Value at risk

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Value at risk

  1. 1. Value at Risk By A V VedpuriswarFebr r 8 20 9 uay , 0
  2. 2. ♦ V Rsummaizes t w stl ov at r A r he or oss er aget hor t tw lnotbe exceeded a a izon ha il t given l elof confidence. ev♦ F exa e, “undernor lmaketcondit t or mpl ma r ions, he mostt porfol ca l he t io n ose ov amont is a er h bout $3 bilion a t 99% confidence l el .6 l t he ev .” 2
  3. 3. ♦ T ma ideabehind V R is t consider t t a he in A o he ot l porfol r a t highest t io isk t he l eloft inst ut ev he it ion.♦ Init ly a ied t maket r it is now used t ial ppl o r isk, o mea e cr r sur edit isk, oper t lr a ent pr w r aiona isk nd er ise ide isk.♦ M ny ba ca now use t ow V R model a a nks n heir n A s s t he ba for t sis heir r ed ca a formaketr equir pit l r isk. 3
  4. 4. V Rca be cacul t using t o br d a oa : A n l aed w oa ppr ches♦ Non par amet ic met : T is t most gener l met w does not r hod his he a hod hich ma a a ke ny ssumpt ion a t sha oft distibut ofr ur bout he pe he r ion et ns.♦ Paramet ic met r hod: V R comput t becomes A aion much ea if a sier dist ibut such a nor l is a r ion, s ma, ssumed.♦ 4
  5. 5. IllustrationAer ge r enue = $5.1 milion perda v a ev l yT a no.ofobser aions = 254 ot l vt .St dev= $9.2 milion d lConfidence l el= 95% evNo. ofobser aions < -$10milion = 11 vt lNo. ofobser aions < -$ 9milion = 15 vt l 5
  6. 6. ♦ Find t point such t tt no. ofobser aions t t l = (254 (.0 = 12.7 he ha he v t o he eft ) 5)♦ (12.7– 11)/ 15 – 11 ) ( = 1.7/4 ≈ .4♦ So required point = -(10-.4) = -$9.6milion l♦ V R= E(W – (- A ) 9.6) = 5.1 – (- = $14 milion 9.6) .7 l♦ Ifw a e ssume anor ldistibut ma r ion,♦ Za 95% confidence int v l 1 t il = 1.64 t er a, a ed 5♦ V R= (1.64 (9.2) A 5) = $ 15.2 milion l
  7. 7. VAR as a benchm ark m easure♦ V Rca be used a compa w yadst t compae r a oss differ maket A n s ny ide r ick o r isks cr ent r s.♦ V Rca aso be used t under a w herr ha A nl o st nd het isk s incr sed ov t ea er ime.♦ V R ca be used t dr l dow int r r t t A n o il n o isk epors o under a w her t higher st nd het he r is due t isk o incr sed v ail yorbiggerbet ea ol t it s. 7
  8. 8. VAR as a potential loss m easure ♦V Rca aso giv abr d ideaoft w stl a inst ut ca incur A n l e oa he or oss n it ion n . ♦T choice oft hor mustcorespond t t he ime izon r o he t r ed forcorect e a ion a l ime equir r iv ct s osses st r t dev op. at o el ♦Corect e a ion ma incl r r iv ct y ude educing t r he isk pr e of t inst ut or r ising new ofil he it ion a ca a. pit l ♦Ba ma use da yV Rbeca of t nks y il A use he l iquidit a r pid t nov in t porfol y nd a ur er heir t ios. ♦In conta , pension funds gener lyinv in l l porfol a a ustt r exposur onl r st al est ess iquid t ios nd dj heir isk es y sl l owy. ♦ So aone mont hor ma mor sense. h izon kes e 8
  9. 9. VAR as equity capital♦ T V Rmea e shoul a t yca ur alt he A sur d dequael pt e l he r fa t inst ut isks cing he it ion.♦ So t r mea e must encompa maket r cr he isk sur ss r isk, edit r oper t l r a ot isk, aiona isk nd her risks.♦ T higher t degr of r a er of t compa he he ee isk v sion he ny, t higher t confidence l el he he ev chosen.♦ If t ba det mines it r pr e by t r ing a he nk er s isk ofil aget pat a cr ricul r edit rt aing, t expect defa tr t he ed ul ae ca be conv t dir l int a n ered ecty o confidence l el ev .♦ Highercr r t shoul l d t ahigher confidence l el edit aings d ea o ev . 9
  10. 10. VAR M ethod s ♦ M apping : Ift porfol consist ofal r number he t io s age of inst ument itw d r s, oul be t compl t model oo ex o each inst umentsepaael T fir st is r r t y. he st ep ma pping. Inst ument ae r a by posit on r s r epl ced ions al ed number of r fa or If w imit isk ct s. e ha e Nr v isk fa or t posit ae a egaed a oss inst ument ct s, he ions r ggr t cr r s. ♦ Local val ion met uat hods ma use of t v l t of t instument a t curent ke he auaion he r s t he r point aong w h t fir , l it he st a per ps, t second pat lder aiv nd ha he ria iv t es. The porfol t io is v l onl once. aued y ♦ Ful val ion met l uat hods, in cont a , r ice t r st epr he inst ument ov abr d r nge r s er oa a ofv l fort r fa or aues he isk ct s. 10
  11. 11. ♦ L rmodel ae ba on t cov r nce mar inea s r sed he aia t ix a oa ppr ch.♦ T mar ca be simpl using fa ormodel he t ix n ified ct s.♦ Non l rmodel t ke int a inea s a o ccountt fir a he st nd second pat lder aiv ria iv t es (ga /conv y) mma exit 11
  12. 12. D elta norm al approach♦ T delanor lmet a he t ma hod ssumes t tt porfol ha he t io mea es ae l ra t r sur r inea nd he isk fa or ae j l nor lydistibut ct s r ointy mal r ed.♦ T delanor lmet inv v asimpl mar he t ma hod ol es e tix mulipl t t icaion.♦ It is comput t ly fa ev w h al r no. of aional st en it age a s beca it r a ea sset use epl ces ch posit byit l r exposur ion s inea e.♦ T disa a a ae t exist of fa t il in ma he dv nt ges r he ence t a s ny dist ibut a t ina it t r ions nd he bil y o ha e non l r inst ument ndl inea r s. 12
  13. 13. F st t a is v l a t init lpoint ir , he sset aued t he ia .V = V 0) 0 (Sdv= dvds | ds = ∆0 ds = (∆0 s)ds/ / ss is t r fa or he isk ct .Porfol V R= |∆0| x V R = |∆0| x (ασS0) t io A Asσ = St dev ofr t ofcha in t pr d n aes nge he iceα = St nor ldev t coresponding t t d ma iae r o he specifiedconfidence l el ev . 13
  14. 14. ♦ F mor compl pa offs, l l v l t is not or e ex y oca auaion enough.♦ T ke t ca ofal sta e, i.e, t pur se a he se ong r ddl he cha of cala aput l nd .♦ T w stpa off(sum oft t o pr he or y he w emiums)w l il be r l ift spotr t eaized he ae does notmov a al e t l.♦ In gener l itis notsufficientt ev l t t a, o auae he porfol a t t o extemes. t io t he w r♦ Alint mediae v l mustbe checked. l er t aues 14
  15. 15. D elta Gam m a M ethod ♦ In l rmodel da yV Ris a ust t ot per byscaing byasquae r of inea s, il A dj ed o her iods, l r oot t fa or ime ct . ♦ T a ust a his dj ment ssumes t tt posit is fixed ha he ion a t da y r ur ae nd he il et ns r independentand ident lydist ibut ical r ed. ♦ T a ust his dj ment is not a opr t for opt ppr iae ions beca opt dela cha use ion t nges dyna lyov mical er t ime. ♦ T dela gamma met pr ides a a l ica he t hod ov n nayt l second or corect t der r ion o t delanor lV R he t ma A . 15
  16. 16. ♦ G mmagiv t r t ofcha in delaw h r a es he ae nge t it espectt t spotpr o he ice.♦ L posit in opt w h aposit e ga ha e l r t n w h al rmodel ong ions ions it iv mma v ess isk ha it inea .♦ Conv sel shor posit in opt ha e gr t er y, t ions ions v eaer r t n impl byal r isk ha ied inea model . 16
  17. 17. H istorical sim ulation m ethod♦ T hist ica simul t met consist of going ba he or l aion hod s ck in t a a ying curent ime nd ppl r w s t at eight o ime ser ies ofhist ica a r ur or l sset et ns.♦ T met ma no specific a his hod kes ssumpt a r ur ion bout et n dist ibut ot t n r ying on r ion, her ha el hist ica daa or l t .♦ T is a impr ement ov t nor l dist ibut his n ov er he ma r ion beca hist ica daat ly use or l t ypical cont in fa t il a t a s.♦ T ma dr w ck of t met is it r ia on a he in a ba his hod s el nce shor hist ica mov w t or l ing indowt o infermov s in maketpr ement r ices. 17
  18. 18. ♦ T sa ing v r t of hist ica simul t V R he mpl aiaion or l aion A is gr t t n forapaa r eaer ha r metic met hod.♦ Longersa e pahs ae r ed t obt in mpl t r equir o a meaningful qua it nt ies.♦ T dil he emma is t t t ma inv v obser aions ha his y ol e vt t t ha ae no l r onger r ev nt el a .♦ Ba use per bet een 250a 750 nks iods w nd days.♦ T is t ken a ar sona e t a offbet een pr his a s ea bl r de w ecision a non st t r y. nd aionait♦ M nyinst ut ae nowusing hist ica a it ions r or l simul t ov a aion er windowof1- yeas, 4 r dul y suppl ed by ement stess t s . r est 18
  19. 19. M onte C arlo Sim ulation M ethod♦ T M e Cal Simul t M hod is simil r t t he ont ro aion et a o he hist ica simul t except t t or l aion, ha mov s in r fa or ement isk ct s ae gener t bydr w fr some pr r aed a ings om e specified dist ibut r ion.♦ T r ma ger sa es pseudo r ndom number he isk na mpl a s fr t dist ibut a t om his r ion nd hen gener t pseudo dola aes l r r ur a befor et ns s e.♦ F ly, t r ur ae sored t pr inal he et ns r t o oduce t desir he ed VR A.♦ T met uses comput his hod er simul t t aions o gener t r ndom pr pahs. ae a ice t 19
  20. 20. ♦ T ae byfa t mostpow fula oa t V R hey r r he er ppr ch o A .♦ T ca a hey n ccountforaw r nge of r incl ide a isks uding pr r v ail yr fa ice isk, ol t it isk, t t il a exteme scenaios a compl int a ions. a s nd r r nd ex er ct♦ Non l rexposur a compl pr pat ns inea es nd ex icing ter ca aso be ha ed. nl ndl♦ M e Cal a l ca dea w h t deca of ont ro naysis n l it ime y opt da y setl s & ions, il tement a t ca fl s ssociaed sh ow a t effect of pr specified ta or hedging nd he e r ding staegies. rt 20
  21. 21. ♦ T M e Cal a oa r es user t ma he ont ro ppr ch equir s o ke assumpt a t ions bout he st st pr a t ocha ic ocess nd o under a t sensit it oft r t t t a st nd he iv y he esuls o hese ssumptions.♦ Differ r ndom number w ll d t differ r t ent a s il ea o ent esuls.♦ Al r numberofit aions ma be needed t conv ge t ast bl V Rmea e. age er t y o er o a e A sur♦ W al t r fa or ha e anor l distibut hen l he isk ct s v ma r ion a exposur ae l r nd es r inea, t met shoul conv ge t t V Rpr he hod d er o he A oduced byt delanor l he t - ma VR A. 21
  22. 22. ♦ T M e Cal a oa is comput t lyquit he ont ro ppr ch aional e demanding.♦ Itr es making t makett w e porfol equir r o r he hol t io over al r numberof age r l t ofunderying eaisaions l r ndom v r bl a aia es.♦ T speed up t pr o he ocess, met ha e been dev hods, v ised t br k t l bet een t o ea he ink w he numberofM e Cal dr w a t numberoft t porfol is ont ro a s nd he imes he t io r iced. epr♦ In t gr M e Cal a oa t porfol is he id ont ro ppr ch, he t io exa l v l ov al ed cty aued er imit numberofgr point id s.♦ F ea simul t t porfol is v l using a or ch aion, he t io aued l r int pol t fr t inea er aion om he exa v l a ct aues t a oining gr point dj id s. 22
  23. 23. ♦ T fir a most cr l st consist of he st nd ucia ep s choosing a pat a st st ricul r ocha ic modelfort he beha iourofpr v ices.♦ A commonl used model in M e cal y ont ro simul t is t G r aion he eometic Br nia mot ow n ion modelw a hich ssumes mov s in t maket pr ae uncorel t ement he r ice r r aed ov t a t tsmal er ime nd ha l mov s in pr ca be descr by: ement ices n ibed♦ dSt = μt St dt+ σt St dz♦ dz is a r ndom v r bl dist ibut nor ly a aia e r ed mal wh it mea zer a n o nd v r nce dt aia . 23
  24. 24. ♦ T r es outpr his ul ocesses w h sudden j for inst nce. it umps a♦ T pr is aso geometic beca alt paa er ae scaed by t curentpr his ocess l r use l he r met s r l he r ice, St.♦ μt a σt r esentt inst nt neous dr a nd epr he a a ift nd v ail y t tca ev v ov ol t it ha n ol e er time. 24
  25. 25. ♦ Int aing ds/ ov afinit int v l w ha e a oximael egr t s er e er a, e v ppr t y:♦ ∆St = St-1 (μ ∆t+ σz√∆t )♦ z is a st ndad nor l r ndom v r bl w h a r ma a aia e it mean zer a unit o nd v r nce. aia♦ St+ 1 = St + St (μ ∆t+ σz1 √∆t )♦ St+ 2 = St+ 1 + St+ 1 (μ ∆t+ σz2√∆t ) 25
  26. 26. ♦ M e Cal simul t ae ba on r ndom dr w z ont ro aions r sed a as fr av r bl w h t desir om aia e it he ed pr bil ydistibut oba it r ion.♦ T fir buil bl is a unifor distibut ov he st ding ock m r ion er t he int v l (0 t t er a ,1) ha produces ar ndom v r bl x. a aia e♦ G r ndom number gener t s must cr t ser ood a aor eae ies t t pa al conv iona t s of ha ss l ent l est independence.♦ Ot w t chaa er ics oft simul t pr her ise, he r ct ist he aed ice pr w lnotobeyt underying ocess il he l model .♦ T next st is t t a m t unifor r ndom he ep o r nsfor he m a number x int t desir o he ed dist ibut t ough t r ion hr he inv se cumul t e pr bil ydistibut er aiv oba it r ion. 26
  27. 27. Selective Sam pling ♦ Sa e aong t pahs t tae mostimpora t mpl l he t ha r t nt o t pr em a ha he obl t nd. ♦ If t goa is t mea e at ilqua il a ael he l o sur a nt e, ccur t y, t e is no pointin doing her simul t t tw l gener t obser aions in t cent e oft aions ha il ae vt he r he dist ibut r ion. ♦ T incr se t a a oft V Rest t , w o ea he ccur cy he A imaor e ca pat ion t simul t n rit he aion r int t o or mor zones. egion o w e ♦ A opr t numberofobser aions is dr w fr ppr iae vt a n om ea r ch egion. 27
  28. 28. ♦ Using mor infor t a t porfol e maion bout he t io distibut r t in mor efficient r ion esuls e simul t aions.♦ T simul t ca pr he aion n oceed in t o pha w ses.♦ T fir pa r at a iona M e Cal he st ss uns r dit l ont ro.♦ T r ma gert exa he isk na hen mines t r oft he egion he r fa or t tca l isk ct s ha use osses aound V R r A.♦ Asecond pa is t per med w h ma mor ss hen for it ny e sa es fr t r mpl om he egion. 28
  29. 29. Backtesting♦ Ba est is done t check t a a oft model ckt ing o he ccur cy he .♦ It shoul be done in such aw y t t t l ihood of d a ha he ikel caching bia in V R for st is t ses A eca s maximized.♦ Longer hor r izon educes t number of independent he obser aions a t t pow of v t nd hus he er t t s. he est♦ T high aconfidence l elr oo ev educes t expect number ofobser aions in t t ila t t he ed vt he a nd hus he pow oft er he t s. est♦ F t int na model a oa t Ba e Commitee or he er l s ppr ch, he sl t recommends a99% confidence l el ev ov a10business da hor er y izon.♦ T r t V R is mulipl by asa y he esuling A t ied fet fa or of 3 t ct o ar e a t minimum riv t he r aor ca a. egul t y pit l 29
  30. 30. ♦ A t confidence l el incr ses, t number of occurences bel V R shr s he ev ea he r ow A inks, l ding t poor mea es ofhigh qua il ea o sur nt es.♦ T e is no simpl w yt est t a99.99% V R her e a o imae A fr t sa e beca it om he mpl use ha t few s oo obser aions. vt♦ Shorer t int v l cr t mor daapoint a t ime er as eae e t s nd fa it t mor effect e cil ae e iv ba t ing. ck est 30
  31. 31. C hoosing the m ethod ♦ Simul t met ae quit fl e. aion hods r e exibl ♦ T ca eit post ae a st st pr hey n her ul t ocha ic ocess or r mpl fr esa e om hist ica daa or l t . ♦ T al ful v l t on t t r daa hey low l auaion he aget t . ♦ Butt ae pr t modelr a sa ing v r t hey r one o isk nd mpl aiaion. ♦ Geaer pr r t ecision ca be a ed by incr sing n chiev ea t number of he r icaions butt ma sl t epl t his y ow he pr dow ocess n. 31
  32. 32. ♦ F l r porfol w e opt l y is nota domina fa or t delanor lmet or age t ios her ionait nt ct , he t ma hod pr ides a ov fa a efficientmet formea ing V R st nd hod sur A .♦ F fa a oximaions ofopt v l dela ga is efficient or st ppr t ion aues, t mma .♦ F porfol w h subst nt lopt component or or t ios it a ia ion s, l ongerhorizons, aful v l t l auaion met ma be hod y r ed. equir 32
  33. 33. ♦ If t st st pr chosen fort pr is unr l ic, so w lbe t est t he ocha ic ocess he ice eaist il he imae ofV R A.♦ F exa e, t geometic Br nia mot or mpl he r ow n ion model a t y descr t dequael ibes he beha iourof v st pr a excha r t butnott tof fixed income secur ies. ock ices nd nge aes ha it♦ In Br nia mot model pr shocks ae ow n ion s, ice r nev r er a pr mov a er ev sed nd ices e s ar ndom a wl ak.♦ T ca be t pr pr fordefa tfr bond pr w mustconv ge t his nnot he ice ocess ul ee ices hich er o t fa heir ce v l a expir t aue t aion. 33
  34. 34. V A R Applications Discl e t shaehol s osur o r der M na a gementr t epors Passive R t r eporing isk R aor r ement egul t y equir s Cont oling rl Seting r l s t isk imit Defensive risks Per ma v l t for nce auaion Ca a al t , pit l locaion Active Al t r locaing isk St aegic business decisions. rt 34
  35. 35. ♦ V R met r esent t cul t of a A hods epr he minaion tend t ads centaized r r ow r r l isk ma gement na .♦ M ny inst ut ha e st red t mea e a it ions v at o sur maket r on a gl l ba r isk oba sis beca t sour ofr ha e mulipl a v ail yha use he ces isk v t ied nd ol t it s incr sed. ea♦ Aporfol a oa giv abeterpict e of r r t t n l t io ppr ch es t ur isk aher ha ooking a differ t ent inst ument r s in isol t aion. 35
  36. 36. ♦ Centaizaion ma sense forcr r ma gement rl t kes edit isk na t oo.♦ Afina linst ut ma ha e myr d ta ct ncia it ion y v ia r nsa ions wh it t sa count pat he me er ry, coming fr v r desks om aious such a curencies, fixed income commodit s r ies a so on. nd♦ E en t v hough al t desks ma ha e ar sona e l he y v ea bl exposur w consider on a e hen ed n indiv lba t idua sis, hese exposur ma a up t a una a e r es y dd o n ccept bl isk.♦ Aso, w h neting a eement t t a exposur l it t gr s, he ot l e depends on t netcurentv l of he r aue conta s cov ed byt a eement r ct er he gr s.♦ Alt st ae notpossibl in t a l hese eps r e he bsence ofa gl l oba mea ementsyst sur em. 36
  37. 37. ♦ Inst ut w w l benefit most fr agl l r it ions hich il om oba isk ma gement syst ae t na em r hose w ae exposed t hich r o: - div se r er isk - a iv posit t king /pr iet r ta ct e ions a opr ay r ding - compl instument ex r s. 37
  38. 38. ♦ V Ris ausefulinfor t r t t . A maion eporing ool♦ Ba ca discl t a egaed r w hout nks n ose heir ggr t isk it r eaing t ev l heir indiv lposit idua ions.♦ Ideal inst ut shoul pr ide summay V R ly, it ions d ov r A figur on a da y, es il w yormont yba eekl hl sis.♦ Discl e ofinfor t is a effect e mea of osur maion n iv ns maketdiscipl r ine. 38
  39. 39. ♦ V Ris aso ausefulr contolt . A l isk r ool♦ Posit l s aone do notgiv acompl e ion imit l e et pict e. ur♦ T sa l on a3 yea tea y, (compaed he me imit 0 r r sur r t 5 yea tea y) ma o r r sur y be mor r e isky.♦ V Rl s ca suppl A imit n ementposit l s. ion imit♦ In v ail env onment V R ca be used a t ol t e ir s, A n s he ba for scaing dow sis l n posit ions.♦ V Ra s a acommon denominaorfor A ct s t compaing v r r a iv ies. r aious isky ct it 39
  40. 40. ♦ V R ca be v ed a amea e of r ca a or A n iew s sur isk pit l economic ca a r ed t pit l equir o suppor afina l a iv y. t ncia ct it♦ T economic ca a is t a egae ca a r ed a acushion a inst unexpect he pit l he ggr t pit l equir s ga ed losses.♦ V Rhel in mea ing r a ust r ur A ps sur isk dj ed et n.♦ W houtcontoling forr ta s ma become it rl isk, r der y r ess. eckl♦ Ift ta ma al r pr , he r es al r he r der kes age ofit eceiv age bonus.♦ Ifhe ma al t w stt tca ha is he kes oss, he or ha n ppen wl il getfined. 40
  41. 41. ♦ T a icaion of V R in per ma he ppl t A for nce mea ement depends on it sur s int ended purposes.♦ Int na per ma mea ementa a er l for nce sur ims t r ading peopl fora ions t ew r e ct hey ha e ful contolov . v l r er♦ T indiv lundiv sified V Rseems t he idua/ er A he a opr t choice. ppr iae♦ E er l per ma mea ement a a xt na for nce sur ims t al t of exist / new locaion ing ca a t pit l o exist ornewbusiness unit ing s.♦ Such decisions shoul be ba on magina a d sed r l nd div sified V R er A mea es. sur 41
  42. 42. ♦ V Rca aso be used a t staegic l elt ident w e shaehol v l is being A nl t he r t ev o ify her r der aue added t oughoutt cor aion. hr he por t♦ V R ca hel ma gement t ke decisions a A n p na a bout w business l t hich ines o expa ma a orr nd, int in educe.♦ A aso a t a opr t l elofca a t nd l bout he ppr iae ev pit l o hol d. 42
  43. 43. ♦ Ast ong ca a al t pr pr r pit l locaion ocess oduces subst nt lbenefit a ia s.♦ T pr amostaw ys l ds t impr ement he ocess l l a ea o ov s.♦ F nce execut es ae for t exa ina iv r ced o mine prospect forr enues, cost a r s ev s nd isks in alt l heir business a iv ies. ct it♦ M na s st r t l r t a t a ger at o ean hings bout heir business t did notknow hey . 43
  44. 44. Extrem e Value Theory (EVT) ♦ E Text t cent a l t em w V ends he r l imit heor hich deas l w h t distibut of it he r ion t a er ge of he v a ident ly a independenty distibut ical nd l r ed v r bl fr a aia es om n unknow distibut t t n r ion o he distibut oft t il r ion heir a s. ♦ T E Ta oa is usefulforest t t il pr bil ies ofexteme ev s. he V ppr ch imaing a oba it r ent ♦ F v y high confidence l el (> 99%), t or er ev s he nor l distibut gener ly ma r ion al under imaes est t pot ia l ent l osses. 44
  45. 45. ♦ E ica distibut sufferfr al ck of mpir l r ions om a daa t in t t il he a s.♦ T ma itdifficul t est t V Rr ia y. his kes t o imae A el bl♦ E T hel us t dr w smoot cur es t ough V ps o a h v hr t exteme t il of t he r a s he dist ibut ba on r ion sed pow fulst t ica t y. er aist l heor♦ In ma ca t tdistibut w h 46 ny ses he r ion it - degr of fr ees eedom is a t dequae t descr t o ibe he t il offina ldaa as ncia t . 45
  46. 46. ♦ E Ta ies t t t il V ppl o he a s♦ Nota opr t fort cent e oft distibut ppr iae he r he r ion♦ Aso cal semi paa r a oa l led r metic ppr ch♦ E Tt em w s pr ed byG V heor a ov nedenko in 1943♦ E Thel us t dr wsmoot cur es t ough t t il V ps o a h v hr he a s oft dist ibut he r ion 46 46
  47. 47. EVT TheoremF(y) = 1 – (1+ € y)-1/€ €≠ 0F(y) = 1 – e-y €= 0y = (x -µ)/ß, ß> 0Nor ldist ibut coresponds t € = 0 ma r ion r oT il disa ra exponent lspeed a s ppea t ia 47 47
  48. 48. EVT Estim ators 2% Normal EVT 0% 48 48
  49. 49. ♦ F t E Tfunct t r hist ica daais fr ughtw h t sa pit ls a V R iting V ions o ecent or l t a it he me fal s A .♦ Once in al ime ev s ca be t ken int a ifet ent nnot a o ccountev bypow fulst t ica t s. en er aist l ool♦ So t need t be compl ed byst ess t ing. hey o ement r est♦ T goa of stess t ing is t ident unusua scenaios t t w d not occur under he l r est o ify l r ha oul st ndad V R a r A models.♦ Stess t s ca simul t shocks t t ha e nev occured or ha e been cov ed highl r est n ae ha v er r v er y unl y. ikel♦ Stess t s ca aso simul t shocks t tr ect per nentst uct a br ks ort r est n l ae ha efl ma r ur l ea empor r y ail cha st t ica pat ns. nged aist l ter 49 49
  50. 50. ♦ St ess t ing shoul be enfor butt pr em is r est d ced, he obl t stess needs t be perinent he r o t t t t ofr o he ype isk t he inst ut ha it ion s.♦ Itw d be difficul t enfor al ed numberof oul t o ce imit r ev ntstess t s. el a r est♦ T compl porfol model ba gener ly empl giv t ilusion of a ae he ex t io s nks al oy e he l ccur t simul t a t aion t he expense ofsubst nce. a 50 50
  51. 51. H ow effective are VAR m od els? VAR and sub prim e ♦ T t he endency of r ma ger a ot ` isk na s nd her execut es t descr ev s in t ms of iv o ibe ent er ‘sigma t l ’ els us al . ot ♦ W ert e is t l a sigma itimpl a henev her ak bout , ies nor l ma dist ibut r ion. ♦ R ll distibut ha e fa t il ea ife r ions v t a s. ♦ G dma Sa chief fina l officer Da id V r ol n chs’ ncia v inia once descr t cr ibed he edit cr a “a25- unch s sigmaev ” ent 51 51
  52. 52. ♦ T cr cr ofl t 20 7w s l r yafa ur of he edit isis ae 0 a agel il e risk ma gement na .♦ R model ofma ba w e una e t isk s ny nks er bl o pr t l ihood , speed orsev it of edict he ikel er y the crisis.♦ At ion t ned pat al t t use ofv l a- tent ur ricul ry o he aue- t risk a amea e oft s sur he r inv v in a porfol isk ol ed t io.♦ W e afewV Rexcept ae expect – 99%, a hil A ions r ed pr l w king modelw d opery or oul st l pr il oduce t o t t ee except a yea – t exist of cl er of w o hr ions r he ence ust s exceptions indicaes t tsomet is wong. t ha hing r 52 52
  53. 53. ♦ Credit Suisse repored 11 except a t t ions t he 99% confidence l el in t t ev he hird quat , Lehma brot s t a 95%, Gol n Sa fiv a rer n her hree t dma chs e t 95%, M n orga St nl six a 95%, Bea St r a ey t r eans 10a 99% t and UBS16a 99%. t♦ Cl ry V Ris at fornor lmaket a it eal , A ool ma r s nd is not designed forst ress sit t uaions. 53 53
  54. 54. What wind ow?♦ Itw d ha e been difficul forV Rmodel t ha e oul v t A so v ca ur alt r maket pt ed l he ecent r ev s, especial a t ent ly s he env onmentw s emer fr aper of r aiv y benign ir a ging om iod el t el v ail y. ol t it♦ At o- r w w yea indow w ca ur t extemes, so on’t pt e he r t he V R it pr A oduces w lbe t l . il oo ow♦ Al ongerwindowis apat lsol ion a best. ria ut t♦ Itw limpr e mat s al te, butitaso sw mps il ov ter itl l a r ev s. ecent ent 54 54
  55. 55. Is shorter wind ow a better thing?♦ Al ongerobser aion per ma pick up aw vt iod y ider v r y of maketcondit aiet r ions, butitw d not necessail al oul r y low V Rmodel t r ctquickl t a exteme ev . A s o ea yo n r ent♦ If t pr em is t tmodel ae notr ct fa he obl ha s r ea ing st enough, some bel e t a er iev he nsw w d in fa be t use shorerw s. oul ct o t indow♦ T model w d be sur ised byt fir out ea ofv ail y, butw d r pidl a pt hese s oul pr he st br k ol t it oul a y da . 55 55
  56. 56. What m od els work best?♦ T best V R model ae t t t ae quicker he A s r hose ha r t o r ct t a st ea o ep- cha in v ail y. nge ol t it♦ W h t benefit of hindsight t t of V R model t t w d a ual ha e w ked it he , he ype A ha oul ct ly v or bestin t he second hafof20 7 w d mostl yha e been a l 0 oul ikel v modeldr en bya iv frequentyupdaed shor daa hist y. l t t t or♦ Or a fr ny equenty updaed shor daa hist y t t l t t t or ha w s mor r eight e ecent obser aions mor hea il vt e vy t n ha mor dist ntobser aions. e a vt 56 56
  57. 57. ♦ In a env onment l t t d quat of 20 7, a n ir ike he hir rer 0 long daa ser w l t ies il incl a ext e per of l ude n ensiv iod ow v ail y, w w l mut t model ol t it hich il e he ’s r ct t a ea ion o sudden incr se in v ail y. ea ol t it♦ At lhough itw lincl episodes ofv ail yfr il ude ol t it om sev a yeas a t w lbe er l r go, hese il out eighed byt int v per ofcam. w he er ening iod l 57 57
  58. 58. The im portance of upd ating♦ In t w ke of t r he a he ecent cr cr a unagua e edit isis, n r bl impr ement seems t be ov o incr sing t fr ea he equency ofupdaing. t♦ M hl orev quat l updaing oft daa ser is t nor ont y en rery t he t ies he m.♦ Shift t w y orev da y updaing w d impr e t ing o eekl en il t oul ov he responsiveness of t modelt a he o sudden cha ofcondit nge ions. 58 58

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