the market rsk assocated wth the tradng book. If at a tme of market dsturbance other losses were beng ncurred smultaneously, the bank mght be n trouble even f ts own captal were adequate for copng wth the market crss alone. In an alternatve approach, the results of stress tests are therefore frequently compared wth rsk captal allocated nternally for securtes tradng or wth the regulatory captal requrements n respect of market rsk assocated wth the tradng portfolo (10-day VaR tmes multplcaton factor). If, n the event of a market dsturbance, any loss ncurred s hgher than the rsk captal allocated for securtes tradng or the regulatory captal requrements n respect of the market rsk assocated wth the tradng portfolo, the bank needs to take urgent acton. In ths regard, the plausblty of stress scenaros s certanly a crtcal factor. If a stress scenaro s hghly plausble, senor management wll take a stress test more serously than f t consders the stress scenaro hghly unlkely. Stress tests gan practcal sgnfcance only when ther results are taken note of and understood by the bodes havng the authorty to call for a reducton of rsk exposure. The Basle Commttee on Bankng Supervson (1996; secton B.5 no 8) notes the followng n ths regard: "The results should be revewed perodcally by senor management and should be reflected n the polces and lmts set by management and the board of drectors. Moreover, f the testng reveals partcular vulnerablty to a gven set of crcumstances, the natonal authortes would expect the bank to take prompt steps to manage those rsks approprately (e.g. by hedgng aganst that outcome or reducng the sze of ts exposures)." Lkewse, the Austran Regulaton on Internal Models for the Lmtaton of Market Rsks calls for the followng n para 6: 18