premija za osiguranje depozita na primeru bankarskog sistema · osiguranje depozita. be-ha banka...
TRANSCRIPT
76
bank
arst
vo 1
201
3
PREMIJA ZA OSIGURANJE DEPOZITA
NA PRIMERU BANKARSKOG SISTEMA BOSNE I HERCEGOVINE
Rezime
Razmotrili smo dilemu u pogledu uvođenja promjenljive stope premije za osiguranje depozita u bankarskom sektoru Bosne i Hercegovine/BiH. Promjenljiva stopa/premija je alternativa fiksnoj, koja je u BiH već 6 godina 0,3%. Rezultat istraživanja nije jednoznačan. Od četiri upotrebljena modela dva sugerišu smanjenje premije, a dva povećanje. Prema modelu “Merton 1977” premija čak nije ni potrebna, jer je tržišna vrijednost aktive banaka u prosjeku veća od bankarskih dugova. Rezultate dobijene primjenom hipergeometrijskog rasporeda takođe interpretiramo kao prjedlog za smanjenje premije. Međutim, drugi prekidni raspored, binomni raspored, sugeriše povećanje premije osiguranja. Motiv povećanja premije je rast loših kredita koji utiče na povećanje vjerovatnoće difolta banke, što vodi ka pomjeranju binomnog rasporeda u desnu stranu. I linearni pristup u istraživanju opravdanosti fiksne premije traži povećanje premije tj. varijabilnu premiju. Istraživanje nije dalo konačan i nedvosmislen stav u odnosu na dilemu da li stopa premije za osiguranje depozita u bankarskom sektoru BiH treba biti promjenljiva ili fiksna. Modeli se značajno razlikuju po smjeru, ali i po veličini, predloženog varijabiliteta. Zato na bazi modela dobijeni varijabilitet premije ne tumačimo na način da premija treba biti varijabilna, već na način da nismo u potpunosti uspjeli dokazati da premija ne treba biti fiksna. Bez novih istraživanja nije moguće dokazati hipotezu o potrebi uvođenja varijabilne stope premije osiguranja. Pošto hipoteza nije potvrđena, tj. samo je djelimično potvrđena, i dalje ostaje stav da stopa premije za osiguranje depozita u BiH treba biti fiksna.
Ključne riječi: osiguranje depozita, stopa premije za osiguranje depozita, varijabilnost, put opcija, Merton 1977, teorija vjerovatnoće, prekidni rasporedi, Bosna i Hercegovina
JEL: E44, G21, G33
UDK 368.025.1:336.717.22(497.6)
originalni naučni
rad
Rad primljen: 11.09.2012.
Odobren za štampu: 27.09.2012.
dr Dragan JovićCentralna banka Bosne i
Hercegovine, Glavna banka Republike Srpske
77
bank
arst
vo 1
201
3
DEPOSIT INSURANCE PREMIUM IN THE BANKING SECTOR OF BOSNIA AND HERZEGOVINA
Summary
The paper examines the dilemma concerning the implementation of variable deposit insurance premium in the banking sector of Bosnia and Herzegovina/B&H. The variable rate/premium is an alternative to the fixed rate, which has in B&H for six years already amounted to 0.3%. The results of our research are not uniform. Out of the four used models, two suggest a reduction of the premium, whereas the other two suggest an increase. According to the “Merton 1977” model, the premium is not even required, given that the market value of the banks’ assets is on average higher than the banks’ debts. The results received through the implementation of hypergeometric distribution have also been interpreted as a suggestion of the premium reduction. However, another discrete distribution - binomial distribution, suggests the insurance premium to be increased. The motive for the premium increase is the growth of non-performing loans, which has caused higher probability of banks’ default, and, in turn, led to the binomial distribution being skewed to the right. The linear approach to examining the justifiability of fixed premium has also asked for an increased premium, i.e. a variable premium. The research, however, has not provided a final and unambiguous conclusion concerning the dilemma of whether the deposit insurance premium rate in the banking sector of B&H should be variable or fixed. The models considerably differ as to the direction, but also the size of the proposed variability. Therefore, based on the applied models, our interpretation is not that the variability of the premium from our research suggests that the premium should be variable, but rather that we have not fully proved that the premium should not be fixed. Without any new surveys, it is impossible to prove the hypothesis about the necessity of introducing a variable insurance premium rate. Given that the hypothesis has not been proven, i.e. that it has only been partially confirmed, there remains the position that the deposit insurance premium rate in B&H should be fixed.Key words: deposit insurance, deposit insurance premium rate, variability, put option, Merton 1977, probability theory, discrete distributions, Bosnia and HerzegovinaJEL: E44, G21, G33
UDC 368.025.1:336.717.22(497.6)
original scientific paper
Paper received: 11.09.2012
Approved for publishing: 27.09.2012
Dragan Jović, PhDCentral bank of Bosnia and Herzegovina,Glavna banka of the Republic of [email protected];
78
bank
arst
vo 1
201
3
Uvod
U okviru tržišno-orijentisane reforme bankarskog sistema u bankarskom sektoru BiH (u daljem tekstu BSBiH) je uvedeno obavezno osiguranje depozita. Be-ha banka koja nije osigurala depozite ne može dobiti dozvolu za rad.
Predmet istraživanja je stopa premije za osiguranje depozita (u daljem tekstu: POD) u BSBiH. Od početka instaliranja šeme za osiguranje depozita, do danas, ona iznosi 3 promila, ili 0,3%. Određena kao fiksna, takva je i ostala. Naš cilj je da odredimo da li POD treba biti fiksna ili varijabilna/promjenljiva. Zalažemo se za drugu opciju, promjenljivu POD, to je hipoteza istraživanja. POD treba biti promjenljiva, a ne konstantna. U širem smislu istraživanje se može tretirati i kao doprinos staroj dilemi: fiksna ili varijabilna POD pro i contra. Obuhvaćen je period od 12/2007. do 12/2011. sa ishodištem u 12/2000. g.
Najduže smo se zadržali na modelu “Merton 1977”, jer je on najsloženiji. Pored njega upotrebljen je binomni raspored i hipergeometrijski raspored. Model linearizacije je najprostiji primjenjeni metod. Poslije prezentovanja metodologije slijedi prikaz rezultata i rasprava o njima. Završna riječ je predstavljena u obliku zaključnih razmatranja.
Materijal i metode
Model “Merton 1977”Model određivanja POD “Merton 1977” je
šire objašnjen i obrazložen u literaturi (Laeven, 2002), a na ovome mjestu ukratko, u skladu sa ciljem rada.
Kao i kod svakog drugog osiguranja, i za osiguranje depozita se plaća premija. Banka uplaćuje POD instituciji za osiguranje depozita. U BSBiH to je Agencija za osiguranje depozita (u daljem tekstu AOD). Bilansna protustavka osiguranim depozitima je aktiva banaka. Iz ovoga odnosa Merton je izvukao analogiju između osiguranja depozita i put opcije: osiguranje depozita je jednako pravu, ali ne i obavezi banke da proda svoju aktivu instituciji za osiguranje depozita po cijeni koja je jednaka vrijednosti obaveza u osiguranim depozitima. Sa aspekta put opcije imovina/aktiva banke (A)
je bazična aktiva (underlying asset), a tržišna vrijednost duga/osiguranih depozita (D) je cijena izvršenja opcije (strike price). Naplata POD proizvodi obavezu institucije za osiguranje depozita da održi njihovu likvidnost, tj. da u krajnjoj liniji isplati deponente, čiji su depoziti osigurani. U osiguranju depozita banka je kupac, a institucija za osiguranje depozita prodavac put opcije. Banka ima pravo da proda aktivu banke po bilo kojoj cijeni, tj. po tržišnoj vrijednosti depozita, a AOD ima obavezu da isplati osigurane depozite. Za kupovinu put opcije banka plaća premiju - POD.
Glavne varijable “Merton 1977” su: A - tržišna vrjednost aktive, D - tržišna vrjednost duga (u primjeni ovoga modela korporativni dugovi korespondiraju depozitima, Laeven, 2002. p. 7), T - vrijeme do dospjeća bankarskog duga, t - frakcija vremena, σ - standardna devijacija stope prinosa na aktivu/ROA, g - POD, δ- prinos od dividende (dividend yield), N - funkcija kumulativne normalne distribucije. Sama specifikacija modela je bitna u mjeri uticaja varijabli na POD.
Formula 1. Premija osiguranja *
( ) ( )tt hND
AhtTNg −
−
−−−= *)1(* δσ
gdje je
( ) ( )
tT
tTD
A
ht−
−+
−
=σ
σδ2
1ln2
Izvor: Laeven, Luc. Pricing of Deposit Insurance. World Bank Policy Research Working Paper 2871, July 2002. p.7.* U orginalnoj formuli tV (tržišna vrijednost aktive) je zamijenjeno, radi lakše notacije sa A.
Uopšteno, prema “Merton 1977” POD je obrnuto proporcionalna odnosu između tržišne vrijednosti aktive i tržišne vrijednosti duga tj. osiguranih depozita. Logika je jasna, sve dok je tržišna vrijednost aktive veća od tržišne vrijednosti duga ne postoji interes banke da aktivira put opciju i da ustupi aktivu za manji iznos nego što ona zaista vrijedi. Dakle, pod pretpostavkom da je sve ostalo jednako, viši A / D daje nižu POD.
Između standardne devijacije stope ROA
79
bank
arst
vo 1
201
3
Introduction
As part of the market-oriented reform of the banking system, obligatory deposit insurance was introduced to the banking sector of B&H (hereafter to the referred to as: BSB&H). Any bank in B&H which failed to insure the deposits cannot obtain an operating license.
The subject of our research is deposit insurance premium rate (hereafter to be referred to as: DIP) in the BSB&H. Since the implementation of the deposit insurance scheme, until today, this rate has amounted to 3 per mills, or 0.3%. Originally defined as such, the rate has remained fixed. Our objective in this paper is to determine whether DIP should be fixed or variable. We are in favour of the latter option - the variable DIP, which is the main hypothesis of our research. DIP should be variable, not constant. In a broader sense, this research may be treated as a contribution to addressing the old dilemma: fixed or variable DIP - pros and cons. The paper has covered the period from 12/2007 to 12/2011, the starting point being 12/2000.
We have devoted most of our time to the “Merton 1977” Model, given that it is the most complex one. In addition, we have resorted to binomial and hypergeometric distributions. Linearization model is the simplest of the applied models. The presentation of methodology is followed by the review of achieved results and a relevant discussion. This is accompanied by the concluding remarks.
Subject Matter and Methods
“Merton 1977” ModelAs a model for defining DIP, “Merton 1977”
has been extensively presented and explained in reference literature (Laeven, 2002), and here we will only present it briefly, in line with the objective of this paper.
As with any other form of insurance, there is a premium to be paid for deposit insurance. A bank pays DIP to a deposit insurance institution. In the BSB&H that is the Deposit Insurance Agency (hereafter to be referred to as: DIA). The balance sheet counter-item to the insured deposits are the banks’ assets. Based on this relationship, Merton drew the analogy
between deposit insurance and put option: deposit insurance equals the right, but not the obligation of a bank to sell its assets to a deposit insurance institution, at a price equal to the value of liabilities in the insured deposits. From the perspective of a put option, the bank’s assets (A) are the underlying asset, and the market value of debt/insured deposits (D) is the strike price. The collection of DIP generates obligation for the deposit insurance institution to maintain their liquidity, i.e. to ultimately pay out the deponents, whose deposits were insured. In the process of deposit insurance, the bank is the buyer, whereas the deposit insurance institution is the seller of a put option. The bank has the right to sell the bank’s assets at any price, i.e. at the deposit’s market value, whereas the DIA has the obligation to disburse the insured deposits. In order to purchase the put option, the bank has to pay the premium - DIP.
The main variables of “Merton 1977” are the following: A - market value of assets, D - market value of debt (in the application of this model corporate debts correspond to deposits, Laeven, 2002, p. 7), T - time until maturity of the bank debt, t - fraction of time, σ - standard deviation of the rate of return on assets/ROA, g - DIP, δ - dividend yield, N - function of the cumulative normal distribution. The specification of the model itself is relevant in terms of the extent of variables’ impact on DIP.
Equation 1. Insurance premium*
( ) ( )tt hND
AhtTNg −
−
−−−= *)1(* δσ
where
( ) ( )
tT
tTD
A
ht−
−+
−
=σ
σδ2
1ln2
Source: Laeven, Luc. Pricing of Deposit Insurance. World Bank Policy Research Working Paper 2871, July 2002. p. 7.Note: * Vt (market value of assets) from the original equation has been replaced with A, for the purpose of easier notation.
In general, according to “Merton 1977”, DIP is indirectly proportionate to the ratio between
80
bank
arst
vo 1
201
3
(σ) i prinosa od dividende (δ), sa jedne strane i POD ,sa druge strane, postoji pozitivna veza. I ovdje je logika više nego jasna. Veći varijabilitet stope ROA izlaže banku većem riziku od gubitka, posebno u uslovima visokog leveridža. Npr. ako je leveridž (leveridž/multiplikator dioničkog kapitala = bilansna aktiva/akcijski kapital) 30, a prinos na aktivu (ROA) 1%, ROE je 30%, dok je ROE je - 30% kada je ROA - 1%. Zato je POD pozitivno korelisana sa varijabilitetom ROA.
Veći prinos od dividende znači manju neraspoređenu dobit i manji pripis dobiti akcijskom kapitalu. Odsustvo rasta, sposobnosti banke da eventualni gubitak pokrije iz kapitala prenosi rizik od gubitka na dug, deponente, tj. instituciju za osiguranje depozita. Veći rizik traži veću naknadu za osiguranje, tj. veću POD i otuda pozitivna korelacija između δ i ROA. Pod pretpostavkom T = 1, t = 0 i δ= 0 odnos između A / D, volatilnosti (σ), ROA i POD je kao na grafikonu 1.
U idealnim uslovima nulte volatilnosti POD je uvijek 0% - ukoliko je A / D ≥ 1 (Grafikon 1). Logičko obrazloženje bi moglo biti da, kada je tržišna vrijednost aktive jednaka, ili veća od duga banke, uz stalno isti ROA, AOD nije izložena riziku isplate osiguranih depozita, jer banka nema apsolutno nikakav interes da aktivira put opciju pošto je tržišna vrijednost aktive banke veća od tržišne vrijednosti duga, a ROA iz godine u godinu ima iste, pozitivne, vrijednosti. Do nulte POD se dolazi i na višim nivoima volatilnosti, ali uz A / D veće od jedan.
Za volatilnost od 1% POD je nula za A / D ≥ 1,05, isto tako i za volatilnost od 3% pri A / D ≥1,10, i tako sve do para A / D, σ (1,15, 5%). Za održavanje POD na niskom nivou, pri visokoj volatilnosti ROA, potrebna je naknada u obliku rasta A / D. Za A / D ≤ 1, bez obzira na nivo volatilnosti, POD je veća od nule. Par A / D σ (1,1, 7%) približava POD vrijednosti POD u BSBiH 0,29% tj. 0,3%. POD raste sa rastom volatilnosti i padom A / D, a u eksperimentalnom uzorku (Grafikon 1) za najekstremnije vrijednosti A / D = 0,75 i σ = 21% iznosi 25,71%, što bi značilo da banka, čija je tržišna vrijednost aktive svega 75% tržišne vrijednosti duga, a volatilnost ROA 21%, trebala uplatiti na ime POD 0,25 novčanih jedinica za svaku jedinicu osiguranog depozita. Banke sa A / D ≥ 1 i stabilnim i uravnoteženim ROA bi plaćale nižu POD od banaka sa A / D < 1 i visokom volatilnošću ROA. Model određuje POD u zavisnosti od rizika difolta banke, a on je funkcija ROA i A / D.
Ako je A / D konstantan, npr. 1 (grafikon
2), POD se povećava sa povećanjem volatilnosti ROA. Volatilnost ROA od nula daje POD od nula, dok volatilnost ROA od 21% daje POD od 8,36%. Isti A / D uz uslov da je sve ostalo jednako, vodi ka linearnoj vezi između volatilnosti ROA i POD.
Rasporedi vjerovatnoćeKoristili smo dva rasporeda vjerovatnoće:
binomni (u daljem tekstu BR) i hipergeometrijski raspored (u daljem tekstu HGR). Oba rasporeda su prekidna. BR ima samo dva ishoda, npr:
81
bank
arst
vo 1
201
3
market value of assets and market value of debt, i.e. insured deposits. The logic behind it is clear - as long as the market value of assets is higher than the market value of debt, it is not in the bank’s interest to activate a put option and sell the assets for a lower amount than they are actually worth. In other words, under the assumption that all other variables are the same, higher A/D implies lower DIP.
There is a positive correlation between the standard deviation of the ROA rate (σ) and dividend yield (δ) on one hand, and DIP, on the other. The logic is also more than clear. Higher variability of the ROA rate exposes the bank to the higher risk of loss, especially when the leverage is high. For example, if the leverage (leverage/equity multiplier = balance sheet assets/equity) is 30, and return on assets (ROA) amounts to 1%, ROE is 30%, and if ROA amounts to -1%, then ROE is -30%. This is why DIP is positively correlated to the variability of ROA.
Higher dividend yield implies lower retained earnings and lower allocation of profit to shareholders’ equity. Lack of growth and bank’s ability to cover potential losses from its capital transfers the risk of losses to depositors, i.e. to the deposit insurance institution. Higher risk calls for higher insurance fee, i.e. higher DIP, which leads to the positive correlation of δ and ROA. Under the assumption that T = 1, t = 0 and δ = 0, the relationship between A/D, volatility (σ), ROA and DIP is as shown in Chart 1 below.
In the ideal circumstances of zero volatility, DIP is always 0% - provided that A/D ≥ 1 (Chart 1). A logical explanation could be that, when the market value of assets is equal to or higher than the bank’s debt, with the same values of ROA, DIA is not exposed to the risk of insured deposits disbursement, given that the bank has absolutely no interest in activating the put option when the market value of the bank’s assets is higher than the market value of debt, and ROA has recorded the same, positive amounts for years. Zero DIP can also be achieved at the higher level of volatility, but when A/D > 1. When volatility is 1%, DIP is zero for A/D ≥ 1.05, and also when volatility is 3% and A/D ≥ 1.10, until the pair A/D, σ (1.15, 5%). In order to maintain DIP at the low level, when ROA is highly volatile, we need compensation in the form of increased A/D. For A/D ≤ 1, regardless of the volatility level, DIP is higher than zero. The pair A/D, σ (1.1, 7%) approximates DIP to the value of DIP in the BSB&H of 0.29%, i.e. 0.3%. DIP increases as the volatility grows and A/D falls, reaching the amount of 25.71% for the most extreme values in the experimental sample (Chart 1) of A/D = 0.75 and σ = 21%. This would imply that a bank whose market value of assets is only 75% of the market value of debt, and whose volatility of ROA is 21%, should pay in the name of DIP 0.25 monetary units for each unit of the insured deposit. The banks whose A/D ≥ 1 and whose ROA is stable and balanced would pay lower DIP than the banks whose A/D < 1 and whose
82
bank
arst
vo 1
201
3
pozitivno/negativno, para/grb, uspjeh/neuspjeh. Prilagođeno cilju istraživanja ishodi su difolt/odsustvo difolta. Difolt znači da AOD mora isplatiti osiguranu sumu.
BR (formula 2) ima tri elementa: n - broj banaka, p - vjerovatnoća difolta banke (u daljem tekstu VD), x - broj banaka koje su proglasile difolt. Dobijeni raspored pokazuju vjerovatnoću da jedna, ili više banaka, proglase difolt.
Formula 2. Binomni raspored
xnxxnx ppxnx
nppxn −− −
−=−
)1(
)!(!!)1(
Izvor: Žižić et al. 1992. Metodi statističke analize. Savremena administracija, Beograd. p. 112.
VD banke određujemo na osnovu relativne vrijednosti loših kredita (u daljem tekstu LK, eng: nonperforming loan), a prema dva scenarija: pesimističkom i optimističkom. LK je udjel loših kredita u ukupnim kreditima.
2000. g. je godina bankarske krize u BiH, sa nastavkom u 2001. g. i 2002. g. Mnoge banke su bile nelikvidne, a neke i nesolventne. Difolt se nije pominjao, iako je bio rasprostranjen. Kriza je “liječena” tolerisanjem nelikvidnosti banaka. Kada to nije pomoglo, usljedila je državna (tj.entitetska) intervencija: neke banke su otišle u stečaj, jedan dio je transformisan, a najviše ih je privatizovano. Prema podacima be-ha emisione banke, tokom 2000. g. LK dostižu svoj maksimum od 21%. Taj broj smo uzeli kao reper za difolt tj. stvaranje obaveze AOD da isplati osigurane depozite - i dali mu vrijednost VD od 1. U trenutku kada LK dostigne 21%, vjerovatnoća da će AOD morati preuzeti obavezu isplate depozita pojedinačne banke je 100% - ovo je osnovna pretpostavka pesimističkog scenarija. Na osnovu reperne vrjednosti LK, odredili smo VD pojedinačne banke u narednim godinama - djeljenjem LK sa LK u baznoj godini (VD20..=LK20../LK2000).
Optimistički scenario se razlikuje “samo” po vrijednosti LK u baznoj godini. Vrijednost LK je hipotetička - iznosi 40%. Po istom mehanizmu kao kod pesimističkog scenarija (djeljenjem LK sa LK u baznoj godini) bazni LK od 40% daje
nižu VD pojedinačne banke. Zato smo ovaj scenario nazvali optimistički ili zbog upotrebe značajno višeg LK, hipotetički.
HGR je sekundarni alat u istraživanju. Ne može biti primaran zato što osim broja banaka, ne uzima u obzir niti jednu drugu empirijsku varijablu iz bankarskog sektora. Elementi HGR (formula 2) su: N - ukupan broj banaka, N1 - broj velikih banaka, N2 - broj ostalih banaka, n - veličina uzorkA, x - broj velikih banaka u uzorku, n-x - broj malih banaka u uzorku. Nalazi BR su pouzdaniji, od nalaza HGR, jer se pesimistički scenario po BR u potpunosti zasniva na empirijskim podacima, a djelom i optimistički po BR, u djelu podataka o LK - osim za 2000. g. Podaci iz ovih scenariJa se koriste u konstrukciji BR, ali ne i u izradi HGR.
Formula 3. Hipergeometrijski raspored (HGR)
)!(!!
))!(()!()!(!!
2
2
1
121
nNnN
xnNxnN
xNxN
nN
xnN
xN
−
−−−−=
−
Izvor: Ibid. p. 117.
Model linearizacijeZasniva se na pretpostavljenoj linearnoj vezi
između VD i POD.
Formula 4.
.3,0*/ 2007...2009,2008...2009,2008 VDVDPOD =
Rezultati i diskusija
“Merton 1977”Na osnovu modela “Merton 1977” ne
možemo odrediti jednu, tačkastu, vrijednost POD. Ali ono što možemo odrediti dovoljno je da zaključimo da postoji potreba prelaska sa režima fiksne na režim varijabilne POD. Podaci o standardnoj devijaciji ROA su empirijski (drugi red tabele 1), ali nemamo podatke o tržišnoj vrijednosti aktive i duga pojedinih banaka pa ne možemo odrediti individualne POD.
83
bank
arst
vo 1
201
3
ROA is highly volatile. The model determined DIP depending on the bank’s risk of default, and it is the function of ROA and A/D.
If A/D is constant, for instance it equals 1 (Chart 2), DIP is increasing as the ROA volatility increases. Zero ROA volatility results in zero DIP, whereas ROA volatility of 21% results in DIP of 8.36%. The same A/D, under the condition that all other variables remain the same, leads towards the linear correlation between volatilities of ROA and DIP.
Probability DistributionsWe applied two probability distributions -
binomial (hereafter to be referred to as: BD) and hypergeometric (hereafter to be referred to as: HGD). Both of these distributions are discrete. BD has only two outcomes, for instance: positive/negative, heads/tails, success/failure. Adjusted to the objective of our research, the possible outcomes are default/no default. Default implies that the DIA must disburse the insured amount.
BD (Equation 2) has three elements: n - number of banks, p - the bank’s probability of default (hereafter to be referred to as PD), x - number of banks in default. The received distribution indicates the probability of one or more banks declaring default.
Equation 2. Binomial distribution
xnxxnx ppxnx
nppxn −− −
−=−
)1(
)!(!!)1(
Source: Žižić et al. 1992. Metodi statističke analize. Savremena administracija, Beograd, p. 112.
The bank’s PD is determined based on the relative value of non-performing loans (hereafter to be referred to as: NPLs), according to the two scenarios - pessimistic and optimistic. NPLs are a share of non-performing loans in total loans.
2000 was the year of a banking crisis in B&H, and it continued in 2001 and 2002. Many banks were illiquid, some even insolvent.
Default was not being mentioned, although it was widespread. The crisis was “cured” by tolerating illiquidity of banks. When this did not help, there ensued a state (i.e. entity) intervention: some banks went bankrupt, some of them were transformed, most of them privatized. According to the data of the B&H issuing bank, in 2000 the NPLs reached their peek at 21%. We took this percentage as the benchmark for default, i.e. for the obligation of DIA to disburse insured deposits - and assigned it the value of PD = 1. At the moment when NPLs reach 21%, the probability that DIA will have to assume its obligation of disbursing deposits of an individual bank is 100% - this is the basic assumption of the pessimistic scenario. Based on the benchmark value of NPLs, we determined the PD of an individual bank in the forthcoming years - by dividing NPLs with NPLs in the basic year (PD20.. = NPLs20.. / NPLs2000).
The optimistic scenario differs “only” in the value of NPLs in the basic year. The value of NPLs is hypothetical - it amounts to 40%. According to the same mechanism as in the case of the pessimistic scenario (dividing of NPLs with NPLs in the basic year), the basic NPLs of 40% result in lower PD of an individual bank. This is why we called this scenario optimistic, or, due to the application of considerably higher level of NPLs, hypothetical.
HGD is a secondary tool in this research. It cannot be primary because, except for the number of banks, it does not take into consideration any other empirical variable from the banking sector. The elements of HGD (Equation 3) are the following: N - total number of banks, N1 - number of large banks, N2 - number of other banks, n - sample size, x - number of large banks in the sample, n-x - number of small banks in the sample. The findings of BD are more reliable than the findings of HGD given that the pessimistic BD scenario is fully based on empirical data, which is the case of the optimistic BD scenario, too, in the part concerning the data on NPLs - except for the year 2000. The data from these scenarios are used in the concept of BD, but not in the preparation of HGD.
84
bank
arst
vo 1
201
3
Na nivou BSBiH do POD se dolazi u nekoliko koraka (Tabela 2). Neto dobit iz 2011. g. diskontujemo sa očekivanom/zahtjevanom
stopom prinosa, dobijamo tržišnu vrijednost dioničkog kapitala, za iznos razlike umanjujemo knjigovodstvenu vrijednost aktive i tako dobijenu tržišnu vrijednost aktive stavljamo u odnos sa knjigovodstvenom vrijednošću duga. A/D za diskontne stope od 0,2, 0,1 i 0,05 je 1,03, 1,07 i 1,14 respektivno. Za te vrijednosti A/D POD je nula.
Modeli binomnog rasporeda(BR)
Prema pesimističkom scenariju, a koristeći podatak o LK u baznoj godini, VD u 2007. g. je 0,143 (3/21).
Vrijednost LK u 2011. g. daje VD 4 puta veću od one u 2007. g.; 0,562 (11,8/21) u odnosu na 0,143.
Tabela 1. Primjena modela “Merton 1977” u BSBiH - odnos tržišne vrijednosti aktive i duga (A/D) i POD
A/D, Volatilnost
Razdoblje2000 - 2011. 2000 - 2002. 2003 - 2007. 2008 - 2011.
0,83% 0,75% 0,20% 0,56%0,75 25,00% 25,00% 25,00% 25,00%0,8 20,00% 20,00% 20,00% 20,00%0,85 15,00% 15,00% 15,00% 15,00%0,9 10,00% 10,00% 10,00% 10,00%0,95 5,00% 5,00% 5,00% 5,00%
1 0,33% 0,30% 0,08% 0,22%1,03 0,00% 0,00% 0,00% 0,00%1,07 0,00% 0,00% 0,00% 0,00%1,14 0,00% 0,00% 0,00% 0,00%1,2 0,00% 0,00% 0,00% 0,00%1,25 0,00% 0,00% 0,00% 0,00%
Izvor: www.cbbh.ba (Obradio autor)
Tabela 2. A/D, BSBiH 31.12.2011. godine*
Neto dobit
Očekivani prinos(u%)
Dionički kapital T.V.**
Dionički i drugi kapitalK.V.***
“Gubitak” AktivaK.V.
Aktiva T.V(A)
Pasiva K.V.(D)
(A/D)
1 2 3 4 5 = 4 - 3 6 7 = 6 - 5 8 9=7/8
141.780 20 708.900 3.058.746 2.349.846 23.726.000 21.376.184 20.667.284 1,03
141.780 10 1.417.800 3.058.746 1.640.946 23.726.000 22.085.084 20.667.284 1,07
141.780 5 2.835.600 3.058.746 223.146 23.726.000 23.502.884 20.667.284 1,14
Izvor: Ibid.* U svim kolonama, osim u koloni 2 i 9 podaci su u 000 KM.**TV - tržišna vrijednost.*** KV - knjigovodstvena vrijednost.
85
bank
arst
vo 1
201
3
Equation 3. Hypergeometric distribution (HGD)
)!(!!
))!(()!()!(!!
2
2
1
121
nNnN
xnNxnN
xNxN
nN
xnN
xN
−
−−−−=
−
Source: Ibid. p. 117.
Linearization ModelThis model is based on the assumed linear
correlation between PD and DIP.
Equation 4.
DIP2008, 2009… = PD2008, 2009… / PD2007 * 0.3
Results and Discussion
“Merton 1977”Based on “Merton 1977” model we cannot
determine a single point value of DIP. However, what we can determine is sufficient for us to conclude that there is a need for transition from the fixed DIP regime to the variable DIP regime. The data on standard deviation of ROA are empirical (second row in Table 1 below), but we do not possess the data on market value of assets and debt of certain banks, which is why we cannot determine individual DIPs.
At the level of the BSB&H, DIP is calculated in several steps (Table 2 below). Net profit for 2011 is discounted by the expected/targeted rate of return; we get the market value of equity, deduce the accounting value of assets by the difference of these two amounts, after which we put thus received market value of assets into relation with the accounting value of debt. A/D for discounting rates of 0.2, 0.1 and 0.05 amounts to 1.03, 1.07 and 1.14, respectively. For these values of A/D, DIP equals zero.
Table 1. Implementation of “Merton 1977” model in the BSB&H - relation of market values of assets and debt (A/D) and DIP
A/D, Volatility
Period2000 - 2011. 2000 - 2002. 2003 - 2007. 2008 - 2011.
0,83% 0,75% 0,20% 0,56%0,75 25,00% 25,00% 25,00% 25,00%0,8 20,00% 20,00% 20,00% 20,00%0,85 15,00% 15,00% 15,00% 15,00%0,9 10,00% 10,00% 10,00% 10,00%0,95 5,00% 5,00% 5,00% 5,00%
1 0,33% 0,30% 0,08% 0,22%1,03 0,00% 0,00% 0,00% 0,00%1,07 0,00% 0,00% 0,00% 0,00%1,14 0,00% 0,00% 0,00% 0,00%1,2 0,00% 0,00% 0,00% 0,00%1,25 0,00% 0,00% 0,00% 0,00%
Source: www.cbbh.ba (Prepared by the author)
86
bank
arst
vo 1
201
3
U optimističkom scenariju, takođe raste VD, ali je on manji zbog većeg LK u baznoj godini. Pretpostavili smo da banka proglašava difolt kada LK dođe tek do 40. VD u 2007. g. od 0,075 (3/40) je duplo manji od VD po pesimističkom scenariju, isto kao i u 2011. g. 0,295 (11,8/40).
VD raste u oba scenarija. Ako se visina POD veže za rizik/vjerovatnoću dešavanja osiguranog slučaja, onda zbog rasta rizika mora rasti i POD. Svaki drugačiji način razmišljanja
je u suprotnosti sa osnovnim principom osiguranja kao djelatnosti.
Scenariji, pesimistički i optimistički, isto kao i pojedinačne vrijednosti VD, otkrivaju rast vjerovatnoće da će AOD morati isplatiti jedan dio osiguranih depozita. U 2007. g. u pesimističkom scenariju vjerovatnoća da neće bankrotirati niti jedna banka
je 0,028 (ili 2,8%) (Grafikon 3). VD za jednu i više banaka je 0,972. VD dvije, tri i četiri banke je 0,20, 0,23 i 0,19 respektivno. Srednja vrijednost BR je 3,3, što prema teoriji BR znači da je najveća vjerovatnoća da će AOD morati
isplatiti osigurane depozite u ukupno 3 banke. VD za 7 i više banaka je svega 0,045. U 2007.g. nije postojala opasnost od masovnog difolta banaka, pa prema tome ni od masovnog angažmana AOD.
U 2011. g. stvari se mjenjaju (Grafikon 4). Sve do brojke od 8 banaka VD je nula, ili blizu nuli. Vjerovatnoća da će difolt proglasiti 8 i manje banaka je 0,007. VD
od 12 do 16 banaka tj. vjerovatnoća masivnog difolta je 0,65. Grafički, do rasta vjerovatnoće masovnog difolta banaka dolazi zbog pomjeranja BR u desnu stranu.
Tabela 3. Pesimistički scenario
2000. 2007. 2008. 2009. 2010. 2011.LK 21 3 3,1 5,9 11,4 11,8VD 1 0,143 0,148 0,281 0,543 0,562
Izvor: Ibid.
Tabela 4. Optimistički scenario
2000. 2007. 2008. 2009. 2010. 2011.LK 40 3 3,1 5,9 11,4 11,8VD 1 0,075 0,078 0,148 0,285 0,295
Izvor: Ibid.
87
bank
arst
vo 1
201
3
Binomial Distribution ModelsAccording to the pessimistic scenario, based
on the data on NPLs in the basic year, PD in 2007 amounted to 0.143 (3/21). The value of NPLs in 2011 results in the PD four times higher than the one in 2007: 0.562 (11.8/21) compared to 0.143.
In the optimistic scenario PD also increases, but it is somewhat lower due to the higher level of NPLs in the basic year. We assumed that the bank does not declare default until the NPLs reach 40. PD in 2007 in the amount of 0.075 (3/40) is two times lower than the PD according to the pessimistic scenario, and the same goes for 2011, when the PD amounted to 0.295 (11.8/40).
PD increases in both scenarios. If the amount
of DIP gets pegged to the risk/probability of occurrence of the insured case, then, due to the risk growth, DIP also has to increase. Every other way of thinking contradicts the main principle of insurance as a business activity.
These scenarios, the pessimistic and the optimistic one, just like the individual values of PD, reveal the growth of probability that the DIA will have to disburse one portion of the insured deposits. In 2007, according to the pessimistic scenario, the probability that none of the banks would go bankrupt amounted to 0.028 (or 2.8%) (Chart 3). PD for one or more banks was 0.972. PD for
two, three and four banks was 0.20, 0.23, and 0.19, respectively. The mean value of BD was 3.3, which, according to the BD theory, implies that the highest probability that the DIA would have to disburse the insured deposits was in 3 banks. PD for 7 and more banks was only 0.045. In 2007 there was no danger of mass default of banks; hence there was no mass engagement of the DIA.
In 2011 things changed (Chart 4). Up to the number of 8 banks, PD was zero, or close to zero. Probability that 8 or less banks would declare default was 0.007. PD for 12 to 16 banks, i.e. the probability of mass default, amounted to 0.65. In graphic terms, the growth of mass default probability occurred because BD skewed
to the right.
Table 2. A/D, BSB&H as of 31.12.2011*
Net profit
Expected return(u%)
Equity M.V.**
Equity and other
capitalA.V.***
“Loss” AssetsM.V.
AssetsM.V.(A)
Liabilities A.V.(D)
(A/D)
1 2 3 4 5 = 4 - 3 6 7 = 6 - 5 8 9=7/8
141.780 20 708.900 3.058.746 2.349.846 23.726.000 21.376.184 20.667.284 1,03
141.780 10 1.417.800 3.058.746 1.640.946 23.726.000 22.085.084 20.667.284 1,07
141.780 5 2.835.600 3.058.746 223.146 23.726.000 23.502.884 20.667.284 1,14
Source: Ibid.* In all columns, except in columns 2 and 9, the data are in KM (convertible marks) thousand.** M.V. - market value*** A.V. - accounting value
Table 3. Pessimistic scenario
2000. 2007. 2008. 2009. 2010. 2011.NPLs 21 3 3,1 5,9 11,4 11,8PD 1 0,143 0,148 0,281 0,543 0,562
Source: Ibid.
Table 4. Optimistic scenario
2000. 2007. 2008. 2009. 2010. 2011.NPLs 40 3 3,1 5,9 11,4 11,8PD 1 0,075 0,078 0,148 0,285 0,295
Source: Ibid.
88
bank
arst
vo 1
201
3
Optimistički scenario je mnogo tolerantniji u pogledu VD i LK. Prag tolerancije je postavljen na mnogo višem nivou, a VD pojedinačne banke je 1 tek kada LK dostigne 40. Zato uprkos rastu LK, VD u optimističkom scenariju, u 2011. g. ne prelazi jednu trećinu. U 2007. g. VD nula banaka je izuzetno visoka 0,16. VD za 3 i manje banaka je 0,91. U ovome scenariju opasnost od masovnog difolta/pomora banaka je ispod 0,007 (više od 6 banaka). Aritmetička sredina rasporeda je 1,7. U 2011. g. raspored je gušći, pomjeren u desnu stranu, simetričan i teži normalnom. Vjerovatnoća da će bankrotirati između 6 i 10 banaka je 0,7, a između 4 i 11 banaka 0,92.
Najveći VD ima brojka od 8 banaka (7,7). Uprkos povećanju LK na 40, tj. procjeni da banke mogu izdržati LK od 40, duplo veći od onoga iz 2007. g., i optimistički model BR poručuje da rizik od isplate osiguranih depozita raste.
Model hipergeometrijskog rasporeda (HGR)U 2007. g. VD samo jedne banke, i to velike
banke, je 0,174, a VD dvije velike banke 0,024 (Tabela 6). Par koji se sastoji od jedne velike i jedne male banke ima šansu od 30% da se obrati AOD (VD = 0,3). Difolt četverca “dvije velike i dvije male banke” je moguć u malo više od desetine slučajeva. (VD = 0,116).
Tabela 5. Parametri BR*
Pesimistički scenario
Optimistički scenario
2007. 2011. 2007. 2011. Aritmetička sredina 3,3 14,6 1,7 7,7Standardna devijacija 1,7 2,5 1,3 2,3
Izvor: Ibid.* O načinu određivanja sredine i devijacije BR vidjeti Žižić et al., 1992. p. 115.
89
bank
arst
vo 1
201
3
The optimistic scenario is much more tolerant in terms of PD and NPLs. The tolerance threshold was set at a much higher level, and PD of an individual bank equals 1 only when NPLs reach 40. Thus, despite the growth of NPLs, PD in the optimistic scenario in 2011 does not exceed one third. In 2007 PD for zero banks is extremely high, and reaches 0.16. PD for 3 and less banks is 0.91. In this scenario, the danger of mass default of banks is below 0.007 (more than 6 banks). Arithmetic mean of the distribution is
1.7. In 2011 the distribution is denser, skewed to the right, symmetric, and with a tendency towards normal. Probability that between 6 and 10 banks would go bankrupt is 0.7, and between 4 and 11 banks 0.92. The highest PD is for 8 banks (7.7). Despite the increase of NPLs to 40, i.e. despite the assessment that banks may survive the NPLs rate of 40, the twice as much as the one from 2007, the optimistic BD model also suggests that the risk of insured deposits disbursement increases.
90
bank
arst
vo 1
201
3
U 2011. g. VD u sve četiri kombinacije je smanjena: “jedna velika banka” 0,154; “dvije velike banke” 0,018; “jedna velika i jedna mala banka” 0,271; “dvije velike i dvije male banke”0,093. Smanjenje VD je posljedica povećanja broja banaka, uz isti broj velikih banaka - tj. promjene elemenata u formuli za HGR. Prema rezultatima HGR u 2011. g. VD za četiri odabrane kombinacije banaka je smanjen u odnosu na 2007. g. Razloga za povećanje POD nema. VD je smanjen za 0,02, 0,005, 0,030, 0,023 - u prosjeku za 0,02. Isključiva i dosljedna primjena principa matematičke vjerovatnoće, HGR, zahtjeva smanjenje a ne povećanje POD. Ali i prema HGR premija osiguranja mora biti promjenljiva.
Model linearizacijePod pretpostavkom potpune pozitivne
korelacije (koeficjent korelacije 1) između vrijednosti VD i POD, POD raste (Tabela 7). U
2009. g. ona je 0,59%((0,28/0,14)*0,3), a u 2011. g. iznad 1; 1,18%. Ovaj model ima logiku, ali je prilično naivan. Na veličinu POD ne utiče visina VD već relativni odnos između VD. Pošto su relativni odnosi koji se formiraju između VD i u pesimističkom i optimističkom scenariju jednaki, POD ostaje ista bez obzira na skoro duplo viši bazni VD u optimističkom scenariju (tabela 8). Za ekstremne vrijednosti scenarija, LK = 21,1, odnosno LK = 40, stopa premije je 2,1% odnosno 4% (zadnja kolona u tabelama 7 i 8). Tumačenje ekstremnog scenarija je da ukoliko je VD pojedinačne banke 1, što je u teorijskom okviru BR nemoguć događaj (vjerovatnoća 0), POD treba, prema pretpostavkama modela linearizacije, povećati na 2,1% , odnosno 4%. Na ove brojke ne utiče odnos A/D jer model linearizacije uopšte ne obuhvata te varijable. Iako model linearizacije u jednom dijelu sadrži empirijske podatke (podaci o LK), on predstavlja izuzetno uproštenu sliku stvarnosti.
Tabela 6. VD jedne ili više banaka prema HGR
2007. 2008. 2009. 2010. 2011. Razlika2011-2007.
Jedna velika banka 0,174 0,167 0,167 0,160 0,154 -0,020Dvije velike banke 0,024 0,022 0,022 0,020 0,018 -0,005Jedna velika i jedna mala banka 0,300 0,290 0,290 0,280 0,271 -0,030Dvije velike i dvije male banke 0,116 0,107 0,107 0,100 0,093 -0,023
Broj banaka 23 24 24 25 26Broj velikih banaka 4 4 4 4 4
Izvor: Ibid.
Tabela 7. POD u modelu linearizacije, pesimistički scenario
2000. 2001. 2002. 2003. 2004. 2005. 2006. 2007. 2008. 2009. 2010. 2011. Pretpostavka
LK u% 21,0 17,9 11,0 9,3 6,1 5,3 4,0 3,0 3,1 5,9 11,4 11,8 21,0
VD 1,00 0,85 0,52 0,44 0,29 0,25 0,19 0,14 0,15 0,28 0,54 0,56 1
POD (u%) 0,3 0,31 0,59 1,14 1,18 2,1
Izvor: Ibid.
Tabela 8. POD u modelu linearizacije, optimistički scenario
2000. 2001. 2002. 2003. 2004. 2005. 2006. 2007. 2008. 2009. 2010. 2011. Pretpostavka
NPL u% 40 17,9 11 9,3 6,1 5,3 4,0 3,0 3,1 5,9 11,4 11,8 40
VD 1,00 0,45 0,28 0,23 0,15 0,13 0,10 0,08 0,08 0,15 0,29 0,30 1
POD (u%) 0,3 0,31 0,59 1,14 1,18 4
Izvor: Ibid.
91
bank
arst
vo 1
201
3
Hypergeometric Distribution ModelIn 2007 PD of only one bank, a large one, was
0.174, and PD of two large banks 0.024 (Table 6). The pair consisting of one large and one small bank had 30% chance of addressing the DIA (PD = 0.3). Default of “two large and two small banks” was probable in a bit more than a dozen cases (PD = 0.116).
In 2011 PD in all four combinations was reduced: “one large bank” 0.154; “two large banks” 0.018; “one large and one small bank” 0.271; “two large and two small banks” 0.093. Lower PD was the result of the increased number of banks, with the same number of large banks - i.e. the change of elements in the HGD equation. According to the HGD results, in 2011 PD for four selected combinations of banks was reduced compared to 2007. There was no reason to increase DIP. PD was reduced by 0.02, 0.005, 0.030, 0.023 - on average by 0.02. The exclusive and consistent implementation of mathematic probability principle, HGD, requires a reduction, not an increase of DIP. But, even according to the HGD, the insurance premium has to be variable.
Linearization ModelUnder the assumption of full positive
correlation (correlation coefficient of 1) between the values of PD and DIP, DIP increases (Table 7). In 2009 it amounted to 0.59% ((0.28/0.14)*0.3), whereas in 2011 it exceeded 1, amounting to 1.18%. This model rests on a sound logic, but is rather naïve. The amount of DIP is not impacted by the level of PD, but by the
relative correlation among PDs. Given that the relative correlations formed among PDs both in the pessimistic and the optimistic scenarios are equal, DIP remains the same, regardless of the almost two times higher basic PD in the optimistic scenario (Table 8). For extreme scenario values, NPLs = 21.1, or NPLs = 40, the premium rate is 2.1%, or 4%, respectively
(as shown in the last column in Tables 7 and 8). According to the interpretation of the extreme scenario, if the PD of an individual bank equals 1, which is an impossible event within the theoretical framework of BD (zero probability), pursuant to the linearization model assumptions, DIP should be increased to 2.1%, or 4%. These figures are not influenced by the A/D ratio, because the linearization model does not include these variables at all. Although the linearization model contains empirical data in one part (data on NPLs), it is an extremely simplified representation of reality.
Table 5. Parameters of BD*
Pessimistic scenario
Optimistic scenario
2007. 2011. 2007. 2011. Arithmetic mean 3,3 14,6 1,7 7,7Standard deviation 1,7 2,5 1,3 2,3
Source: Ibid.* For more details about determining arithmetic mean and standard deviation, see Žižić et al., 1992. p. 115.
Table 6. PD of one or more banks according to HGD
2007. 2008. 2009. 2010. 2011. Difference2011-2007.
One large bank 0,174 0,167 0,167 0,160 0,154 -0,020Two large banks 0,024 0,022 0,022 0,020 0,018 -0,005One large and one small bank 0,300 0,290 0,290 0,280 0,271 -0,030Two large and two small banks 0,116 0,107 0,107 0,100 0,093 -0,023
Number of banks 23 24 24 25 26Number of large banks 4 4 4 4 4
Source: Ibid.
92
bank
arst
vo 1
201
3
Zaključna razmatranja
Dilemu fiksna ili varijabilna POD smo testirali preko 4 modela. Jedan od njih (“Merton 1977”) je posuđen, a ostala tri smo konstruisali prema prjedlozima teorije vjerovatnoće i linearne algebre.
Namjera modela “Merton 1977” - da smanjenje tržišne vrijednosti aktive banke nadoknadi povećanjem premije - je očigledna. Tako za A/D od 0,75 premija ide na 25%, da bi se tržišna vrijednost aktive i tržišna vrijednost duga ponovo doveli u ravnotežu (1:1). Prema toj logici za volatilnost ROA od 0 i A/D = 1 nema potrebe za POD, jer su A i D u savršenoj ravnoteži. Pri A/D >=1,15 uz nisku volatilnost ROA (do 5%) takođe ne postoji potreba za POD. Poruka modela u slučaju BSBiH, pod pretpostavkom realnosti izabranih diskontnih stopa i načina određivanja tržišne cijene aktive i duga je da BSBiH uopšte ne treba POD, tj. osiguranje depozita, jer je A/D BSBiH iznad 1 (za diskontne stope od 0,2, 0,1 i 0,05, A/D je 1,05, 1,09 i 1,16 respektivno). BSBiH je još vitalniji nego što se to iz podataka o A/D vidi, jer smo prema specifikaciji modela “Merton 1977” u D (debt, dug) unijeli sve dugove, a ne samo osigurane depozite koji su u BSBiH značajno manji od ukupnog duga.
Rasporedi vjerovatnoće, BR i HGR, takođe predlažu varijabilnu POD. Prvi raspored (BR) se ne slaže sa “Merton 1977” u pogledu smjera varijabiliteta, a drugi (HGR) se slaže. BR kao raspored VD određenog broja banaka razvijamo u dvije krajnje varijante: pesimističku i optimističku. VD je u prvoj računata na bazi LK od 20,1 (2000. g.) za koju smo vezali VD, odnosno vjerovatnoću isplate osiguranih depozita od 1. U drugoj, optimističkoj varijanti, LK u 2000. g. smo postavili na visokih 40. U oba scenarija rasporedi vjerovatnoće su zbog rasta LK pomjereni značajno udesno u odnosu na 2007. g. U desnom djelu rasporeda se nalaze obilježja veće vrijednosti, ili prevedeno na jezik statistike: raste VD većeg broja banaka. U 2007. g. VD za više od 6 banaka je zanemarljiva, ispod 1% (optimistički scenario), ali je zato u optimističkom scenariju 10%. U 2011. g. stvari su bitno izmjenjene. BR se pomjerio u desno u odnosu na onaj u 2007. g. Vjerovatnoća da AOD mora isplatiti depozite u više od 12, a manje
od 16 banaka, je 0,658. Rast VD zahtjeva rast POD - ako se pridržavamo osnovnog načela osiguranja, da veći rizik povlači veću premiju osiguranja.
Rezultati primjene HGR na četiri kombinacije između, sa jedne strane četiri velike banke, i sa druge strane banke koje po metodologiji AOD nisu velike, zahtjevaju smanjenje POD. U sva četri slučaja VD je smanjena - 2007. g. u odnosu na 2011. g. Vjerovatnoća da će bankrotirati jedna velika banka i niti jedna banka iz grupe “ostale banke” je sa 17,4% (2007), smanjena na 15,4% (2011), isto kao i vjerovatnoća da će se dvije velike banke obratiti AOD za isplatu depozita: 0,024% (2007) i 0,018% (2011). Do ovih promjena je došlo zbog rasta broja banaka članica sistema za osiguranje depozita sa 23 (2007. g.) na 26 (2011. g.), uz isti broj velikih banaka.
Model linearizacije, kao i model “Merton 1977” daje numeričke vrijednosti POD, ali ne uključuje niti jedan parametar iz modela “Merton 1977”. Pretpostavljena linearna veza (savršena linearna korelacija između LK i VD) u 2008, 2009, 2010. i 2011, daje POD od 0,31, 0,59, 1,14 i 1,18 respektivno. Prema ovom modelu kada LK dođu do 21,2 odnosno 40 zahtjevana POD je 2,1 odnosno 4%.
U radu smo koristili istorijske vjerovatnoće - od 12/2011 pa unazad. Rizici su porasli, BP je pomjeren udesno, ali AOD nije intervenisala. Kako to objasniti? To što neki događaj, prema modelu, ima veliku vjerovatnoću javljanja ne mora značiti da će se on zaista i desiti, isto kao što se može realizovati neki događaj sa malom vjerovatnoćom javljanja. Rasporedi vjerovatnoće kazuju vjerovatnoću i u vezi sa tim rizike sa kojima se suočava AOD. Promjena rasporeda vjerovatnoće i percepcije rizika sugeriše korekciju POD makar se ti veći rizici i nematerijalizovali. U tome je smisao primjene teorije vjerovatnoće u analizi POD i u cijelom bankarstvu. Odnos u trouglu model-vjerovatnoća-stvarnost se najbolje vidi iz primjera hedž fonda LTCM (Long Term Capital Market). Gubitak koji je hedž fond realizovao tokom 1998. g. je bio 14 standardnih devijacija udaljen od očekivanog/prosječnog prinosa na portfolio (Dowd, 2002). Desio se događaj čija je vjerovatnoća dešavanja ravna nuli!
Primjenjeni modeli se ne slažu u pogledu veličine POD, smjera njenih promjena.
93
bank
arst
vo 1
201
3
Concluding Remarks
In this paper we tested the dilemma “fixed or variable DIP” through 4 models. We borrowed one of them (“Merton 1977”), whereas the remaining three we constructed in line with the principles of probability theory and linear algebra.
The intention of the “Merton 1977” model - to offset the reduction in market value of a bank’s assets by increasing the premium - is obvious. Thus, for A/D of 0.75 the premium goes up to 25%, in order to regain the balance (1:1) between market value of assets and market value of debt. According to this logic, for ROA volatility of 0 and A/D = 1, there is no need for DIP, given that A and D are perfectly balanced. When A/D ≥ 1.15, with low ROA volatility (up to 5%), there is also no need for DIP. The message conveyed by the model in case of BSB&H, under the assumption that the selected discounting rates and manner of determining market values of assets and debt are realistic, is that BSB&H does not need DIP, i.e. deposit insurance, at all, given that A/D in the BSB&H is above 1 (for discounting rates of 0.2, 0.1, and 0.05, A/D equals 1.05, 1.09, and 1.16, respectively). BSB&H is even more buoyant than it might be indicated by the A/D data, bearing in mind that, according to the specification of the “Merton 1977” model, within the variable D we recorded all debts, and not only the insured deposits, which are in the BSB&H considerably lower than the total debt.
Probability distributions, BD and HGD, also
suggest a variable DIP. The former distribution (BD) does not comply with the “Merton 1977” concerning the direction of variability, whereas the latter one (HGD) does comply. As a distribution of PDs of a certain number of banks, BD is developed in two ultimate variants: pessimistic and optimistic. In the former, PD is calculated on the basis of NPLs rate amounting to 20.1 (2000), for which we pegged the PD, i.e. the probability of disbursement of insured deposits equalling 1. In the latter, optimistic variant, we set the NPLs rate in 2000 to the high level of 40. In both scenarios probability distributions, due to the growth of NPLs, considerably skewed to the right, compared to 2007. The right section of the distribution is marked by higher values, or, in the language of statistics - the PD increases in a larger number of banks. In 2007 for more than 6 banks PD was negligible, i.e. below 1% (optimistic scenario), but within the pessimistic scenario it reached 10%. In 2011 things considerably changed. BD skewed to the right compared to the situation from 2007. Probability that DIA must disburse deposits in more than 12, and less than 16 banks, was 0.658. The growth of PD requires an increase of DIP - if we follow the main principle of insurance, that higher risk entails higher insurance premium.
The results of implementing HGD on four combinations, including “four large banks”, on one hand, and banks that are not large according to the DIA methodology, on the other hand, require a reduction of DIP. In all four cases the PD was reduced - comparing
Table 7. DIP according to the linearization model, pessimistic scenario
2000. 2001. 2002. 2003. 2004. 2005. 2006. 2007. 2008. 2009. 2010. 2011. Estimate
NPLs in % 21,0 17,9 11,0 9,3 6,1 5,3 4,0 3,0 3,1 5,9 11,4 11,8 21,0
PD 1,00 0,85 0,52 0,44 0,29 0,25 0,19 0,14 0,15 0,28 0,54 0,56 1
DIP in % 0,3 0,31 0,59 1,14 1,18 2,1
Source: Ibid.
Table 8. DIP according to the linearization model, optimistic scenario
2000. 2001. 2002. 2003. 2004. 2005. 2006. 2007. 2008. 2009. 2010. 2011. Estimate
NPLs in % 40 17,9 11 9,3 6,1 5,3 4,0 3,0 3,1 5,9 11,4 11,8 40
PD 1,00 0,45 0,28 0,23 0,15 0,13 0,10 0,08 0,08 0,15 0,29 0,30 1
DIP in % 0,3 0,31 0,59 1,14 1,18 4
Source: Ibid.
94
bank
arst
vo 1
201
3
Iako rezultati svih modela govore u korist promjenljive POD, velike razlike u smjeru i veličini predloženog varijabiliteta POD tumačimo na način da nemamo dovoljno dokaza da predložimo varijabilnu umjesto fiksne POD. Smatramo da hipotezu o potrebi uvođenja varijabilne POD nismo dokazali, odnosno da smo je samo djelimično dokazali, pa zato nemamo još uvijek dovoljno razloga i dokaza da osporimo, i predložimo zamjenu, fiksne POD promjenljivom. Istraživanje smo započeli sa navođenjem činjenice da je POD u BSBiH fiksna. Nismo u potpunosti uspjeli dokazati da bi trebalo da bude varijabilna. Jedan model čak smatra da POD treba biti nula, pa zbog svega toga fiksna POD i dalje ostaje kao važeći model “varijabiliteta” POD u šemi za osiguranje depozita u BiH.
Ne treba se zanositi mišljenjem da je moguće potpuno precizno odrediti cijenu osiguranja depozita/POD. Ali isto tako ne treba prestati razvijati modele za odredjivanje POD, analizirati već postojeće modele, a nove i stare modele upoređivati i prilagođavati stvarnosti i poželjnim karakteristikama bankarskog sistema. Nije uvijek najkomplikovaniji model i najbolji model. Najbolji model je onaj koji najbolje i najpribližnije podražava stvarnost, ma koliko prost, ili složen, on bio. Neka ovo istraživanje bude jedan od malih koraka u smjeru razvoja što boljeg modela za određivanje POD.
Literatura / References
1. Dowd, Kevin. Measuring Market Risk, John Wiley & Sons Ltd, 2002. p.11.
2. Laeven, Luc. Pricing of Deposit Insurance. World Bank Policy Research Working Paper 2871, July 2002.
3. Žižić et al. Metodi statističke analize. Beograd. Savremena administracija, 1992.
4. Zakon o osiguranju depozita, Službeni glasnik BiH 20/02, 18/05, 100/08 i 75/09.
5. Odluka o visini stope premije za 2007. g., Službeni glasnik BiH br. 89/06.
6. Odluka o visini stope premije za 2012. g., Službeni glasnik BiH br. 89/11.
7. Centralna banka Bosne i Hercegovine, www.cbbh.ba.
8. Agencija za osiguranje depozita Bosne i Hercegovine, www.aod.ba.
95
bank
arst
vo 1
201
3
2007 with 2011. Probability that one large bank and no banks from the group of “other banks” would go bankrupt came down from 17.4% (2007) to 15.4% (2011), just like the probability that two large banks would address DIA for disbursement of deposits - from 0.024% (2007) to 0.018 (2011). These changes were caused by the increased number of banks members of the deposit insurance system from 23 (2007) to 26 (2011), while the number of large banks remained the same.
Linearization model, just like “Merton 1977”, provides numerical valued of DIP, but it does not include a single parameter used in the “Merton 1977” model. The assumed linear relation (perfect linear correlation between NPLs and PD) in 2008, 2009, 2010 and 2011 results in DIP amounting to 0.31, 0.59, 1.14, and 1.18, respectively. According to this model, when NPLs reach 21.2, or 40, the required DIP amounts to 2.1%, or 4%.
In the paper we used historical probabilities - starting from 12/2011 backwards. The risks have grown, PD was skewed to the right, but DIA failed to intervene. How can we explain that? The fact that a certain event, according to some model, has a high probability of occurrence does not necessarily mean that it will actually occur, just like an event with low probability of occurrence might actually occur. Probability distributions indicate the probability, and, in this respect, the risks DIA is facing. Changes in probability distribution and risk perception suggest a correction of DIP, even though these high risks may not actually materialize. This is the point of implementing probability theory in the analysis of DIP and in banking overall. The relationships in the triangle model-probability-reality are best illustrated by the example of a hedge fund in the long-term capital market (LTCM). The loss this hedge fund recorded in
1998 was by 14 standard deviations removed from the expected/average return on portfolio
(Dowd, 2002). An event with zero probability of occurrence actually occurred!
The applied models differ in terms of the size of DIP or the direction of its changes. Although the results of all models are in favour of the variable DIP, there are huge differences in the direction and extent of the proposed DIP variability, which we interpret as having insufficient evidence to actually propose a variable DIP instead of the fixed one. We believe that the hypothesis about the necessity of introducing a variable DIP has not been proven, i.e. that it has been only partially proven, and hence we still do not have sufficient reasons and evidence to dispute the fixed DIP and propose its replacement with a variable DIP. We started this research by stating the fact that DIP in the BSB&H is fixed. We failed to fully prove that it should be variable. One model even suggested that DIP should be zero. Taking all this into account, the fixed DIP still remains the valid model of DIP “variability” within the deposit insurance scheme in B&H.
One should not get carried away thinking that it is possible to precisely determine the price of deposit insurance/DIP. However, one should not stop developing models for determining DIP, analyzing the already existent models, comparing the old models with the new ones, and adjusting them to the reality and desirable characteristics of the banking sector. The most complicated model is not always the best one. The best model is the one which simulates reality in the best and closest way, no matter how simple or complex it may be. Let this research be a small step in the path of development of the best possible model for determining DIP.