VaR

1. Value at Risk
By A V Vedpuriswar
Febr r 8 20 9
uay , 0

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. ♦ 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. 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. Illustration
Aer ge r enue = $5.1 milion perda
v a ev l y
T a no.ofobser aions = 254
ot l vt .
St dev= $9.2 milion
d l
Confidence l el= 95%
ev
No. ofobser aions < -$10milion = 11
vt l
No. ofobser aions < -$ 9milion = 15
vt l
5

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. 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. 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. 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. 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. ♦ 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. 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. F st t a is v l a t init lpoint
ir , he sset aued t he ia .
V = V 0)
0 (S
dv= dvds | ds = ∆0 ds = (∆0 s)ds/
/ s
s is t r fa or
he isk ct .
Porfol V R= |∆0| x V R = |∆0| x (ασS0)
t io A As
σ = St dev ofr t ofcha in t pr
d n aes nge he ice
α = St nor ldev t coresponding t t
d ma iae r o he specified
confidence l el
ev .
13

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. 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. ♦ 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. 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. ♦ 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. 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. ♦ 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. ♦ 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. ♦ 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. ♦ 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. ♦ 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. ♦ 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. ♦ 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. 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. ♦ 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. 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. ♦ 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. 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. ♦ 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. ♦ 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. 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. ♦ 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. ♦ 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. ♦ 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. ♦ 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. ♦ 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. ♦ 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. ♦ 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. ♦ 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. ♦ 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. 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. ♦ 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. ♦ 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. EVT Theorem
F(y) = 1 – (1+ € y)-1/€ €≠ 0
F(y) = 1 – e-y €= 0
y = (x -µ)/ß, ß> 0
Nor ldist ibut coresponds t € = 0
ma r ion r o
T il disa ra exponent lspeed
a s ppea t ia
47
47

48. EVT Estim ators
2%
Normal
EVT
0%
48
48

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. ♦ 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. 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. ♦ 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. ♦ 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. 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. 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. 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. ♦ 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. 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