metodologías de muestreo

7/30/2019 Metodologas de Muestreo

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Bank Sup erv ision and Exam ina t ion Process

Sam pl ing M ethodo logies

C o m p t ro l l er s H an d b o o k

A ugust 19 98

EP-SM

Comptroller of the Currency

Administrator of National Banks

EP


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C o m p t ro l l e r' s H a n d b o o k i Sa m p l i n g M e th o d o lo g i e s

Sam pli ng M etho dol ogies Tab le o f Con ten ts

In t roduc t ion 1

B a c k g ro u n d 1O C C Po l i c y 2Samp l in g O b jec t ives 3Sa mp l i n g M e th o d s 5

N on stat ist i ca l Sam p l i ng S Judgmenta l 5Statis tica l Sam pl in g S Propor t iona l 5Statis tica l Sam pl in g S N u m e r i c a l 6A p p l i c a ti o n o f M e th o d s o f Sa mp l i n g 6

Statist ica l Sam pl in g A ssuranc e 9Prec is ion 9Re l iab i l i t y 11Samp l in g R isk 12

Sam pl in g Plans 12Popu l a tion Se lec t ion 13Samp le D esign and Se lec tion 14Samp le Eva lua t ion and In te rp retat ion 19Prob ab i l i t y Statemen t 25Repo r t o f Exam ina t ion (RO E) Com m ents 27

Examinat ion O bject ives 2 9

Examination Procedures 3 0Prop or t ion a l Samp l in g 30

N u m e r i c al Sam p l i n g 3 2

Appendix 3 4A. Prop or t ion a l Sam p l i ng Eva lua t ion W orksheet 34B . N u m e r i ca l Sa mp l i n g Ev a lu at i o n W o rk sh e e t 3 7C. Sta tis tica l Sam pl in g O versta tem ents 38D . Sta tis tica l Sam pl in g U nd ersta tem ents 39

Glossary 4 0


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C o m p tro l l er ' s H an d b o o k 1 Sam p l in g M eth o d o lo gi es

Sam pli ng M etho dol ogies I n t ro d u c t i o n

Background

I t i s usua l ly im prac t ical o r im po ssib l e to rev iew a l l i tems o r fi les w henexami n in g an a rea o f bank o pera tion s, espec ia l l y i f the vo l um e o f in fo rm ationis la rge. Exam in ers use sam pl in g to ob serve a rando m sub set to learn abo utth e mu l t i tu d e o f i t em s f ro m w h ic h th e y are d ra w n . U p o n d ra w in g stat i st i c alin ferences f rom th is sub set , they can sta te w i th a cer tain l eve l o f co nf id encetha t the in fe rences app ly to the po pu la t ion as a w ho le .

Benef i ts o f us ing sta tis tica l sam pl in g inc l ud e:

C The ab i l i t y to q uan t i fy resu l ts and re la te them to the en t i re po r t fo l io be ingre v ie w e d .

C The ab i l i t y to q uan t i fy samp l in g r i sk ( i .e ., the r i sk tha t the sam p le i s no tind ica t ive o f the en t i re po r t fo l io ) .

C Effec t ive use o f l im i ted exam in er resou rces.

Th i s bo ok le t d iscusses sta tist ica l sam pl in g in genera l , as w el l as spec i f icmethods o f des ign ing, se lec t ing, and eva luat ing s ta t is t ica l ly va l id samples.

The tw o typ es o f stat i st i ca l sam p l i ng m ethods d iscussed m ost p rom inen t ly inth i s b o o k le t are n u m e r i ca l sa mp l i n g a n d p ro p o r t i o n a l sam p l i n g . I n n u m e r i ca lsa mp l i n g , ea ch i t e m i n a p o p u la ti o n i s e q u a l l y l i k e l y t o b e d raw n . I n

p rop or t ion a l samp l in g , the l i ke l iho od o f an i tem b e ing se lec ted isp rop or t ion a l to the i tem s size .

A n exam iner s cho ice o f a samp l in g metho d depen ds on the spec i f i cob jec t ives o f the sup erv iso ry ac t iv i ty . Som et im es, exam iners m ay choo se asamp l in g m ethod tha t i s no t stat i st i ca l tha t i s, they m ay w an t to re ly onj u d gm en t o r sp ec i f i c k n o w led ge ab o u t a p o p u lat i o n i n sel ec t i n g fi l es fo rrev iew . Exam iners do n o t use the resu l ts f rom a jud gm enta l l y de r ived samp leto d raw co nc lu sion s abou t a la rge r po pu la t ion . O f ten , the spec i f i ckno w ledge o r ju dgm ent used to d e r ive the non stat ist i ca l sam p le is used todeve lop stat i st i ca l l y va l id sam p les tha t d iv id e the pop u la t ion in to g roup s.Each group , or st ra tum , can then be rev iew ed, in tens ive ly i f necessary . Suchsamp l in g im prov es the exam ina t ion p rocess.

Th is bo ok l e t p rov ides gu idance on w h ich samp l in g m ethods a re best fo rspec i f ic areas o f exam in at ion i n terest . A l tho ugh th e d iscussio n is gearedtow ard samp l in g loan p o r t fo l io s, o the r types o f i tem s in vestm en ts,dep os i ts, and o f f -ba lance-sheet acco un ts can be sam pl ed. By sam pl in g,


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Sam p l i n g M eth o d o lo gi es 2 C o m p tro l l er ' s H an d b o o k

exam in ers can test the e f fec t iven ess o f pro cesses, po l ic ies, co ntro ls ,m anagem ent in fo rm ation systems , o r r i sk m anagem ent p rac t ices.

O CC Pol icy

The O CC genera l l y do es no t requ i re the use o f any spec i f i c samp l in gm ethodo logy . U n less spec i f i ca l l y add ressed in a handb oo k sec t ion o r o the rpo l i cy gu idance , the use o f samp l in g in a sup erv iso ry ac tiv i ty , as w e l l as thetyp e o f sam pl in g used, is le f t to the d iscre tio n o f the exam in er-in -charge (EIC).The Sam p l i ng O b jec t ives po r t ion o f th is boo k le t addresses m atte rs tha texami ners m ust conside r in d e term in i ng an app ropr ia te sam p l i ng approach aspart o f a ban k s sup erv isory s t rategy.

Fro m t im e to t im e , O C C se n io r m a n ag em e n t ma y re co m m e n d a sp e c i f i csamp l in g m ethod fo r exam in i ng ce r tain on - o r o f f -ba lance-shee t accou n ts.They m ay also p rov id e gu idance on w h ich pa ram eters to use in se lec ting asamp le . Such gu i dance m ay be par t o f a year s O CC op erat ing p lan , as w e l l

as o the r O CC issuances. Fo r exam p le , the exam ina t ion p rocedu res fo r fai rl e n d in g a n d c o m m u n i t y b a n k c o n su m e r co m p l i a n c e h av e sp e c i f i c gu id a n c eo n sa mp l i n g m e th o d s.

W hen con du c t ing stat i st i ca l samp l in g , exami ners sho u ld u se the fo l low inggu ide l ines :

C The pop u la t ion s to be sam p led shou ld be the po r t fo l io s iden t i f ied in thebank s appro ved sup erv isory st ra tegy. I f the focus is on th e in terna l l yra ted no nc lassi f ied po r t ion o f the bank s loan p o r t fo l io , the po pu la t ionsho u ld general l y exc lud e Shared N a tion a l Cred i t (SN C) loans . H ow ever ,

there m ay be c i rc um stances (e.g . , test ing fo r pro cess, po l ic y o ru n d e rw r i t i n g ex c e p t i o n s) i n w h i c h e x am in e rs a re j u st i fi e d i n i n c lu d in gSN C lo a n s i n t h e sa mp le p o p u la ti o n . T h e p o p u la ti o n s h o u ld a l so e x c lu d e c red i t b aske t loans (sm a l l bu siness loans requ i r in g l im i tedd o c u m e n tat i o n a s o u t l i n e d i n t h e M a rc h 3 0 , 1 9 9 3 I n terag en c y P o l i c yStatemen t on D ocu m enta tion o f Loans ).

If th e b an k s m an ag em en t i n fo rm at i o n sy stem ac cu rat el y rep o rtslegal l y b ind ing com m i tm en ts, the samp le sho u ld b e se lec ted on thec o m m i tm e n t a mo u n t . W h e n th e sa mp le ca n b e se lec ted b y e i th e rthe no te (an ind i v id ua l loan ) o r the bo r row er , exami ners sho u ldc h o o s e th e b o r ro w e r.

C The sam p l i ng p lans fo r banks tha t are pa rt o f m u l t ib ank ho ld i ngcom pan ies sho u ld be con sisten t fo r a l l na t iona l banks in the com pany .For exam p le , i f the com pany st rategy ca l l s fo r u sing p ropo r t iona lsa mp l i n g w h e n re v iew in g th e q u a l i ty o f c o m m e rcia l l o an s i n o n e o f th ef ive na t iona l b ank subsid i a r ies, the EIC sho u ld use p ro po r t iona l sam p l i ngon the com m erc ial lo ans a t each o f the o th e r sub sid i a ry b anks.


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C The EIC sho ul d d eem sta tis tica l sam pl in g reason able and feasib le w i threspec t to the nat iona l bank be ing exam ined . The size and co m po si t iono f the samp le sho u ld be com m ensura te w i th the r i sk charac te rist i cs o f thepo pu la t ion be ing tested . Com m on sense and judgm ent a re c r i t i ca l inde te rmi n in g the focus and ex ten t o f test ing . The exam iner sho u ld

con side r any kno w n resou rce const rain ts on the bank o r exam in i ngperson ne l re la ting to t im e , pe rson ne l , and co sts. These inc lu de , bu t a reno t l im i ted to , ac tua l o r p ro jec ted samp le sizes, ava i lab i l i t y o f exam in i ngand b ank sta ff , ava i lab i l i ty o f data pro cessin g hardw are and sof tw are, andany o ther per t inent fac tors .

C A l th o u g h p ro p o r t i o n al a n d n u m e r i c al sa mp l i n g c an b e d o n e m a n u al l y , ana u to m a te d sa mp l i n g p ro g ra m o r m o d u le c an b e m o re e ff i c i en t a n d l e ssbu rdensom e. Exam iners sho u ld t ry to use a bank s ow n au tom atedsamp l in g p rog ram , i f ava i lab le . Exam iners m ay also use o the r avai lab leau tom ated p rog ram s.

C Because p rec isio n and re l iab i l i ty leve l s (i .e . , sta tist ica l assuranc e) af fec tthe size o f samp les, the O CC recom m ends tha t exam iners use thefo l lo w ing gu id e l ines. Fo r p ropo r t iona l samp l in g , exami ners sho u ld useprec ision leve ls o f 5 p e rcen t , 10 pe rcen t , 15 pe rcen t , o r 20 pe rcen t andre l iab i l i t y leve ls o f 80 p e rcen t , 86 pe rcen t , 90 pe rcen t , o r 95 p e rcen t . Fo rnu m er ical samp l in g , exam iners sho u ld use p rec ision leve ls o f 5 p e rcen to r 10 p e rcen t and re l iab i l i t y leve ls o f 90 pe rcen t o r 95 pe rcen t . Th isbooklet d iscusses stat is t ical assurance in a later sect ion.

Sampl i ng O bject ives

Sup erv isory st ra teg ies for nat io na l b anks sho ul d spec i f ica l ly n ote i f theexami na t ion p ro cess w i l l u se sam p l i ng . Based upo n the ob jec t ives o f thesuperv isory ac t iv i t ies , the s t ra tegy should ident i fy the por t fo l ios to sample, thetype o f sam p l i ng to use , and the pu rp ose o f the samp l in g . I f exami na t ionp lann ing ac t iv i t ies ind ica te a p rev ious ly un i den t i f ied need fo r samp l in g , theEIC sho ul d ch ange the st ra tegy to n ote th i s.

In de te rm in i ng the type o f sam p l i ng to use, exam iners con side r the qu an t i ty ,qu a l i t y , and n a tu re o f the pop u la t ion to be rev iew ed ; the bank s r i skmanagement sys tems; the bank s appet i te for r isk ; the ob jec t ives and benef i tso f the d i f fe ren t samp l in g m ethods ; the pu rp ose and ob jec t ive o f the samp le ;and resou rce const rain ts. Exam iners m ay choose w h ich o f the th ree samp l in g

m e th o d s ju d g me n ta l , p ro p o r t i o n al , o r n u m e r i ca l w i l l b e st m e et th eob jec t iv es o f superv isory st ra tegy.


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The fo l l ow ing l i st h igh l igh ts som e st rategic o b jec t ives tha t exami ners m ayw an t t o m e et b y u sin g sa mp l i n g .

C Com m erc ia l loans, com m erc ia l rea l estate loans, f loo r p l an , andreceivab le f inanc in g :

SVa l ida te r i sk management and in te rna l p rob lem loan iden t i f i ca t ionsystem s or test p ro cess effect iv eness.

S Iden t i fy add i t ion a l c red i t r i sk expo sure in the samp led po r t fo l i o .

S D e te rm in e c o m p l i a n c e w i th u n d e rw r i t i n g stan d a rd s.

S Iden t i fy adm in ist ra tiv e w eaknesses (e.g . , f in anc ia l sta tem ent or o therdocumenta t ion excep t ions ) .

S A ssess the adeq uacy o f the a l lo w ance for l oan and l ease losses

(ALLL).C Reta i l lo ans (e.g . , con sum er paper, c red i t card , check cred i t , resid ent ia l

real estate , and ho m e equ i ty lend ing ) :

S V a l ida te adh erence to app ropr ia te pe r fo rm ance repo r t ing stand ardsby check in g ex tension o r re -ag ing h i sto ry .

S D eterm ine l i en pe r fec t ion s ta tus.

S A ssess com p l i ance w i th un derw r i t ing stand ards th rough a rev iew o fov err ides, ex tens ion s, renew als or o th er loans.

S Dete rmine comp l iance w i th laws and regu la t ions (e .g . , consumerc o mp l i a n c e ) .

C M un ic ip a l investm en ts o r de r iva t ives:

S Val idate r isk management sys tems.

S Iden t i fy c red i t o r m arket r i sk exp osure .

S D e te rm in e c o m p l i a n c e w i th i n v e stme n t s ta n d ard s.

S Iden t i fy adm in ist ra tiv e w eaknesses (e.g . , f in anc ia l sta tem ent or o therdocumenta t ion excep t ions ) .


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C D epos i t accou n ts:

S V er i fy the accuracy o f the in te rest ra te , term s, and co nd i t ion s w hencom pared to the d isc losed con t rac tua l in fo rm ation .

S

D e te rm in e c o m p l i a n c e w i th a b an k s d ep o si t p o l i c i e s.S Iden t i fy w eaknesses in a bank s dep os i t operat ion s.

S D e te rm in e c o m p l i a n c e w i th a p p l i c a b le l aw s a n d re gu la ti o n s .

C C o n s u me r c o mp l i a n c e :

S D e te rm in e c o m p l i a n c e w i th f ai r l e n d in g l a w s a n d re gu la ti o n s .

S D e te rm in e c o m p l i a n c e w i th t ru th -i n - l en d in g an d o th e r c o n su m e rcomp l iance d isc losu re requ i rements .

S Eva lua te the re l iab i l i t y o f a bank s com p l i ance m anagem ent system.

Sampl ing Methods

N on stat i st i cal Sam p l i ng S Judgmental

Jud gm enta l samp l in g is sam p l i ng w i tho u t stat i st i ca l m easurem ent . The O CChas h is tor ica l ly used, and cont inues to use, nonsta t is t ica l judgmenta lsa mp l i n g i n i t s e x am in a ti o n s . U sin g so u n d j u d g me n t a n d k n o w le d g e o f abank s po l i c ies, con tro ls , and system s, exam in ers id ent i fy th e bank s areas o f

greatest r isk exp osure and se lec t i tem s for rev i ew .

Jud gm enta l samp l in g a l low s exami ners to rev iew an iden t i f ied p e rcen tage(coverage) o f a spec i f i c po pu la t ion . A l thou gh exam iners canno t stat i st i ca l l yre la te the resu l ts o f th i s sam pl e to the ent i re po pu la t ion o f i tem s, they caniden t i fy spec i f i c excep t ion s. The resu l ts o f the jud gm ental sam p le a recons ide red when examiners eva lua te the qua l i t y o f the popu la t ion rev iewed .Exam iners sho u ld com m ent on excep t io ns, iden t i fy ing the roo t causes o fthose excep t ion s. Fo r exam p le , excep t ions no ted in a rev iew o f loando cum entat ion o n in stalm en t loan ex tension s cou ld b e the resu l t o f bankperson ne l s lack o f tra in ing o r inadequ a te know ledge o f bank po l i cy .

Stat is t ica l Sampl ing SPropor t iona l

Prop or t ion a l samp l in g is approp r ia te w hen the do l l a r am ou n t o f i tem s isre levan t to the ob j ec t ive o f a p roced ure , pa r ti cu l a r ly w hen tho se do l l a ram ou n ts va ry sign i f i can t ly . In p ropo r t iona l sam p l i ng , the po pu la t ion to besamp led is de f ined by do l la r am ou n t . Large do l la r am ou n ts have a g rea te r


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chan ce o f b e ing selec ted th an sm al ler on es; a l l i tem s greater than a cer tainam ou n t and a rep resen tat ive nu m ber o f sm a l le r i tems are se lec ted .Prop or t ion a l samp l in g is use fu l to exam iners eva lua ting the q ua l i t y o f a loanpo rt fo l i o b ecause o f the e f fec t la rger do l la r i tem s can have on asset qua l i ty .Som et im es, a st rategic o b jec t ive w i l l ca l l spec i f i ca l l y fo r th is app roach .

The o b jec t ive o f the sam p le i s to rev iew i tem s fo r a spec i f i c ch a rac te rist i c ,w h ich is a lso ca l led the featu re o f in te rest . The O CC h as h is to r ica l l yendo rsed the u se o f p ro po r t iona l sam p l i ng to d iscover add i t iona l c lassi f iedloans in com m erc ial loan po r t fo l i os . P rop or t ion a l samp l in g a lso isapprop r ia te w hen exam iners w an t to test popu la t ion i tem s fo r m on e taryerrors (i .e . , inco rrec t f inance ch arges, inco rrec t la te charges) or co m pl ianceer ro rs (i .e . , com p l i ance w i th un derw r i t ing stand ards, incom p le te d isc losu restatem ents).

Stat is t ica l Sampl ing S N u m e r i c a l

I n n u m e r i ca l sam p l i n g , t h e p o p u l a ti o n to b e sa mp l e i s d e f i n ed b y th e n u m b e ro f i tem s. N um er ical samp l in g is usua l ly u sed to reveal the p resence (o rabsence) o f a de f ined ch arac te rist i c in a po r t fo l io o f i tem s w i th s im i la rcharac te rist i cs. Each i tem i n the po pu la t ion h as the sam e p robab i l i t y o fse lec t io n as any o th er . Therefore , exam in ers m ay eva luate the resu l ts o fapp ly ing nu m er ical samp l in g and the re la ted exami na t ion o f se lec ted i tem son ly in te rms o f the nu m ber o f e r ro rs o r excep t ion s. Th is stat i st i ca l samp l in gm e th o d i s a p p ro p r i a te f o r e x am in a t i o n p ro c e d u re s i n w h i c h th e f re q u e n c y o fe r ro rs, excep t ion s, o r ano the r featu re o f i n te rest i s o f p r im ary con cern and thedo l la r am ou n t o f the excep t ion is no t cons ide red relevan t .

Th is m e thod is a val id sam p l i ng p rocedu re fo r de te rmi n in g adh erence to arequ i rem ent , such as a bank s und erw r i t ing s tandards o r in te ragencyc lassi f i ca tion po l i c ies fo r de l inq uen t loans. The O CC has h is to r ica l l yendo rsed the use o f nu m er ical samp l in g to evalua te retai l c red i t p o r t fo l io ssuch as in sta lm ent lo ans and res ident i a l rea l esta te loan s. Exam in ers can u senu m er ical sam p l i ng to gain a b road p e rspec t ive abou t the adequacy o f abank s adm in is tra t ive con tro ls and prac t ices. Sam pl e resu l ts can ind icate theef fec t iveness o f these sys tem s bu t do no t pro v id e a quant i ta t ive m easure o fthe resu l ts. D epend i ng up on th e sam p le ob jec t ives, resu l ts a re ind i ca ted byth e l e v el o f c o m p l i a n c e w i th a b a n k s ad m in i st rat i v e c o n t ro l s, b a n k in g l a w sa n d re gu la t i o n s, b a n k p o l i c y , o r O C C p o l i c y .

A p p l i ca ti o n o f M e th o d s o f Sa m p l i n g

Fol lo w in g are suggest ion s for app l y in g sta t ist ica l sam pl in g p lans and spec i f icpro cedu res to areas o f exam in at ion i n terest :


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Pro gram Exam p l es o f Sam p l i n g Pro ced u res

D u e Fro m Ban k s U se p ro p o rti o n al sam p l i n g to sel ec t acco u n tsw ho se reconc i l em en ts a re to be rev iew ed .

In v estm en t Secu r i t i es U se p ro p o rti o n al sam p li n g to sel ec tm u n ic ip a l se c u r i ti e s a n d m o n e y m a rk e th o ld in g s to d e te rm in e c o m p l i a n c e w i thin vestm ent standards.

B an k D e aler A cti v it i es U se p ro po rti on al sam p l i ng to sel ec t trad in gaccoun t secur i t ies fo r exam ina t ion .

Lo an Po rtfo l i o U se p ro p o rti o n al o r n u m er i cal sam p l i n g toM an agem en t v al i d ate i n tern al l o an rev i ew .

C o m m erc ial Lo an s U se p ro p o rti o n al o r n u m er i cal sam p l i n g to

A cco u n ts Recei v ab l e ev alu ate c red i t q u al i ty , co m p li an ce w i thFl o o r Pl an u n d erw r i ti n g stan d ard s, accu racy o fC o m m erc ial Real Estate i n tern al r i sk rati n g.Com m erc ial Lease Financ in gInd i rec t D eale r L ines

In stalm en t Lo an s U se n u m er i cal sam p l i n g to test:Cred i t Cards S The accuracy o f M IS, such as bank -C h eck C red i t p rep ared p ast d u e, p ro b lem l o anH o m e Eq u i ty l i st i n g, an d i n si d er l o an s.Resid enti a l Real Estate S Renew als, deferra ls and ex tensio ns for

c o m p l i a n c e w i th p o l i c y , d e gre e o fusage, accu racy o f repo rt ing.

S Score ove r r ides fo r com p l i ance w i thp o l i c y g u id e l i n e s a n d fai r l e n d in g l a w sand regu la t ions , documenta t ion ,reason ablen ess o f c red i t dec is ion .

S Recen t ly ex tended loans fo rc o m p l i an c e w i t h u n d e rw r i ti n g p o l i c y ,c red i t c r i te r ia , law s and regu la t io ns.

O th er Real Estate O w n ed U se p ro p orti o nal sam p l i ng to test fo r p o li cyadherence , w hen appro pr ia te , based on

n u m b e r an d v o l u m e .

D ep o si t A cco u n ts U se n u m er i cal sam p l i n g to sel ec t acco u n ts totest com pu tat ion o f in te rest , ea r ly w i thd raw a lp e n a l ty , c o m p l i a n c e w i th l a w s a n dregu la t ions.


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Fi d u c iary Acco u n ts U se n u m er i cal sam p l i n g to test co m p l i an cew i th t rus t agreem ents.

O ff -b al an c e-sh ee t ac co u n t s D e p en d i n g u p o n th e sam p l e o b j ec ti v es, u see i th e r p ro p o r t i o n al o r n u m e r i c al sa mp l i n g .

C o nsu m er C o m pl i an ce U se n um er i cal sam p li n g to id en ti fy a sam p lefo r T ru th - in -Lend in g o r T ru th -in -Sav ingsre v iew s, o r t o t est th e i n te gr i t y o f H M D A a n dCRA smal l bus iness lend ing reports .

C o m m u n i t y Re i n v est m e n t A c t U se n u m e r i c al sam p l i n g to se l ec t sam p l e fo rcom par ison o f c red i t ex tended ins ide andou tsid e a bank s assessm ent area or toper fo rm a lend in g test .

Examp les of how to sampl e for specif ic object ives:

O b jec t i v e Su ggested M eth o d

Id en ti fy un reco gn iz ed Pro po rt i o nal sam p le o f al l lo an s th at arec l assi fi ed l o an s i n n o t i n tern al l y rated .c o m m e rcia l l o a n p o r t fo l i o s .

V a li d at e c u rr en t i n ter n al r i sk Pr o p o rt io n al o r n u m e ri c al sam p l e o f al lrat i n gs an d i d en ti fy co m m erc ial l o an s, b o th th o se th at arec la ssi f i e d l o an s i n c o m m e rc ia l i n te rn a l l y rated a n d th o se th a t a re n o t .loan po r t fo l ios .

Test fo r co m p l ian ce w i th N u m e ri cal o r pro po rti on al sam p le fro mu n d e rw r i ti n g p rac ti c es an d , n e w asse ts b o o k ed si n c e t h e l ast p o l ic y , e .g .,c red i t c r i ter i a, ex am i n ati o n fo r a d efi n ed p er i o d (e.g., 3 0d o cu m en tat i o n , p r i c i n g to 9 0 d ay s).and te rm s.

T est f o r c o m p l i an c e o f c re d it N u m e ri c al sam p l e o f n e w l o a n s th atsco re l oan ov err i des w i th sco red bel ow a cu to ff , b u t w erep o l i c y an d fai r l en d i n g l aw s ap p r o v ed i n th e r ec en t p ast (e. g., 3 0 to 9 0an d regu l at i on s b y c hec ki ng d ay s).

c o m p l i a n c e w i th g u id e l i n e s,do cum entat ion o f reason fo rove r r ide , and approp r ia tenesso f c red i t dec ision .


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Test loan renew a ls and N um er ical sam p le f rom the en t i reex ten si o n s fo r c o m p l ian c e p o p u lati o n to test u sage an d ac cu rac y o fw i th p o l i c y , d e gr ee o f u sag e, r ep o r ti n g, o r n u m e ri c al sam p l e fr o m t h ean d ac cu rac y o f r ep o rti n g. b an k s r en ew al an d ex ten si o n l isti n g to t est

f o r co m p l i an c e w i t h p o l i c y .D eterm i n e accu racy o f th e N u m eri cal sam p l e fro m t he en ti rebank s m anagem ent po pu la t ion and t race repor tab le i tem s toi n fo rm ati o n sy stem . ap pro pr i ate l i sti n gs, e.g., p ast d ue, ren ew a l s

and ex tens ions, re-ag ings, prep aym ents, andins ider loans.

Id en ti fy r i sk ex p osu re Pro po rt i o nal sam p le o f al l m u ni c i p al b on dsi n th e m u n i c ip al bo nd an d ev al u ate th e sam p le fo r asset q ual i ty .Por t fo l io .

D eterm i n e accu racy o f th e N u m eri cal sam p l e fro m t he en ti reb a n k s e x te rn a l re p o r ts, su c h p o p u l a ti o n t o t est th e ac c u rac y o f re p o r te das H M D A an d C RA sm al l d ata.business reports.

D eterm i n e co m p l i an ce o f N u m er i cal sam p l e o f d ep osi t acco un tsd e p o si t ac co u n t s w i th p o l i cy b o o k ed w i th i n th e last si x m o n t h s o r si n c eg u id e li n es, d ep o si t c o n tr ac t t h e l ast e xam i n at io n an d d ete rm i n eterm s, a n d a p p l i c ab le l a w s c o m p l i a n c e w i th b a n k p o l i c y . En su rean d regu l ati o n s. th at rates an d term s o f th e d ep o si t are i n

agreem ent w i th the con t rac t and anyapp l icab l e law s and regu la t ions.

D eterm i n e co m p l i an ce o f N u m er i cal sam p l e o f al l acco u nts o rf id u c i ar y ac co u n t s w i th t ru st ac co u n t s b o o k ed si n c e th e l astagreem en ts. ex am i n ati o n an d ev alu ate th e acco u n ts to

ensure tha t the accoun ts are be ing h and led inaccordance w i th the t rus t agreem ent .

Statistical Sampling Assurance

Precis ion

P rec ision i s the exam iner s to le rance fo r excep t ion s in the sam p le .N orm a l ly , p rec ision im p l i es a range o f accep tab le va lues. M ost exami na t ionpro cedu res are designed to test except io ns to a bank s r isk m anagem entsystem s, i .e ., i ts po l ic ies, prac t ices, and p roced ures. Sin ce few except i on ssho u ld ex i st , samp l in g p rocedures a re con cerned p r im ar i l y w i th the upperp rec ision l im i t . Exam iners w an t to kn ow the g reatest ef fec t (the upp er


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Sam p l i n g M eth o d o lo gi es 1 0 C o m p tro l l er ' s H an d b o o k

prec ision ) tha t sam p l i ng excep t ion s w i l l have on the bank s con d i t io n . Theysho u ld adequa tely d ocu m ent in w ork i ng papers the i r reason s fo r se lec t ing ace r tain p rec ision va lue . Exam iners sho u ld con side r qu an t i ty o f r i sk , d i rec t iono f r i sk , and q ua l i t y o f r i sk m anagem ent in d e term in i ng p rec ision leve ls to use.In d esign in g sam pl es, the prec is ion l im i t a f fec ts the sam pl e size; the sm al ler

the prec i sio n l i m i ts, the la rger the size o f the sam pl e se lec ted.Propo r t i ona l Samp l i ng

W hen exam iners use p rop or t ion a l samp l in g , p rec ision is se t using apercen tage o f T ier 1 cap i ta l p lu s the a l lo w ance for lo an and l ease losses(ALLL). The larger the quan t i ty or num ber o f except io ns the EIC can to lera te ,the la rge r the p rec ision l im i t sho u ld be . Exam iners sho u ld base the p rec isionl im i t fo r p rop or t ion a l samp les on the i r kno w ledge o f a bank s f inanc ia l andopera t ing cond i t ions .

Exam iners sho u ld con side r :

C T h e c o m p o si t i o n o f t h e b an k s p o r t f o l i o . Fo r e x am p le , th e e x am in e r m a yto le ra te m ore excep t ions in a loan po r t fo l i o segmen t sup po r ted by l iqu idor marketab le co l la tera l than in one secured by rea l es ta te construc t ionloans.

C The bank s r i sk m anagem ent systems and con t ro ls. The be t te r the bank sr isk m anagem ent system, the m ore excep t ion s an exami ner m ay to le rate(in th e be l ie f tha t the bank w i l l i den t i fy de f ic ienc i es).

C The am ou n t o f p rev io usly i den t i f ied c lassi f ied lo ans. I f a bank h as a h igh

leve l o f c lassi f ied lo ans, the exam iner m ay se lec t a low er p rec ision leve lbecause she o r he i s less to lerant o f add i t ion a l c lassi f ied lo ans in thep o r t f o l i o .

C The loca l econom y. I f the loca l econ om y is st rong and stab le , theexami ner m ay to le ra te m ore excep t ions than i f the econ om y isexper ienc in g a dec l in e .

Ind i v id ua l bank c i rcum stances m ay sup po r t a p rec ision l im i t o f 5 pe rcen t , 10p e rc en t , 1 5 p e rc e n t, o r a ma x im u m o f 2 0 p e rce n t fo r p ro p o r t i o n a l sa mp l i n g .(A ny va lue less than 20 pe rcen t can be cho sen ; fo r d iscussion pu rposes in th isbo ok l e t , inc rem ents o f f i ve are used . ) W hen an exami ner can to le ra te few

excep t ion s, a p rec ision o f 5 pe rcen t i s no rm a l ly chosen . W hen an exami nercan to le ra te a la rge ra te o f excep t io ns, a p rec ision o f 2 0 pe rcen t i s no rm a l lycho sen . P rec ision leve ls g rea te r than 20 p e rcen t a re no t recom m ended .

For example, assume that s ince i ts las t examinat ion, a bank began extend inga sign i f i can t am ou n t o f new loans to the cab le te lev ision i nd us try . The bank sloan rev iew d iv ision has no t pe r fo rm ed an in -dep th rev iew o f th is a rea be fo re


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C o m p tro l l er ' s H an d b o o k 1 1 Sam p l i n g M eth o d o lo gi es

the sched ul ed exam in at ion date . Severa l o f these cred i ts appear on thede l in qu ency repor t . Based on repo r ted de l in qu enc ies in a po r t fo l i o no t ye tin te rna l l y rev iew ed , the exam iner m ay se lec t a p rec ision o f 5 p e rcen t and thesamp le size w i l l b e re lat i ve ly la rge .

O n the o the r hand , w hen a bank s in te rna l c lassi f ied f igu re is low , i t i ssu f f i c ien t ly cap i ta l i zed , the exami ner has con f idence in the in te rna l loanrev iew sys tem , sou nd con tro l sys tem s are in p lace, and the no nc l assi f iedc o m m e rcia l l o a n p o r t f o l i o i s to b e rev ie w e d , a p rec i si o n o f 2 0 p e rc en t a n d are la ti ve ly sma l l sam p le m ay be app ropr ia te .

N u m e ri c al Sa m p l i n g

A n e x am in e r se ts a p rec i si o n l im i t i n n u m e ri c a l sa mp l i n g b y d e c id in g h o wm a n y e x c ep t i o n i t e m s c an b e to l e rated i n t h e sa mp le p o p u la ti o n . T h e m o reexcep t ion s the exam iner can to le ra te , the h i gher the p rec ision l im i t sho u ldbe . Because non com p l i ance ind i ca tes w eakness in p o l i c ies, systems , o r

con t ro ls, bankers and exam iners sho u ld have a low to le rance fo r excep t ion sin th at area. Exam in ers sho ul d con sid er set t ing the prec isio n leve l a t 5percen t o r 10 pe rcen t .

Rel iab i l i t y

Rel iab i l i t y i s the leve l o f con f id ence in samp le resu l ts. Se lec ting are l iab i l i t y l eve l w i l l a ffec t the size o f a samp le : the h igher the re l iab i l i t y leve l ,the greate r the num ber o f i tem s exami ners w i l l rev iew . Exam iners sho u lddo cum ent in w ork in g papers w hy they se lec ted a ce r ta in re l iab i l i t y leve l .They sho u ld no t se lec t re l iab i l i t y leve ls w i thou t conside r in g the bank s

f inanc ia l cond i t ion , ri sk p ro f i le and r i sk m anagem ent systems . The m orecon f idence exam iners have in the in st i tu t ion and i ts r i sk m anagem entp rocess, the few er O CC exam iner resou rces sho u ld be needed to eva lua tetransactions.

Rel iab i l i ty fac tors are numbers that re f lec t re l iab i l i ty leve ls (95 percentre l iab i l i t y equa tes to a 3 .0 fac to r ; 80 pe rcen t re l iab i l i t y equa ls a 1 .6 fac to r ) .Re l iab i l i ty fac tors are used to determ in e sam pl e siz es and p rec isio nad jus tm en t fac to rs. W hen excep t ion s a re fou nd , exam iners use re l iab i l i t yfac tors to ad ju st prev io us ly se lec ted prec i sio n l i m i ts to eva lu ate sam pl e resu l tsand p e r fo rm stat i st i ca l sam p l i ng p ro jec t ions . (See exam p les in th i s bo ok l e t ssec t ion Samp l in g Plans un der Sam p le D esign and Se lec t ion and

N um er ical Samp le Eva lua t ion W orksheet Exam p le . ) The re l iab i l i t y fac to rsin th is bo ok l e t , w h ich a re taken f rom Po isson p rob ab i l i t y d ist r ibu t io ns (seeg lossary fo r de f in i t ion ), are app rox im ation s o f the p rob ab i l i t y o f f ind in g a tleast on e excep t ion in a samp le o f selec ted i tem s a t a given re l iab i l i t y leve land error ra te . Re l iab i l i ty fac tors and the i r assoc i a ted rel iab i l i ty leve ls andprec ision ad jus tm en t fac to rs a re no ted in app end ix es C and D and a recom m on re fe rences fo r aud i t samp l in g pu rpo ses.


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Exam iners sho u ld con side r fou r d i f feren t rel iab i l i t y leve ls w hen u singprop or t ion a l s ta ti st i ca l samp l in g S 95 p e rcen t , 90 pe rcen t , 86 pe rcen t , and 80percen t . These leve ls a l low exami ners som e flex ib i l i t y in st ruc tu r ing thesam pl e based on an assessm ent o f the fac tors m ent io ned a t the beg in n i ng o fth i s sect ion and th e resu l tant to lerance for except i on s. These leve ls also

a l low exami ners to co n t ro l the assoc ia ted degree o f sam p l i ng r i sk (de f inedb e l o w ) .

T w o re l i a b i l i t y l e v el s sh o u ld n o rm a l l y b e c o n sid e red fo r n u m e r i c al sa mp l i n g 9 0 p ercen t an d 9 5 p ercen t. Becau se th e o b j ec t i v e o f n u m er i cal sam p l i n gis general l y to de te rm ine w he the r the bank adh eres to a po l i cy , system, o rcon t ro l , the O CC desi res a h igh d egree o f con f idence (i .e . , m in i m a l sam p l i ngrisk) in the results.

Sam pl in g Risk

Sam pl i ng r i sk i s the d i f ference o f one m inu s the re l iab i l i t y leve l . W i th 95

percen t re l iab i l i t y , the sam p l i ng r i sk i s 5 pe rcen t . Th is m eans tha t 5 pe rcen to f the t im e the resu l ts o f the samp le m ay no t be t ru ly ind ica t ive o f the en t i repo r t fo l i o . W i th 80 pe rcen t re l iab i l i t y , the sam p l i ng r i sk i s 20 pe rcen t . Th ism eans tha t 20 pe rcen t o f the t im e , o r one t im e in f i ve , the resu l ts o f thesamp le m ay no t be tru ly in d ica t ive o f the en t i re po r t fo l i o . Because theob jec t ive o f sam p l i ng is to test fo r dev i a tion s f rom a bank s po l i c ies,p roced ures o r p rac t ices, the O CC w an ts to m a in tain sam p l i ng r i sk a t leve lstha t al lo w a h igh degree o f con f iden ce in sam p le resu l ts and the i r va l id i ty .Sampl ing r isk greater than 20 percent is not acceptab le .

Samp lin g Plans

W hen sam p l i ng is used , exam iners dev ise a samp le p lan to m ake the m oste f f ic ient and e f fec t ive use o f resou rces to m eet the ob jec t iv es o f the rev iew .Each samp le p lan d esign inv o lv es the sam e con cep ts:

C Popu la t ion se lec t ion .C Samp le d esign and sam p le se lec t ion .C Sample eva luat ion and in terpre ta t ion o f resu l ts .

T h e fo l l o w in g c o m m e n ts a n d e x a mp l e s a re p ro v id e d to i l l u st rate th e sa mp l i n gp lan design p rocess fo r the th ree samp l in g metho do log ies. A l thou gh thec o m m e n ts a n d e x a mp l e s b e lo w re late to t h e c o m m e rcia l an d i n stalm e n t l o a n

port fo l ios , examiners can use sampl ing in any asset , l iab i l i ty , o r o f f -ba lance-sheet account .


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Pop u la t ion Se lec tion

In popu la t ion se lec t ion , exami ners dec id e w h ich po r t fo l i os to samp le . Theydo so b y co nside r in g the approved st rategy fo r the b ank and the ob jec t ives o fthe exam ina t ion . St rategies m ay cal l fo r exam iners to rev iew the en t i re

com m erc ial loan po r t fo l i o o r focus on p a r ti cu l a r types o f loans. Types a reg roup ed by c red i t , indus try af f i l i a tion , o r bank lend ing d iv ision . Se lec t ing ave ry b ro ad ca tegory , such as the en t i re com m erc ial lo an po r t fo l i o , can resu l tin a ve ry large sam p le size . W hen po ssib l e , exami ners sho u ld con side rfu r the r segmen t ing such la rge po r t fo l io s to reduce the w ork lo ad . To makestatist ical ly val id co nclu sions, examiners mu st d efine or str at i fy (group ) theselected pop ulat io n as m uch as possible b y t heir characteri st ic s.

For O CC pu rpo ses, assets genera l ly can be group ed in to tw o categor i es. Inon e category a re asse ts tha t typ ica l l y u se com m on , un i fo rm un derw r i t ingstandards (e .g . , one-to-fou r-fam i l y res ident i a l rea l esta te lo ans, co nsum erins ta lm en t loans, c red i t card loans, hom e im prov em ent loans, hom e equ i ty

lo ans, and ov erdra f t l ines o f c red i t ). In the o th er category are assets w i thb roader co m m on charac te rist i cs, such as type o f c red i t , ind ust ry , o r b ankd i v is ion (e .g . , com m erc ia l rea l esta te loans, rea l esta te con struc t io n o rdeve lop m ent loans, m un ic ip a l investm en t secur i t ies, p r iva te p lacem ents, o i land gas lo ans, and m ortgage w arehou sin g).

Exam p le o f Pop u la t i on Se lec ti on Jud gm en ta l Sam p l i n g

The exam iner i s concerned abo u t the accuracy o f the bank s r i sk g rad ingsystem for com m erc ia l real esta te lo ans id ent i f ied as pro b l em cred i ts. Inj u d gm en tal sam p l i n g, an ex am in er m ay d ec i d e to rev iew fi l es fo r co m m erc ial

rea l esta te lo ans o f $5 00 ,00 0 or m ore that are in terna l ly c l assi f ied . Theexam in er rev iew s a l l f i les se lec ted.

Exam p le o f Popu la t i on Se lec ti on Propo r t i on a l Sam p l i n g

The exami ner w an ts to de te rmi ne w he the r the nonc l assi f ied lo ans in a bank sasse t -based lend i ng d iv ision po se un recogn iz ed r i sk . P rop or t ion a l sam p l i ngcan b e used e f fec t ive ly to selec t a sta tis tica l sam pl e o f lo ans in terna l ly ra tedpass. Th is po r t fo l i o i s con side red g roup ed b ecause the popu la t ion inc lu desa l l no nc lassi f ied lo ans in th is pa rt i cu la r d iv ision .

Exam p le o f Pop u la t i on Se lec ti on N um er i cal Sam p l i n g

The exam iner i s con cerned abou t the num ber o f ove r r ides in a bank sins ta lm en t loan po r t fo l io . The exam iner can use num er ical samp l in g to testt h e e x te n t o f c o m p l i a n c e w i th t h e b a n k s o v e r r i d e p o l i c y .


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Sam ple D esign and Se lec tion

In samp le design and selec t ion , the exami ner de te rmi nes w h ich i tem s sho u ldbe in the sam pl e and bases se lec t io n o f the sam pl e i tem s on se lec tedre l iab i l i ty and prec i sio n leve ls . Exam in ers can cond uct a sta tis tica l sam pl e

m a n u al l y o r b y u sin g a n a u to m a te d sa mp l i n g p ro g ram .

Sam p le Selec t i on Jud gm en ta l Sam p l i n g

The exami ner uses sou nd jud gm ent to de term ine and selec t i tem s fo r rev iew .For exam p le , the se lec ted l oans m igh t in c lud e ten loans ex tended s ince thelast exam in at ion , f ive sign i f icant d ou bt fu l -ra ted c lassi f ied lo ans, seven l arge-do l la r sub stand ard loans, tw o n ew loans to in side rs, and any o the r type o floan tha t the exami ner dec ides to rev iew . The exam iner de term ines w he the rthe in te rna l lo an ra ting i s accu rate (by rev iew ing th e loans qua l i t y ) andw he ther the un derw r i t ing stand ards are sa fe and sound .

Sam p le Se lec t i on Propo r t i ona l Sam p l i n g

Sam pl e design , w i th a pro po rt ion a l sta t ist ica l sam pl e, cons ists o f se lec t in g there l iab i l i t y and p rec ision .

To se lec t sam p le i tem s f rom loan p o r t fo l io s, the exam iner m ay use the sam ecr i te r ia fo l lo w ed by the bank s in te rna l loan rev iew . A l te rna t ive ly , thee x am in e r c an s am p le f ro m e v ery l o a n i n t h e p o p u la ti o n o r , t o e l im in a te aloan rev iew o f sm a l l do l la r loans, the exam iner can spec i fy tha t the samp le istaken o f al l lo ans exceed ing a ce rtain d o l l a r am ou n t .

W h e n e x a m i n in g th e i n tern a l l y rated , n o n c la ssi f i e d c o m m e rcia l l o a npo r t fo l i o , lo ans to be exc l ud ed f rom the sam p le a re ones ex tended as pa r t o ft h e m in im a l l o a n d o c u m e n tat i o n p ro g ram , i . e. , c re d i t b a sk e t l o a n s.A dd i t ion a l l y , sha red na tion a l c red i ts m igh t be exc lu ded f rom sam p lesdes igned to test r isk ra t in g accuracy b ecause they are rev iew ed separate ly aspar t o f a spec i f i c p rog ram.

W i th t h e i n tern a l l y rated , n o n c la ssi f i ed c o m m e rc ia l l o a n p o r t fo l i o , e x am in e rsm igh t cons ide r using a p rec ision leve l o f 20 pe rcen t and a re l iab i l i t y leve l o f80 pe rcen t . These leve ls can be jus ti f ied w hen the bank h as adequa tecap i tal , accep tab le i n te rna l loan rev iew , sou nd r i sk m anagemen t systems , andgoo d asset qua l i ty .

O nce exam iners estab l i sh p rec ision and re l iab i l i t y , the sam p le is se lec ted .The size fo r a p rop or t ion a l sam p le (based o n selec t ing the samp le by no te ) i sest imated as:


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2 . I f th e d e si re d p re c i si o n l e v e l i s 5 p e rce n t an d th e rel i a b i l i t y l e v e l i s 9 5percen t , the equ a tion fo r the m on e tary in te rval i s :

$ 3 4 5 M M x .0 5 $ 1 7 .2 5 M M= = $ 5 .7 5 M M

3 3

The est im a ted samp le size is equa l to the samp le pop u la t ion d iv id ed bythe m on e tary in te rva l .

$ 1 , 3 0 0 M M= 2 2 6 l o an s

$ 5 . 7 5 M M

O nce the app ropr i a te samp le design is com p le ted , samp le i tems need to be

se lec ted . The exam iner m ust beg in the sam p le se lec t ion f rom a randomstar t ing po in t . Th is star t ing po in t i s a random ly cho sen num ber be tw een ze roand the m on e tary in te rva l .

Fo r e x a mp le , i f th e m o n e tary i n te rv al i s $ 5 ,7 5 0 ,0 0 0 , t h e ran d o m n u m e r i c alstar t i n g p o in t m u st b e a n u m b e r b e tw e en z e ro a n d 5 ,7 5 0 ,0 0 0 . T h e ran d o mnu m ber m ay be ob ta ined f rom va r ious metho ds , such as a tab le o f rand omnu m bers o r the se r ial num ber o f a do l la r b i l l . Au tom ated sam p l i ng so f tw arew i l l n o rm a l l y h a v e a ran d o m n u m b e r g en e rato r f ea tu re .

D iscussed b e low a re tw o sam p le m ethods fo r se lec t ing i tem s using a stand ardca lcu la to r and the bank s t r ial b a lance o r o the r repo r t l i st ing sam p lepo pu la t ion i tem s. Fo r i l l u st rat ion , the fo l l ow ing exam p les use 46 2 ,02 1 as thesamp le s random nu m er ical star t .

Cumu lat ive tota l . Beg inn in g w i th the fi rst i tem o n the tr ia l ba lance , th ism e th o d i n v o l v e s a d d in g th e d o l l a r am o u n t o f e ac h i t e m to a n o n g o in g to tal .The i tem w ho se ba lance resu l ts in th e sub to tal eq ua l ing o r su rpassing therandom nu m er ical s ta r t (e .g. , $46 2 ,02 1) i s chosen as the f i rst samp le i tem .The rem a in ing sam p le i tem s a re se lec ted by con t inua l l y add ing i temam ou n ts f rom the t r ial b a lance and se lec t ing each i tem w ho se ba lance causesthe sub to ta l to equa l o r exceed each i nc rem ent o f the m on e tary in te rva l ( i .e . ,$ 6 ,2 1 2 ,0 2 1 , $ 1 1 ,9 6 2 ,0 2 1 , e tc . ).

Negative/Positive. B e gin n in g w i th t h e ran d o m n u m e r i ca l star t e n te red i n toan add in g m ach ine as a negat ive num ber (e .g. , -46 2 ,02 1) , the do l la r am ou n tso f the t r ia l ba lance i tems are add ed u n t i l th ey sub to tal ze ro o r a po si t i venu m ber. The i tem that t riggers th is even t is se lec ted as the f i rst sam pl e i tem .From the sub to tal , the random nu m er ical s ta r t i s then co n t in ua l l y sub t rac tedun t i l the sub to tal again resu l ts in a negat ive num ber . Then the do l la r


19/44


am ou n ts o f the rem a in ing t r ia l ba lance i tems are add ed un t i l the sub to tal i saga in ze ro o r a pos i ti ve nu m ber . The i tem th a t t r igge rs the ze ro o r po si t i vesub to ta l is the next sam pl e i tem se lec t io n. Th i s pro cess is repeated to se lec teach subsequen t samp le i tem un t i l the po pu la t ion o f i tems is exhausted .

Sam p le Se lec t i on N um er i cal Sam p l i n g The samp le size fo r a num er ical sam p le is de te rm ined b y the re l iab i l i t y andprec i sio n l eve ls se lec ted.

re l iab i l i t y fac to r (f rom tab le 1 )sam p l e si z e =

prec i sio n (as a dec im al)

The fo l lo w ing ch art sho w s the samp le sizes assoc ia ted w i th O CC d esi redprec ision and re l iab i l i t y leve ls fo r num er ical samp l in g .

Sam pl e Sizes

Rel i ab i l i ty - 9 0 % Rel i ab i l i ty - 9 5 %

Prec i si o n 5 % 4 6 6 0

Prec i si o n 1 0 % 2 3 3 0

W hen re l iab i l i t y i s 95 p e rcen t (the co r respo nd ing re l iab i l i t y fac to r i s 3 .0 , f romappend ixes C and D ) and p rec ision is 5 p e rcen t , the exami ner se lec ts 60

i tems .

W hen re l iab i l i t y i s 90 p e rcen t (the co r respo nd ing re l iab i l i t y fac to r i s 2 .3 , f romappend ixes C and D ) and p rec ision is 10 pe rcen t , the exam iner se lec ts 23i tem s. A l thou gh a sam p le o f few er than 30 i tems can be se lec ted andrev iew ed , exami ners sho u ld no t p ro jec t sam p le resu l ts based o n such a sm a l lsamp le because o f the h i gh degree o f e r ro r in he ren t in such a sm a l l samp lep o p u l a t i o n .

Exam in ers sho ul d u se a bank s autom ated sam pl in g sof tw are, i f ava i lab le , top e r fo rm n u m e r i ca l sa mp l i n g . H o w e v er , a n u m e r i c al sa mp l e c an b e se lec ted

m a n u a l l y .W h e n se lec t i n g a n u m e r i ca l sa mp le m a n u al l y , e x a m in e rs sh o u ld d i v i d e th epo pu la t ion size by the samp le size to de te rm ine the samp l in g in te rval .


20/44


p o p u la ti o n si z e i n n u m b e r o f i te ms= sam p li n g i n terv al

sample s ize

(I f the resu l t i s a f rac t ion , the ru le o f thum b is to ro un d d ow n to the n ex tw h o l e n u m b e r. )

Fo r exam p le , i f the re are a to ta l o f 1 ,0 00 over r ide i nstalm en t loans, thesamp l in g in te rval i s 33 w hen re l iab i l i t y i s 95 pe rcen t and p rec ision is 10percent (30- i tem sample s ize) .

1 , 0 0 0= 3 3

3 0

The i tem tha t co in c ides w i th the random star t ing po i n t (using a rand omnu m ber se lec ted f rom a do l la r b i l l , rand om nu m ber tab le , o r o the r sou rce ) i sthe fi rst samp le i tem se lec ted fo r rev iew . The exam iner con t in ues cou n t in gand se lec t ing sub sequen t i tem s tha t co in c ide w i th the samp l in g in te rva l .

The samp l in g in te rval fo r nu m er ical sam p l i ng can a lso be de r ived using o the rse lec tion techn iq ues. These techn iqu es inc l ud e m easured in te rva l , spec i f i cpo si t ion , and te rm ina l d i g i t , and a re app l ied a f ter de term in i ng the rand omstar t ing po in t .

C M easured i n te r va l uses a set d i stance (e.g., in ch es) to select i tem s forrev iew . Each sub sequen t sam p le i tem w i l l b e the sam e measured in te rva lf rom the last sam p le i tem . I f the d istance f rom the f i rst samp led i tem on atr ia l ba lance to th e secon d is five in ches, the exam in er m easures everyf ive in ches on the t r ia l ba lance and se lec ts a sam pl e i tem .

C Spec i f i c p os i t ion uses a set po si t io n on each p age o f a l is t to se lec t i tem sfo r rev iew . I f , fo r examp le , the fi rst se lec ted sam p led i tem w as the lasti tem on a page , the exam iner cou ld se lec t tha t same i tem f rom eachsub sequ ent p age.

C T e rm i n a l d i g i t se lec ts sam pl e i tem s us ing the sam e term in a l d i g i ts, i .e . , theon e o r m ore d ig i ts fu r thest to the r igh t . Those i tem s hav ing the sam e

term in a l d i g i tsS

f o r ex a mp le , 0 0 8 9 , 0 1 8 9 , 0 2 8 9 . . . 9 9 8 9S

w o u l d b eselected.


21/44


Sam pl e Eva lu atio n and In terpre tat ion

In samp le eva lua t ion and in te rp re tat ion , exam iners rev iew the samp le resu l tsand d raw con c lus ions abou t the en t i re po pu la t ion o f da ta . By design in g asamp le p lan , exam iners a ttemp t to con t ro l the r i sk o f a sign i f i can t

de te r io ra ting cond i t ion rem a in ing und e tec ted . The eva lua t ion o f the samp lehe lp s exami ners ach ieve tha t ob jec t ive .

Stat ist i c ians recom m end tha t a samp le be a t least 30 i tems . W hen sma l le rsamp les a re used to m ake p ro j ec t ions abou t the popu la t ion f rom w h ich th eyare draw n, the degree o f error is too great . Exam in ers can st i l l p u l l sam pl es o fless than 30 i tem s, bu t they sho u ld no t be used to m ake p ro jec t ions abo u t thela rge r popu la t ion .

Jud gm en ta l Sam p l i n g

Sam ple resu l ts from no nstat ist i ca l sam p l i ng canno t be p ro jec ted beyon d the

loans samp led . H ow ever , excep t ion s d iscovered w hen evalua t ing thesecred i ts m ay suggest a la rger pro b l em . The resu l ts o f a ju dgm enta l sam pl e arecon side red w hen exam iners eva lua te the qu a l i t y o f the po pu la t ion f romw h ich the samp le w as se lec ted . Exam iners sho u ld com m ent on excep t ion sand id ent i fy the nature and p ossib le root causes o f the excep t ion s. Fore x am p le , a n i n d i v i d u a l b a n k e m p lo y e e s l a ck o f t ra i n i n g o r i n a d eq u a tekno w ledge o f bank po l i cy cou ld cause excep t ion s. Exam iners sho u ld d iscussexcep t ion s and roo t causes w i th bank m anagem ent .

Propo r t i ona l Samp l i ng

O ne o f the O CCs ob jec t ives in p e r fo rm ing a p ropo r t iona l stat i st i ca l samp lein a c o m m e rcia l l o an p o r t f o l i o i s t o i d e n t i fy e x c ep t i o n s. A n e x c ep t i o n i n t h i scase is, fo r exam p le , a loan c lassi f ied b y the O CC bu t no t c lassi f ied b y thebank . Such excep t io ns can e i the r be fu l l excep t ion s (the en t i re loan am ou n tis c lassi f ied ) or p ar t ia l except io ns (on ly a po r t ion o f the l oan i s c lassi f ied ).

W hen rev iew ing a samp le o f lo ans a bank has no t c lassi f ied , an exami nerm igh t conside r sc reen ing loans using c red i t f i l e in fo rm ation . D o in g so cou l dreduce f i le rev iew t im e . Since no ne o f the loans in the sam p le has beenc la ssi f i e d b y th e b a n k , o n l y a m in im a l fi l e re v iew m ig h t b e w a rran te d .H ow ever , sc reen ing requ i res exper ience and kno w ledge (see the C lassi f i ca tion o f Cred i t sec t ion o f the C o m p t ro l l er s H a n d b o o k ). W h en

sc reen in g loans, exam iners cou ld answ er the fo l l ow ing q uest ions :

C I s the pu rpose o f the loan id en t i f ied?

C I s the sou rce o f repaym ent iden t i f ied and is the lo an pay in g as agreed?

C I s the loan secured by m arke tab le o r l iq u id co l l a te ral?


22/44


C Is the f inan c ia l sta tem ent curren t and do es i t sup po rt the sou rce o fre p a y me n t?

C D oes the n a tu re o f the b usiness w ar ran t fu r the r con side ra t ion?

Based o n the answ ers to these qu est ions , exam iners dec ide w he the radd i t ion a l lo an f i le ana ly sis is necessary . I f screen in g suggests that the lo ansho u ld be c lassi f ied , exam iners mu st ana lyze i t m ore ex tensive ly usingt rad i t iona l me thods .

In th is exam p le o f rev iew ing p ass loans fo r ra t ing accuracy , O CC exam inersassign lo an ra t ings (pass, spec i a l m ent io n, substand ard, do ub t fu l , l oss) to a l lsamp le loans rev iew ed . The degree o f c lassi f i ca tion (sub stand ard , dou b t fu l ,or lo ss) is no t fac tored i n to a sta tis tica l p rob abi l i ty eva lu at ion ; the sign i f icantfac to r i s that the O CC con side rs the lo an to b e c lassi f ied and the bank sin terna l loan rev i ew sys tem has no t c lassi f ied i t . I f the O CC c l assi f ies a loan

tha t the bank d oes no t , the d i f fe rence is an excep t ion o f o ve rstatemen t .

W hen an exam iner rev iew s a po r t fo l i o con tain i ng bo th c lassi f ied andno nc lassi f ied lo ans, the evalua t ion is con du c ted in a sl igh t ly d i f fe ren t m anner .Even i f ra tin gs are som ew hat d i f fe rent ( i .e . , the O CC c l assi f ies the lo ansub stand ard , w h i l e in te rna l loan rev iew ra tes i t do ub t fu l ), no excep t io n ex is tsfo r stat i st i ca l samp l in g pu rp oses. Bu t an excep t ion cou ld ex i st i f samp l in gw as do ne on a popu la t ion o f lo ans a l l o f w h ich a re ra ted sub stand ard by theb a n k a n d a p o r t i o n o f w h i c h a re rated d o u b t fu l b y t h e O C C . I f i n te rn a l l o a nrev iew ra tes a loan as c lassi f ied and th e O CC c on sid ers i t a pass or spec ia lm en t ion l oan , the d i f ference is an excep t ion o f und erstatemen t .

Bo th un derstatemen ts and overstatements are con side red w hen in te rp re t ingsample results.

I f no except i on s are fou nd , the des i red sta tis tica l assuranc e (re l iab i l i ty leve land p rec ision leve l ) has been a t ta ined and no fu r the r evalua t ion is requ i red .W hen excep t io ns a re foun d , exami ners sho u ld fu r the r ana lyze and eva lua tethe excep t ions . Exam iners sho u ld a ttemp t to de te rm ine the roo t causes o fexcep t ion s and w he the r excep t ion s a re iso la ted occu r rences o r a p a tte rn o rp rac t ice . Som e possib i l i t ies to exp la in an excep t ion co u ld b e :

C The inexp er ience o f a bank o f f i ce r .

C A n in ten t iona l d i sregard fo r p o l i c ies and p rocedures.

C Excep t ion i tem s un iqu e to a pa r ti cu l a r type o f asse t , d iv ision in the bank ,o r ind ust ry .


23/44


24/44


PROPORTIONAL

SAMPLEEVALUATIONW

ORKSHEETI

Example:A

statistical

samplewasconductedofallcommercialloansratedpassbythebanksInternalLoanReview(

ILR).ILRide

ntifiedatotalof

$362,4

13,0

00classifiedcommercialloans(105percento

fTier1+A

LLL).A

reviewo

fthesampleitemsresultedinfourloans(all

belowt

hecutoff,

i.e.,

themonetaryinterval)beingclassifiedbytheexaminerwhichthebankconsideredPass.

Thisexampleworksheetiscompletedtoshowh

owt

he

valueofthoseexcept

ionsrelatetotheprecisionfactor.

Tier1Capital+A

LLL:$

345MM

Reliability:

90%P

recision:

10%

MonetaryPrecision(MP)$34.5

MM

MonetaryInterval(M

I):$15MM

OCC

Rating

Borrow

er

Loan

Balance

(L)

Sample

Exception

(SE)

Sample

Interval

MI/L=SI

Cutoff

Loans

Population

Exception

SExSI=PE

Rank

Precision

Adjustment

Factor

(P)

Precision-

adjusted

Exception

PExP

$2,1

88

$2,1

88

6.8

556

$15,0

00

1

1.5

9

$23,8

50

$6,0

07

$2,8

57

2.4

971

$

7,1

34

3

1.3

6

$

9,7

02

$3,8

50

$3,8

50

3.8

961

$15,0

00

2

1.4

4

$21,6

00

$

200

$

40

75.0

000

$

3,0

00

4

1.3

2

$

3,9

60

TOTALS

$8,9

35

$40,1

34

$59,1

12

RESULTS:

Prec

ision-adjustedExceptions

=

$

59,1

12

Prec

isionLevelof(as%o

fTier1+A

LLL)=

+

$

34,5

0

0

AdditionalProjectedClassifiedLoans

=

=

$

93,6

12

BankReportedClassifiedLoans

=

+

$

362,4

1

3

AdjustedProjectedClassifiedLo

ans

=

=

$

456,0

25

THEREFORE:

With

90

%r

eliability,weinferthatactualclassifiedcommercialloansshou

ldnotexceed132%o

fTier1CapitalplusALLL.


25/44


PROPORTIONAL

SAMPLEEVALUATIONW

ORKSHEETII

Example:Thissituatio

nissimilartothepreviouspageind

ataused.

However,inthisexample

thesamplewastakenofawholeco

mmercialloan

portfolioconsistingofbothclassifiedandnonclassifiedloans.

Thesampleresultedinthreeloans(allbelowt

hecutoff,

i.e.,

themonetaryinterval)not

classifiedbythebank

beingclassifiedbyexaminers,andoneinternallyclassifiedloanbeingra

tedpassbyexaminers(denotedby

amountin

parenthesesbelow).

Thisworksheetreflectstheimpactoftheunderstatementandtheoverstat

ementstotheprecisionfactor.

Tier1Capital+A

LLL:$345MM

Reliability:

90%

Precision:

10%M

onetaryPrecision(MP)$34.5

MM

MonetaryInterval(M

I):$15MM

OCC

Rating

Borrow

er

Loan

Balance

(L)

Sample

Exception

(SE)

Sample

Interval

MI/L=SI

Cutoff

Loans

Population

Exception

SExSI=PE

Rank

Precision

Adjustment

Factor

(P)

Precision-

adjusted

Exception

PExP

$2,1

88

$2,1

88

6.8

556

$15,0

00

1

1.5

9

$23,8

50

$6,0

07

$2,8

57

2.4

971

$

7,1

34

2

1.4

4

$10,2

73

($3,8

50)

($3,8

50)

3.8

961

($15,0

00)

1

.10

($

1,5

00)

$

200

$

40

75.0

000

$

3,0

00

3

1.3

6

$

4,8

08

TOTALS

$5,0

85

$10,1

34

$36,7

03

RESULTS:

Prec

ision-adjustedExceptions

=

$

36,7

03

Prec

isionLevelof(as%o

fTier1+A

LLL)=

+

$

34,5

0

0


=

=

$

71,2

03


=

+

$

362,4

1

3

AdjustedProjectedClassifiedLo

ans

=

=

$

433,6

16

THEREFORE:

With

90

%r

eliability,weinferthatac

tualclassifiedcommercialloanssho

uldnotexceed126

%o

fTier1CapitalplusALLL.


26/44



I n o u r e x am p le , t h e o b je c ti v e o f p e r fo rm in g a n u m e ri c a l sa mp l e o n o v e r r i d eins ta lm en t loans is to de te rm ine w he the r they a re sa fe ly and sou nd lyu n d e rw r i t te n a n d i n c o m p l i a n c e w i th an y o v e r ri d e p o l i c y . A n e x c e p ti o n

w o u ld b e a l o a n th at i s n o t i n c o m p l i a n c e w i th p o l i c y o r n o t u n d e rw r i t te np ru d e n t l y .

T h e sa me e v a lu at i o n g u id a n c e n o ted i n Pro p o r t i o n a l Sa mp l i n g a b o v e i sa p p l i c ab le t o w h e th er e x c ep t i o n s are fo u n d o r n o t .

H o w e v er , ex a m in e rs u se th e fo l l o w in g n u m e ri c a l e v alu a ti o n w o rk sh e e t tode te rmi ne the p rec ision -ad jus ted v a lue o f the excep t io ns.

N um erical Sampl e Evaluation W or ksheet Examp le

A n e x am in e r p e r fo rm e d a n u m e r i c al sa mp l e o f t h e i n stalm e n t l o a n

d e p a rtme n t t o d e term in e c o m p l i a n c e w i th t h e b an k s o v e r r i d e u n d e rw r i t i n gstand ards. The sam p le w as designed w i th a 95 pe rcen t rel iab i l i t y and 10p e rc en t p rec i si o n . T w o e x c ep t i o n s w e re fo u n d .

Prec i si o n (u p p er l i m i t o f th e ex cep ti o n rate) P 1 0 %Po p u l at i o n si z e N 1 0 0 0Rel i ab i l i ty fac to r R 3 .0Sam p le Si z e n 3 0Sam p l i n g i n terv al I 3 3N u m b er o f erro rs e 2Su m o f th e p rec isi on ad j ustm e n t fac to rs = 1 . 75 + 1 . 56 = S 3 .3 1

Erro r Lo an Prec i si o nN u m b er N u m b er A d j u stm en t

Factors

1 1 2 3 4 5 1 .7 5

2 5 4 3 2 1 1 .5 6

TO TA LS 3 .3 1

3 3 x (3 .0 + 3 .3 1 )P' (rev i sed u p p er p rec i si o n l im i t) = = .2 0 8

1 0 0 0


27/44


The rev ised up per p rec ision l im i t , .20 8 o r 21 p e rcen t , exceeds the samp ledesign upp er p rec ision l im i t o f 10 p e rcen t . There fo re , the exam iner m us teva lua te the e r ro rs and a ttemp t to d e term ine the i r cause .

I f th is leve l o f except ions is unacceptab le , the examiner shou ld d iscuss the

resu l ts w i th approp r ia te bank m anagem ent and o b ta in m anagem ent sc o m m i tm e n t t o u n d e r ta k e a re v ie w a n d c o r re c ti v e a c ti o n s .

Probab i l i t y S ta tement

A pro babi l i ty s tatem ent is a dec lara tio n o f sta tis tica l assuranc e. Suchassurance is a com b in a tion o f p rec ision and re l iab i l i t y . I f an excep t ion ra te ina po pu la t ion exceeds som e m ate r ial l eve l (p rec ision ), the exam iner can statew i th a cer tain d egree o f con f id ence (i .e . , the resu l ts have a cer ta in re l iab i l i ty )tha t the stat i st i ca l sam p le w i l l co n ta in a cer tain n um ber o r am ou n t o fexcep t ion s. In o th er w ord s, resu l ts o f the sta tist ica l sam pl e are used to m akein fe rences regard in g the en t i re po r t fo l i o (pop u la t ion ) .

T h e p ro b a b i l i t y statem e n t o n l y a p p l i e s t o t h e p o p u l a ti o n f ro m w h ic h i t em sw ere se lec ted stat i st i ca l l y . I f exam iners e l im ina ted a group o f i tem s f rom thepo pu la t ion b e fo re the sam p le se lec t ion , they canno t evalua te tha t g rou p o fi tem s sta tist ica l ly .

P rob ab i l i t y statements cann o t b e used w i th n on stat ist i ca l jud gm enta lsam pl in g because the resu l ts cann ot b e sta tist ica l ly re la ted to th e ent i rep o p u l a t i o n .

Propo r t i ona l Samp l i ng

I n o u r e x a mp le , w h e re th e O C C u s es p ro p o r ti o n a l sa mp l i n g to d e term in eaddi t iona l c lass i f ied loans in a bank s nonc lass i f ied in terna l ly ra tedc o m m e rcia l l o a n p o r t f o l i o , a p ro b a b i l i t y statem e n t c an i n fo rm b a n km a n ag em e n t o f t h e est imatedm a x imu m a mo u n t o f c l a ssi f i ed l o a n s i n t h a tp o r t f o l i o .

Exam p le w i th no excep t ion s: Cur ren t in te rna l l y iden t i f ied c lassi f iedcom m erc ial loans a re 30 p e rcen t o f T ie r 1 cap i ta l p lus the ALLL . Exam inersused an 8 0 p e rcen t re l iab i l i t y l eve l and a 20 p e rcen t p rec ision leve l to rev iewno nc lassi f ied com m erc ial loans. Samp le resu l ts d isc losed no excep t ion s. Aprob ab i l i t y statement fo r th is sam p le w ou ld be :

W i th 80 pe rcen t rel iab i l i t y , w e in fe r from ou r stat i st i ca l samp le tha t theamo un t o f c lassi f ied com m erc ial loans w i l l n o t exceed 50 p e rcen t (bank siden t i f ied 3 0 p e rcen t p lu s O CCs p rec ision o f 20 pe rcen t ) o f T ie r 1 cap i talp lu s the A LLL.


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Exam p le w i th excep t io ns (see the exam p le i n the f i rst w orksheet ): Cur ren tin te rna l l y id en t i f ied c lassi f ied com m erc ial lo ans a re 10 5 p e rcen t o f T ie r 1cap i tal p lus the A LLL. Exam iners used a 90 p e rcen t re l iab i l i t y l eve l and a 10percen t p rec ision l eve l to exami ne non c lassi f ied com m erc ial loans. Fou rexcep t ion s w ere foun d . A f ter com p le t ing the Prop or t ion a l Loan Eva lua t ion

W ork sheet , resu l ts d i sc lo sed the ad ju sted prec is ion o f those excep t ion s to be17 pe rcen t . A p ro bab i l i t y statemen t fo r th is samp le w ou ld be :

W i th 90 pe rcen t rel iab i l i t y , w e in fe r from ou r stat i st i ca l samp le tha t theamo un t o f c lassi f ied com m erc ial loans w i l l n o t exceed 13 2 pe rcen t o f Tie r1 cap i ta l p l us the A LLL (bank s in te rna l l y c lassi f ied 1 05 pe rcen t p lu s O CCprec ision o f 10 pe rcen t p lu s ad jus ted p rec ision va lue o f excep t ion s 17percen t . )

Note : For o f f i c ia l pu rposes in the repor t o f exami na t ion and O CCs elec t ron icin fo rm ation systems , the am ou n t and pe r cen t o f c r i t i c iz ed and c lassi f iedasse ts sho u ld be d e r ived f rom the bank s in te rna l l y i den t i f ied p rob l em asse ts

ad ju sted for O CC f in d i ngs ra ther than the sta tis tica l l y ex trapo la ted f igures.A ccord i ng to the d a ta in the f i rst w orksheet , the am ou n t o f c lassi f ied lo ans tobe re flec ted in the repo r t and i n O CC e lec t ron ic da ta bases w ou ld am ou n t toth e m o re th a n $ 3 6 2 m i l l i o n i d e n t i fi e d b y th e b a n k p lu s th e $ 9 m i l l i o niden t i f ied by O CC exam iners as add i t ion a l c lassi f ied lo ans.


W h e n th e O C C u s es n u m e ri c a l sa mp l i n g to d e term in e a d h e re n c e to b a n kpo l ic ies o r con t ro ls, o r com p l i ance w i th law s and regu la tion s, exam iners canuse a p robab i l i t y statement to i n fo rm bank m anagem ent o f the est im a tedexcep t ion ra te in a spec i f ied po r t fo l i o .

In ou r examp le , exam iners used n um er ica l samp l in g to test the accuracy o fthe ins ta lm en t loan o ver r ide un derw r i t ing stand ards.

Exam p le w i th no excep t ions : Exam iners se t the rel iab i l i t y leve l at 95 pe rcen tand p rec ision l eve l at 10 p e rcen t . Th i r ty loans w ere rev iew ed and noexcep t ion s d iscovered . A p ro bab i l i t y statement fo r th is sam p le w ou ld be :

W i th 9 5 pe rcen t re l iab i l i t y , o u r s ta ti st i ca l samp le resu l ts ind ica te tha texcep t ion s to the ove r r ide po l i cy in in stalm en t loans do n o t exceed 10percen t o f the ins ta lm en t loan po r t fo l io .

Exam p le w i th tw o excep t ion s: Exam iners se t the rel iab i l i t y leve l at 95percen t and the p rec ision l eve l at 10 pe rcen t . They rev iew ed 30 lo ans andd iscovered tw o excep t ion s (see the fo rego ing Exam p le o f a N um er icalSam p le Eva lua t ion W orkshee t ) . A p robab i l i t y statemen t fo r th is sam p lew o u l d b e:


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W ith 9 5 pe rcen t re l iab i l i t y o u r s ta ti st i ca l sam p le resu l ts ind ica te tha texcep t ion s to the ove r r ide po l i cy in in stalm en t loans do n o t exceed 21percen t o f the ins ta lm en t loan po r t fo l io .

I f the p ro jec ted l eve l o f excep t io ns is sign i f i can t o r con side red u naccep tab le ,

e x am in e rs sh o u ld d i sc u ss th e l e v el w i t h b a n k m a n ag em e n t an d rec o m m e n dtha t m anagemen t rev iew the si tua t ion , de te rm ine the ex ten t o f the p rob lem ,a n d im p le m e n t c o r rec t i v e ac t i o n .

Repo r t o f Exam ina t ion (RO E) Co m m ents

W hen exami ners use stat i st i ca l samp l in g and n o te sign i f i can t o r un accep tab leleve ls o f excep t ion s, they sho u ld con side r in c lud ing appro pr ia te language inth e ap p l i c ab le R O E c o m m e n t . T h e l an g u a ge sh o u ld i n c lu d e :

C The fac t that sta tis tica l sam pl in g w as used.

C The m ethod o f s ta ti st i ca l sam p l i ng u sed .

C The num ber and typ e o f excep t ion s no ted , the und er ly ing roo t cause o fexcep t ion s, and e i the r suggested im prov em ents o r m anagem entc o m m i tm e n ts f o r c o r rec t i v e ac t i o n .

Exam in ers sho ul d u se the i r ow n w ord s, rather than sta t ist ica l langu age, forre p o r t c o m m e n ts. I n ad d i t i o n , rep o r t c o m m e n ts m u st b e su p p o r ted b y a n dbased on a su f f i c ien t ly la rge enou gh sam p le size (general l y a m in i m um o f 30i tem s in keep i ng w i th accepted s tat ist ica l in du stry standards).

Exam p les o f po ssib l e RO E com m ents, inc lu d in g p rob ab i l i t y s ta tem ents:C Pro p o r t i o n a l sa mp l i n g

Cur ren t ly , b ank - iden t i f ied c lassi f ied l oans in the (desc r ibe po r t fo l i orev iew ed) are (ra t io o f c lassi f ied lo ans to T ier 1 p lus the ALLL). D ur i ngou r exam ina t ion w e rev iew ed a p rop or t ion a l stat i st i ca l samp le o fin te rna l l y rated , no nc lassi f ied (iden t i fy po r t fo l i o rev iew ed) loans. O ursam p le d i sc losed (num ber o r do l la r am ou n t o f ) excep t ion s ind ica t ing tha tadd i t io na l un iden t i f ied c lassi f ied loans o f pe rcen t o f T ie r 1 cap i talp l us the ALLL m ay ex i st . The causes o f the sam pl e excep t ion s w ere(reason fo r the excep t ions ). W e recom m end tha t m anagem ent (suggested

correc t ive ac t ion) .

Note : For o f f i c ia l pu rposes in the repor t o f exami na t ion and O CCs elec t ron icin fo rm ation systems , the am ou n t and pe rcen t o f c r i t i c ized and c lassi f iedasse ts sho u ld be d e r ived f rom the bank s in te rna l l y i den t i f ied p rob l em asse tsad ju sted for O CC f in d i ngs ra ther than the sta tis tica l l y ex trapo la ted f igures.


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U sin g the f i rst w ork sheet s data , the am ou nt o f c l assi f ied l oans to b e re f lec tedin t h e re p o r t an d i n O C C e le c tro n i c d a ta b a se s w o u ld a mo u n t t o t h e m o reth an $ 3 6 2 m i l l i o n i d e n t i f i ed b y th e b a n k p lu s th e $ 9 m i l l i o n i d e n t i f i ed b yO CC exami ners as add i t io na l c l assi f ied l oans.

C

N u m e ri c al sam p l i n gD u r in g o u r e x am in a ti o n w e re v iew e d a n u m e ri c a l stat i st i c al sa mp le o f(i d e n t i f y p o r t fo l i o rev ie w e d ) to d e term in e c o m p l i a n c e w i th (d esc r i b e th espec i f i c featu re o f in te rest ). O ur samp le d isc losed (nu m ber ) excep t ionsrepresent in g percen t o f the (id ent i fy po r t fo l i o ) . The causes o f thesam p le excep t ions w ere (reason fo r the excep t ions ). W e recom m end tha tmanagement (suggested correc t ive ac t ion) .


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Sam pli ng M etho dol ogies Ex am in a ti o n O b je c ti v e s

1 . D e te rm i n e w h e th e r sam p l i n g is an ef fi c i en t an d e ff ec ti v e t o o l i neva luat in g areas o f exam in at ion i n terest .

2 . Se l ec t t h e sam p l i n g m e t h o d th a t w i l l ac h i ev e th e o b j ec ti v e s o f th esupervisory strategy.

3 . U se a sam p l e to d r aw c o n c l u si o n s ab o u t th e d at a f ro m w h i c h i t i s t ak e n .


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Sam pli ng M etho dol ogies Exam in at ion Procedu res

Prop ort ional Sampl i ng

Exam iners can use these p roced ures w hen do l la r am ou n ts a re o f pa r ti cu l a rim po r tance and qu an t i fy ing excep t ions o r d i f ferences in d o l l a rs i sapprop r ia te , e.g ., w hen sam p l i ng the in te rna l l y ra ted , no nc lassi f ied po r t ionso f a bank s loan po r t fo l io s.1 . D e te rm i n e sam p l i n g o b j e c ti v e s b y re v i ew i n g t h e ap p r o v e d su p e rv i so r y

stra tegy for th e bank .

2 . I d en ti fy a n d se lec t t h e p o p u l at io n t o b e re vi ew e d an d i d e n ti fy w h y i t i sb e in g rev ie w e d .

3 . D e fi n e th e fe at u re o f i n t er est fo r w h i c h th e i d en t i fi e d p o rt fo l i o i s b e i n gsam p led . Fo r exam p le , in the rev iew o f a no nc lassi f ied com m erc ial loanpo r t fo l i o , the fea tu re o f in te rest o r excep t io n m ay be d e f ined as anin te rna l l y un iden t i f ied c lass i f ied commerc ia l loan .

4 . I d en t i fy t h e d esi r ed r e l i ab i l i t y an d p r ec i si o n l e v e l s f o r th e sam p l e .

Prec i si o n l ev el = %

Rel i ab i l i ty l ev el = %

M o n etar y i n terv al = $

($ T ie r 1 Cap i ta l + ALLL) x p rec ision as a dec im a lre l iab i l i t y fac to r (f rom append ix C based on re l iab i l i t y % )

I f rev iew ing p o r t ion s o f lo an po r t fo l i os tha t the bank h as no t c lassi f ied ,c o n sid e r t h e fo l l o w in g :

C Bank l oan iden t i f i ca t ion systemS Ban k rev i ew s al l l o an s ex ceed i n g $

C In tern al i d en ti f i ed c l assi f i cat i o n l ev el $ %

C D ocu m ent accuracy o f in te rna l id en t i f i cat ion o f p ast c lassi f i ca t ions.S H o w d o b a n k rat i n g s c o m p a re w i th O C C c la ssi f i c at i o n s?

C Sam p le Po p u lat i o n $(Exc lu de c red i t baske t loans and SN C lo ans i f w ar ran ted . )


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A p p e n d ix B s N u m e r i ca l Sa mp l e Ev a lu at i o n W o rk sh e e t c an b eprepared m anua l ly to accom p l i sh th is. I f the sam p le size is 30 i tem sor m ore , conside r fo rm u la t ing a p rob ab i l i t y statement .

C Com pare the rev ised p rec ision l im i t w i th the o r ig ina l p rec ision

l im i t . I f the rev ised l im i t exceeds the o r ig ina l one , evalua te theexcep t ion s and a t tem pt to d e term ine the i r ro o t cause .

C I f the except io n l eve l is un acceptab le , d i scuss the resu l ts w i tha p p ro p r i a te b an k m a n ag em e n t an d o b tain a c o m m i tme n t f o rco r rec t ive ac tion .

8 . D o c u m e n t resu l ts i n w o r k in g p ap e rs an d i n t h e O C C s e le ctr o n i c d at abase ( i f s ignif icant).

9 . I f w ar ran t ed , p re p ar e c o m m e n ts f o r t h e r ep o r t o f ex am i n at i o n , f o cu si n gon the leve l o f excep t ions and the i r ro o t causes.


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PROPORTIONALSA

MPLEEVALUATIONW

ORKSHEET

Tier1Capital+A

LLL:

$

Reliability

:

%

Precision:

%

MonetaryInterval(MI):

$

OCC

Rating

Borrower

Loan

Balance

(L)

Sample

Exception

(SE)

Sample

Interval

MI/L=SI

Cutoff

Loans

Populatio

n

Exceptio

n

SExSI=P

E

Rank

Precision

Adjustment

Factor

(P)

Precisio

n-

Adjusted

Exception

PExP

TOTALS

RESULTS:

Precision-adjustedExceptions

=

$

PrecisionLevelof(as%o

fTier1+A

LLL)=

+

$


=

$


=

+

$

AdjustedProjectedClassifie

dLoans

=

$

THEREFORE:W

ith

%r

eliability,weinferthatac

tualclassifiedloansshouldnotexceed

%o

fTier1capitalplusALLL

.

Sam pli ng M etho dol ogies A p p en d i x A


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Ran k : Ran k th e p o p u lat i o n ex cep ti o n s sep aratel y . T h eexcep t ion s sho u ld be ranked i n descend i ng o rde r o fam ou n ts because o f the b ias g iven to la rge r do l la r loansam p le s i n p ro p o r t i o n a l sa mp l i n g . W h e n e x c ep t i o n s h a v ethe sam e va lues, rank each separate ly . Loans exceedi ng

the cu to f f a re no t ranked .Prec isio n: Enter the ad ju stm ent fac tors for ov ersta tem ents (app end ix

C) o r u nd erstatemen ts (append i x D ) based o n there l iab i l i ty o f the sam pl e. These fac tors are used tocon ver t the est im a ted excep t ion s in the po pu la t ion in top rec ision -ad jus ted excep t ion s. N o p rec ision ad jus tm en tfac tor is requ i red for cuto f f loans.

Prec i si o n En ter th e d o l l ar v al ue o f each cu to ff l oan . Fo r th e o th erA d ju stm e n t sam p le ex cep ti o ns, m u l ti p l y th e p op ulat i o n ex cep ti o n byEx cep ti o ns: i ts p rec isi on ad ju stm e n t fac to r to y i el d th e p rec isi o n-

ad ju sted except i on s. The ov ersta tem ent ca lcu la t ion s haveincreased (and the unders ta tement ca lcu la t ions havedec reased) the p rec ision l im i t based o n the samp leexcep t ion s so that the sam e re l iab i l i ty lev e l can be u sedto eva lua te the sam p le .

The to tal o f th is co lu m n and the m on e tary p rec ision (T ie r1 cap i ta l and A LLL x prec is ion p ercent) represents thepo ten t ial add i t iona l am ou n t o f c lassi f ied lo ans in thepo r t fo l i o . Th is f igu re is added to the kno w n c lassi f iedlo an to ta ls to est im ate the up per l i m i t o f c lassi f ica t io ns.

A p rob ab i l i t y s ta tem ent such as those in th is book le t ssec t ion Prob ab i l i t y Statement can then be m ade usingthis data.

Add i t iona l Eva lua t ion :

Exam iners ana lyze and eva lua te the samp le excep t ion s to d e term ine th eroo t cause and d ec ide w he the r the samp le excep t ion s a re a pa tte rn o rprac t ice .

Cons ide r :C

Inexper ience o f a lo an o f f i ce r .C A n e x c ep t i o n b y t y p e , d i v i si o n , o r i n d u st ry .C D i f fe rences by ind iv id ua ls assign in g ra tings in adh er ing to

in terna l c lass i f ica t ion def in i t ions .C Timel iness o f bank ra t ing changes.


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Sam pli ng M etho dol ogies A p p e n d i x B

N U M ERICAL SAM PLE EVALU ATIO N W O RKSH EET

Samp le D esignPrec i si o n PPo p u l at i o n si z e NRel iab i l ity fac to r (Fro m ap pen d i x C , 2 .3 fo r 9 0% , 3 .0 fo r 9 5% ) R

Sam p le si z e = R nP

Sam p l i n g i n terv al = N In

Samp le Evaluat ion N u m b er o f erro rs fo u n d eSu m o f th e p rec i si o n ad j u stm en t fac to rs S

ERRO R LO A N A D JU STM EN TN U M BER N U M BER FA C TO R

PRECISIO N

(Froma p p e n d i x C )

TOTALS

Rev i sed u p p er p rec i si o n l im it P' = I(R + S)N


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Sam pli ng M etho dol ogies A p p en d i x C

Statist ic al Sampl ing O verstatem ents (O CC c lassi f ied , bank non c lassi f ied)

Rel i ab i l i ty Fac to rs (R) 1 .6 2 .0 2 .3 3 .0

Rel

metodologías de muestreo

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