A C T A U N I V E R S I T A T I S L O D Z I E N S I S
F O LIA O E C O N O M IC A 175, 2004
Agata Szczukocka*
S E L E C T E D M E T H O D S O F C R E D IT R ISK E V A L U A T IO N
Abstract. Over the last few years credit risk and its m inim alization have been widely discussed. Therefore the problem o f credit risk and m ethods o f its evaluation seem to be quite important. In the article there were presented various m odels o f credit risk using statistic information and they ware shortly characterized. It should be emphasized that the discussed methods in m any cases situations can make it easier to take difficult credit decisions.
Key words: credit, credit risk, risk m ethods, default m ode, mark to market.
1. IN T R O D U C T IO N
N ow adays th ere is a tendency to search for new m eth o d s th a t, with the use o f a w ell-developed statistic base, allow to evalu ate the cred it risk. In fo rm atio n th a t wc receive d u e to the m ethod o f credit risk evalu atio n , help to tak e a decision to g ra n t o r refuse credit to a p o ten tial d eb to r. T h e recently introduced m eth o d s o f credit risk differ in con cep t, specification, basic p aram eters and th e way o f results ev aluatio n.
T ak in g in to co n sid eratio n the concept a p p ro a c h th ere ca n be selected the follow ing risk m ethods:
• D E F A U L T M O D E (D M ) - estim ating the value o f the unexpected losses (the, so called, unexpected losses ap p ro ach ), this m odel includes C red it R isk M eth o d + C redit P ortfo lio View;
• M A R K T O M A R K E T m odel - including:
- E D F m odel (neu tral estim ation o f the risk), the a p p ro a c h p repared by K M V C o rp o ra tio n ,
- R N V (risk n eu tral valuation),
- C R E D IT M E T R IC S m odel o f discounted c o n tra c tu a l cash flow. T h e first d ra w in g presents the division o f credit risk m odels th a t m ak e us o f statistic in fo rm atio n :
Fig. 1. Classification o f credit risk m odels
It should be em phasized th a t th ere are m an y various m eth o d s o f credit risk valu atio n an d analysis. T h e com plexity o f the problem o f credit risk m akes it difficult to p re p are the sim ple classification o f th e m eth o d s o f risk analysis ( B o r y s 1995). T h e aim o f this analysis is the p resen tatio n o f the m odel o f expected defau lt frequency and its usability in tak in g credit decisions.
2. E X PE C T E D D EFA U LT FR EQ U EN C Y
T he exam ple o f the m odel connected with capital m a rk e t (stock valuation) is the E D F m odel (expected default frequency), prepared by K M V C o r p o ra tio n . T his ap p ro ach is based on assets evaluation , the m eth o d p repared by R. M erto n in 1974 w ith the use o f o p tio n ’s theory. A ccording to K M V m etho d, it is assum ed th a t the process o f a co m p an y ’s insolvency is an endogenous process (depends on the com pany itself) and is determ ined by the co m p an y ’s capital stru ctu re. F ailure to m eet th e credit liabilities is caused by the decline in the assets’ value o f the d e b to r below th e level necessary for the loan atten d an ce. C redit is considered to be th e derivative instru m ent based on assets value o f a deb to r. T h e m ost ch aracteristic featu re o f this a p p ro a c h is the fact th a t it links directly and strongly the m ark et value o f a co m p an y w ith w ith b an k ru p tcy p ro b ab ility . T h e changes in insolvency pro b ab ilities are in terd ep en d en t with sh areh o ld ers’ equity. A ccording to K M V C o rp o ra tio n ap p ro ach this co nn ectio n is crucial, since it allow s to link the in fo rm atio n on the co m pan y v alu atio n (stocks value) with the cred itw o rth in ess/cred it rating. It is assum ed th a t insolvency o f a com pany is likely to a p p e a r when a co m p an y ’s assets value is low er th an the specified critical value. T his m eth o d aim s at statin g the expected default frequency ( J a w o r s k i 2001). T his m ethod is always in tro d u ced in stages.
D u rin g th e first stage m a rk e t value o f a com pan y is defined to g eth er with the variability o f this value, estim ated on the basis o f flu ctu a tio n o f a co m p an y ’s stock prices and the bookk eeping value o f a co m p an y ’s liabilities. D u rin g the second stage the default p o in t is evaluated on the basis o f th e c u rre n t liabilities value o f a com pany. D u rin g th e th ird stage a special m easu re, called the distance to insolvency, is decided. In the fourth stage, on the basis o f the historical d a ta , th e expected d efault frequency - E D F -is estim ated.
In the above m en tio n ed ap p ro ach it is assum ed th a t a co m p an y becom es insolvent th e m o m en t its m a rk e t value (goodw ill) falls below th e certain critical level. F ig u re 2 presents th e m om en tary forecast o f the futu re o f a co m p an y ’s value on the basis o f the value o f its assets. T h e E D F space is the p ro b ab ility o f a co m p an y ’s insolvency. It is influenced by the level o f liabilities and assets value.
a v arag c (a c liv ) vali M ark et v a lu e
E x p e c ta tio n (a c tiv ) in c re a se C u rre n t (a c tiv ) vali
T h e d e n sity o f th e p ro b a b ility fu tu re (a c tiv ) v alu e
S ta n d a rd slo p e fu tu re (a c tiv ) v a lu e A v erag e in c re a se in v a lu e
lia b ilitie s scrv icc
O n in c re a se in v a lu e lia b ilities sc rv ic c
S h ap e fu n c tio n s d e n sity o f the p ro b a b ility fu tu re (a c tiv ) v a lu e
A t p re sen t A v a lu e lia b ilitie s I y e a r T im e serv is
Fig. 2. The schem e o f the valuation o f insolvency probability in K M V m ethods
In case o f the listed com panies m ark e t value o f th eir cap ital can be estim ated on the basis o f their stock prices. A ddition ally, using th e o p tio n s ’ theory, m a rk e t value o f capital can be equal to value o f the p u rch ase optio n ( J a w o r s k i 2 0 0 1).
m ark et value o f ca p ital = /(lia b ilitie s ’ bookkeepin g value, m a rk e t value o f assets, variability o f assets, tim e) (1)
Using B L A C K -S C H O L E S m odel and the fo rm u la fo r o p tio n v alu atio n , we will get th e follow ing form ula ( H u l l 1997):
E = A N ( d {) — D c ~rtN ( d 2) (2)
with the following:
E - m a rk e t value o f capital (value o f options),
D - b ook keeping value o f liabilities (price o f o p tio n m aking), A - m a rk e t value o f assets,
t - tim e,
r - re tu rn ra te o f risk-free investm ent o f assets,
N - d istrib u a n t o f norm al division, whose d l and d2 are as follows:
o a - stan d ard v a ria tio n o f assets.
In the e q u a tio n (1) and (2) there are two unknow ns: m a rk e t value o f assets (A) and variability o f assets’ value. H ow ever, there is a possibility to w ork ou t a n o th e r e q u a tio n from the form ulas (1) and (2) by differentiating
both sides o f eq u atio n :
variability o f capital = h (liabilities’ bookkeeping value, m a rk e t value o f assets, variability o f assets, tim e) (3)
O n the basis o f B L A C K -S C H O L E S form ula, the au th o rs o f the ap pro ach w ork o u t the fo rm u la fo r variability o f capital value, achieving the follow ing equation:
(4)
a e - variability o f capital evaluated on the basis o f histo rical d a ta , o a - variability o f the assets’ value,
the rem aining variables - as in the above m en tio n ed form ulas.
T h e tw o u n k n o w n s are the m ark e t value o f assets (A) and the variability o f assets value (ста). T hey are follow ed by: expected assets’ value in the given tim e and insolvency point.
A n investor having som e type o f assets expects th a t he will have re tu rn on the investm ent and ad ditio n ally will get incom e equal to th e expected ra te o f re tu rn from assets. T h e expected ra te o f re tu rn is con sidered in
term s o f the system atic risk connected w ith analyzed assets. A cco rdin g to K M V the system atic risk o f assets m eans the expected ra te o f re tu rn on assets on the basis o f historical profitability o f assets.
T he fu tu re value o f a co m p an y ’s assets (/1,) is calculated using the follow ing form ula:
Using logarith m s we achieve the following:
In A, = In A0 + ( J u - + a flV/ t Z ^ j (6)
where:
A0 - value o f assets at the beginning,
A, - value o f assets at the p articu lar m om ent t, Z , ~ N (0,1),
u - average ra te o f re tu rn on a com p an y ’s assets, n a - stan d ard v aria tio n o f the rate o f re tu rn o n assets.
T he value o f assets A, can be substituted by fa cto rin g logarithm ically- n orm al o f the value expected in a given m o m en t t, presented w ith the follow ing form ula:
E ( A t) = A0eul (7)
It should be em phasized th a t from the very beginning it was assum ed th a t a com p an y w ould becom e insolvent w hen th e to tal m a rk e t value o f its assets should achieve a critical value. T h e b o o k keeping value o f its liabilities is considered to be this critical value. In such situ atio n the value o f a co m p an y ’s assets will only enable the com p any to pay all the dues. W ith the use o f the em pirical analysis o f the b an k ru p tc y o f com pan ies it has been observed th a t in m an y cases the loss o f liquidity ap p e ars w hen the to tal assets are low er th a n the level o f to tal liabilities. O n th e basis o f historical d a ta it seems th a t the m ost com m on p o in t o f a co m p an y ’s insolvency is the m o m e n t w hen the value o f assets is equal to sh ort-term liabilities enlarged w ith 50% o f long-term s liabilities. T hese o bserv atio n s m ake it possible to m a rk th e p o in t o f insolvency w ith the use o f the follow ing fo rm u la ( J a w o r s k i 2 0 0 1):
W hen having the expected value o f a co m p an y ’s assets in given tim e and its insolvency p o in t (default point), in the th ird stage this m eth o d defines the percentage loss o f a co m p an y ’s value, th a t can lead to b a n k ruptcy, i.e. to the d efau lt point. F o r instance, if the expected co m p an y ’s value d u rin g one year period is 100, and its d efault p o in t is 25, it can be concluded th a t the dow nfall o f 75% in the assets’ value will lead a com pany to the d efau lt point. N ext step is defining the, so called, distance to the p oint o f insolvency. T his can be m ad e using the fol lowing form ula:
T he possibility o f th e loss o f liquidity shall be m ark ed as ? def. T h e critical p oint o f assets A def, in which a com pan y becom es insolvent can be presented with the follow ing form ula:
It m eans th a t for a given co m pany with th e ra tin g X e { A A A , A A , A, BBB, B B , B, C C C ) th ere can be defined such a value Z Ccc. fo r which the dow nfall o f the value o f a c o m p a n y ’s assets below this level will m ean the insolvency o f a d eb to r.
K now ing the value Z ccc for the stan d ard n o rm al fa cto rin g o f assets’ value, the p ro b ab ility o f the loss o f liquidity can be defined:
distance to the p o in t o f insolvency = expected assets’ value — d efau lt p o in t
Pdcf = P ( A < Ала) = P(ln A, ^ In A dd) (1 0)
( I D
w here the stan d ard iz ed ra te o f re tu rn r ~ N [0, 1]:
r = in
a.aл/ <
Zccc is the p o in t in the stan d ard norm al factoring co rresp o n d in g to the possibility o f loosing liquidity P ^ . It m eans th a t the critical value o f assets when there ap p e ars insolvency (A M) is the one in which Z ccc = — d 2:
T h e above m entioned fo rm u la presents in a form al way m easure o f the distance to insolvency.
T h e aim o f the m easu re distance to insolvency is the co m p arativ e analysis o f com panies. D istan ce to insolvency is a m easu re allow ing the rating o f com panies. H ow ever, it does no t give direct in fo rm atio n o n the probability o f b an k ru p tc y . In o rd e r to m ak e a fu rth e r use o f this m easu re o f risk o f b an k ru p tc y p ro b ab ility , K M V C o rp o ra tio n analyses the historical d a ta on the co m panies th a t went b an k ru p t. T h e know ledge o f the level o f m easure o f d istan ce to insolvency for the com panies th a t in the p ast lost liquidity m akes it possible to evaluate the p ro b ab ility o f insolvency as the fu n c tio n o f “ d ista n c e to insolv en cy ” . It m ean s th a t on th e basis o f experience an d histo rical d a ta , after calculating the distance to insolvency, we are able to estim ate the p ro b ab ility o f loosing liquidity - E D F . T he historical d a ta show th a t the probability o f the ban kru p tcy (E D F ), depending on the level o f “ d istance to insolvency” tends to be as Fig. 3.
I aking into co n sid eratio n the above m entioned g rap h the bigger value o f the d istance to insolvency, the sm aller p ro b ab ility o f a c o m p a n y ’s b ankruptcy . It can be proved o n the follow ing exam ple:
Let us assum e th a t the value o f a co m p an y ’s assets is A = 2000, the expected m o n th ly inscrease o f assets is 2 0% , it m eans th a t the expected value o f assets in a year will be A = 2400, the yearly variability o f assets = 100, and the p o in t o f insolvency - 2000. W ith these d a ta the m easure o f distance to insolvency is as follows:
Fig. 3. The estim ation o f the values o f probability o f bankruptcy on the basis o f historical data
T ak in g into co n sid eratio n the historical d a ta , on the basis o f w hich one can claim th a t in the g ro u p o f 8000 com panies th a t achieved the value o f the distance to insolvency o f 4, only 60 w ent b a n k ru p t one year later, it can be concluded th a t the p rob ab ility o f b an k ru p tc y o f a given co m pan y, counted with E D F m easure, will be as follows:
E F = = 0.0075 = 0.75% .
3. C O N C L U SIO N S
T he E D F m odel is the new ap p ro ach in ban k in g , th a t uses the stock exchange d a ta for the ev a lu a tio n o f a com pany. The forecasted value o f this m eth o d results from the fact th a t the c u rren t value o f a co m pan y determ ines its futu re value. Because o f the fact th a t the fu tu re value o f a co m p an y ’s assets is educed only from the m ark e t value o f a c o m p a n y ’s capital, the m odel E D F depends com pletely on the in fo rm atio n given by the m ark e t ev a lu a tio n o f the co m p an y ’s stocks. A d dition ally, it is w orth m entioning th a t credit in stitu tio n s present careful a p p ro a c h to new m eth o d s helping in m a k in g decisio ns. H ow ever, using o f th e ab o v e m en tio n ed m ethod to g eth er w ith the ones already checked w ould facilitate tak in g difficult decisions.
Selected M ethods oľ Credit Risk Evaluation
R E FER EN C ES
B o r y s С . (1995), C redit R isk M anagem ent in Banking, I’W N , W arszawa W rocław. H u l l J. (1997), Futures a n d O ptions, WIG PRESS, W arszawa.
J a w o r s k i W (2001), Banks in Poland. Challenges and D evelopm ent Trends, Poltex, Warszawa.
Agata Szczukocka
W Y BR A N E M E T O D Y S Z A C O W A N IA RYZYKA K R ED Y TO W EG O
W ostatnich latach wiele miejsca poświęca się ryzyku kredytowem u i jego minimalizacji, dlatego też słuszne wydaje się poruszenie tematu zw iązanego z m etodam i szacow ania ryzyka kredytowego.
W artykule starano się przedstawić podział m odeli ryzyka kredytow ego wykorzystujących informacje statystyczne oraz dok on an o krótkiej ich charakterystyki. N ależy zauważyć, iż om ów ione m etody nie są metodam i całkow icie eliminującymi ryzyko, ale w wielu przypadkach m ogą ułatwić podjęcie trudnych decyzji kredytowych.
