299
      ECONOMIC AND BUSINESS REVIEW  |  VOL. 19  |  No.  3  |  2017  |  299-324
TESTING THE HYPOTHESIS OF THE 
ADEQUACY OF THE DISTANCE-TO-
DEFAULT AS AN INDICATOR OF CHANGES 
IN BANKS’ RISK EXPOSURES
BOŽO JAŠOVIČ
1
 Received: June 6, 2016
 Accepted: December 1, 2016
ABSTRACT: A distance to default indicates the distance measured in standard deviations of 
the market value of assets from the default point. The hypothesis that distance to default is 
indicative of changes in the levels of risk of the banking system since it precedes accounting 
data that indicate similar changes was tested on the basis of selected financial ratios. We have 
applied a modification developed by Toda and Yamamoto of the standard Granger causality 
test to see whether there is causality between distance to default and the selected financial 
ratios. Contrary to expectations, we could only prove Granger causality from lagged values 
of distance to default (6–12 months) to a leverage ratio, whereas we were not able to obtain 
similar relationship with other ratios. 
Keywords: financial stability, market discipline, distance to default, default risk, augmented Granger causality
JEL Classification: G21, G28
DOI: 10.15458/85451.43
Introduction
In this paper, we aim to determine whether the distance-to-default (dd) indicator based on 
market data reflects better the changes in banks’ risk profile in comparison with standard 
financial ratios calculated solely by using accounting information. We have chosen the 
Black-Scholes option pricing theory adapted to calculate the implied value of assets and 
their volatility as the theoretical basis for assessing the selected indicator. In the case of 
the Slovenian banks, the distance-to-default indicator could not be used as an “off-the-
shelf” tool for a number of reasons. According to traditional B-S model distance-to-
default indicator is calculated by using series of individual bank market share prices. We 
have followed this approach and derived the aggregate indicator as a weighted average of 
individual indicators. In the observed period only shares of three banks were traded on a 
stock exchange (NKBM, Abanka Vipa and Probanka) and in addition, in an earlier part of 
this period only shares of Probanka were listed. Due to this and low liquidity of Slovenian 
capital market we consider the sample as not representative and therefore present the 
calculation for an illustrative purposes only. Therefore, the traditional approach has been 
adjusted to take into account the specific features of the local environment and has been 
1 Gorenjska banka d.d, Kranj, Slovenia, e-mail: bjasovic@siol.net

300 ECONOMIC AND BUSINESS REVIEW  |  VOL. 19  |  No. 3  |  2017
calculated by making use of indirect market data. Indirect market data (e.g. daily changes 
in interest rates, selected stock-exchange indices, specialised indices or individual prices 
of company shares, which may be representative for certain sectors of the economy) 
complement static accounting information and bring in market dynamics (volatility), 
which has a considerable influence on the value of bank portfolios and, in turn, also on 
their financial results. We have empirically tested on an aggregate level the fundamental 
hypothesis that the estimates of numerous market participants, which are reflected in 
prevailing market prices, may indicate in advance (precede) changes in a bank’s risk 
profile in comparison with static financial ratios made available at intervals and referring 
to the past periods.
The results of empirical testing are not fully in line with the expectations based on the 
proposed hypothesis given the fact that the results obtained confirm it only up to a point. 
With the Toda-Yamamoto version of the Granger causality test, however, we have been 
able to prove that the adjusted distance-to-default measure indicates (precedes) 6 to 12 
months in advance changes in the leverage ratio (capital to total assets ratio). A few other 
empirical studies also underline the significance of the leverage ratio, since it better reflects 
a bank’s insolvency risk in comparison with other indicators. One of the explanations 
for the absence of Granger causality between the distance-to-default and other financial 
indicators is derived from the finding that the regulatory framework leaves quite some 
room for discretion at measurement of bank assets at fair value or at amortised cost at a 
considerable time lag.
The sections in the paper are arranged as follows: we start by presenting the empirical 
studies carried out to date that examined the application of the distance-to-default 
concept. Then we present the theoretical basis for the valuation of a company’s equity by 
using the option pricing model. We proceed by describing the proposed changes to the 
calculation of the indicator by using indirect market data; we then present in the next 
section the empirical testing to demonstrate that changes in the computed distance-to-
default indicator precede changes in the standard ratios (indicators) of bank performance. 
In the last section we wrap up by drawing some conclusions.
1. OVERVIEW OF EMPIRICAL STUDIES USING THE MODEL FOR THE 
VALUATION OF EQUITY AND LIABILITIES 
Empirical studies of the distance-to-default have gained popularity both in the research 
sphere and in practical sense. The key guiding principle for the use of that approach is 
that the dd combines market data of numerous independent market participants in a 
single indicator. In addition, the fact that the indicator is used so often is attributable to 
the recognition that market participants’ estimates, unlike periodical, static reports for 
supervisors, are prospective, i.e. turned into the future and are continuously available.
Gropp et al. (2002, 2004) empirically demonstrated that dd, calculated on the basis of 
the movements in market pricing of bank shares, indicates deterioration in the bank’s 

301 B. JAŠOVIČ  |  TESTING THE HYPOTHESIS OF THE ADEQUACY OF THE DISTANCE-TO-DEFAULT ...
credit rating with the lead time of 6 to 18 months. They proved by means of partial 
derivatives with regard to the value of assets, debt (financial leverage) and assets volatility 
completeness and unbiasedness of dd indicator (Gropp et. al., 2002, p. 10).
The distance to default as a bank risk indicator has been also used by Takami and Tabak 
(2007). They find the distance-to-default indicator to be significantly sensitive to the 
interest rate: the higher the interest rate, the lower the value of the distance to default and 
the higher the default risk. Having analysed the indicator on a sample of banks whose 
shares were listed on a stock exchange, they demonstrated that the indicator reflected 
fairly well the relative risk of each bank (the deviation of dd for individual banks from 
reference value).
Gray and Walsh (2008) have shown different possible uses of distance-to-distress measure 
calculated by using the Black-Scholes-Merton model: from the indicator that reflects risk 
exposure of individual institutions, to aggregate–sector-based indicator and its correlation 
with macroeconomic variables. Despite their affirmative position regarding the use of the 
aforementioned approach to analyse risk exposure of individual banks and the banking 
sector, they point out the limitations for the use of option pricing model, which arise from 
the lack of market-based information. In an aggregated sectoral analysis, imbalances pile 
up for a longer period and market participants begin to incorporate them consistently 
in their price estimates. The authors of the paper have merely indicated in their research 
study that there is a significant correlation between distance-to-default indicator and 
traditional risk measures with different time leads or lags. 
Chan-Lau and Sy (2006) favour the indicators derived from market-based risk measures 
over balance-sheet indicators, which reflect changes in riskiness of the observed 
institutions with considerable time lags. The two authors have empirically calculated and 
compared the distance-to-default indicator for individual banks and concluded that it has 
proved useful for predicting bank rating downgrades. However, the indicator should be 
treated with a dose of scepticism, since the indicator disregards the probability that a bank 
will be subject to remedial regulatory actions. What they had in mind was maintaining a 
capital adequacy threshold set for banks and monitored by supervisors. Chan-Lau and Sy 
adjusted the dd indicator by raising the insolvency threshold using the quotient λ
2
, which 
reflects the expected bank’s capital adequacy ratio and named it distance-to-capital. It 
is worth noting that the two authors tested the empirical calculation of the indicator on 
individual banks; however, in the conclusions they point out that the dd approach could 
apply to analyse the entire banking sector, i.e. stability of the financial system.
The analysts from the ECB also analysed the banking system fragility by using the dd 
indicator. They emphasised that it is a measure based on market prices of shares that 
generates information regarding market asset value and asset volatility. By using a pre-
defined point of insolvency the indicator shows how vulnerable the banking sector is 
2  The authors increased liabilities in equation (1) by factor λ = 1/(1-PCAR). PCAR in the quotient stands for 
expected capital adequacy (Chan-Lau & Sy, 2006, p. 10).

302 ECONOMIC AND BUSINESS REVIEW  |  VOL. 19  |  No. 3  |  2017
(how many standard deviations away from the point of insolvency). Given the rising 
popularity market discipline has for supervisory purposes, the ECB analysts warn that 
the aforementioned approach should not be taken “at face value”–as a substitute for the 
conventional analysis based on balance-sheet data (ECB, 2005, p. 91).
Vassalou and Xing (2004) investigated the probability of default of companies. The 
authors examined a vast number of companies (more than 4,000 in the last part 
of the observed period) between 1971 and 1999. They calculated the indicator of a 
company’s default probabilities where default occurs when value of the indicator dd in 
a cumulative probability function of normal distribution (N(-dd)) is negative. Based on 
such comprehensive empirical research, they concluded that insolvency risk (default) is 
closely linked to the size of a company and the ratio between the book to market value of 
a company. The empirical research confirms that the probability of default in the observed 
corporate sector decreases monotonically as the company size increases and as the ratio of 
book to market value of equity decreases. The authors argue that asset volatility implicitly 
calculated from the daily fluctuations in market share prices is the key information for the 
estimates of default probabilities (Vassalou & Xing, 2004, p. 833).
Chan-Lau, Jobert and Kong (2004) have empirically tested the use of the distance-to-default 
indicator for banks that operate in emerging markets and have arrived at a conclusion that 
the dd measure could be used as a forecasting tool for distress looming on the banking 
system. They concluded that the early warning indicator predicts difficulties in banking 
systems with up to 9-month lead time (Chan-Lau et al., 2004, p. 13). Furthermore, the 
research study highlights that the risk-free rate of return is not a proper parameter in a 
risky world. In addition, it also points at the unsuitability of constant debt assumption 
which should be revisited. Despite the previously mentioned weaknesses, their conclusion 
is that the dd indicator could be useful tool in supervising banks. The research also uses 
the probit and logit regression models to assess the ability to predict the occurrence of a 
negative credit event (default or rating downgrade) and the conclusion drawn is that the 
dd can be useful for forecasting bank distress/vulnerability. 
Gapen, Gray, Lim and Xiao (2004) have examined in their research study the corporate 
sector vulnerability by applying the option pricing model. Their key conclusion is that the 
approach combines balance-sheet data with market-based data where asset volatility is the 
key determinant of default probability. By taking into account asset volatility in the model, 
we are able to account for the fact that companies with a similar financing structure of 
(debt to equity ratio) have different values of indicator dd, i.e. probability of default. 
Asset volatility is largely related to the economic activity (industry) (Crosbie & Bohn, 
2003, p. 9), i.e. its technological characteristics, while a company’s financial leverage only 
increases its underlying asset volatility, which is then reflected on higher equity volatility. 
The research study underlines non-linear links in the Black-Scholes model, which enables 
a more reliable estimate of basic function driven by changes in underlying parameters.
Gapen et al. (2004) have warned that the model has its shortcomings since it uses normal 
distribution probability when calculating the distance-to-default indicator. Also Crosbie 

303 B. JAŠOVIČ  |  TESTING THE HYPOTHESIS OF THE ADEQUACY OF THE DISTANCE-TO-DEFAULT ...
and Bohn (2003, p. 18) underline that using normal distribution for the calculation of dd 
is a bad choice. All authors underscore that in order to obtain more reliable estimates for 
the indicators, empirical distribution should be used.
In an analogy with the use of the model to value assets and liabilities of individual 
companies or banks based on market data, a similar approach could be followed at the 
sector-based level. Persson and Blavarg (2003) have shored up the thesis that the credit 
portfolio risk in banks largely reflects the corporate sector risk to which they are exposed 
by comparing time series of default probabilities for seven economic sectors (industries). 
Their conclusion is that increased credit risk in individual banks estimated with dd could 
be a consequence of increased risk in the corporate sector (Persson & Blavarg, 2003, p. 
24). To explain the reasons that influence the indicator movement in banks, we should 
analyse the indicator for the corporate sector that account for the bulk of a bank’s credit 
portfolio and has direct impact on its riskiness. Moreover, as regards the corporates, the 
two authors draw attention to the fact that only the shares issued by larger companies are 
traded on a stock exchange. They assess that expectations of market participants regarding 
the financial instruments issued by larger companies should also reflect up to a point the 
expectations of a sector (industry) as a whole and eventually influence the development of 
smaller, non-listed companies in a particular industry.
Willem van den End and Tabbae (2005) have focused their research on the sector-based 
approach. They assume that a sector-based analysis has an advantage over a traditional 
analysis based on macroeconomic aggregates, since with the latter, some risks might be 
hidden. Furthermore, at the sector-based level, it becomes possible to identify foreign 
exchange and balance-sheet structural imbalances, as well as the shortage of capital. The 
most significant advantages of the sector-based approach include interdependence and 
the possibility of a spill-over effect (contagion) between sectors. The authors distinguish 
in the research study two indicators, i.e. measures of risk: probability-of-default measure 
and loss measure. The latter presents, in accordance with the option pricing model, the 
value of put option, i.e. loss incurred by the excess of liabilities over the value of assets. 
The value of a put option for the banking sector is the assessment of the necessary capital 
that sector needs in order to absorb losses, i.e. the value of an implied government-backed 
guarantee to ensure macrofinancial stability. The authors have calculated both measures of 
risk for five sectors: banking, pension, insurance, corporate sector, and household sector. 
Given the fact that market asset value and asset volatility could not be calculated for all 
sectors by using direct market data, they have used alternative approaches: company-
specific balance-sheet data provided that they are marked-to-market, discounted future 
cash flows or implied market values derived from option market prices (Willem van den 
End & Tabbae 2005, p. 9). We highlight the described approach since it indicates how to 
overcome the lack of direct market data (prices) when applying the Black-Scholes model.
Based on the above overview, we could summarise our observations in the following 
conclusions:
- Numerous studies point out the usefulness of information content inherent in 
market-based data, their forward-looking nature, the large number of participants 

304 ECONOMIC AND BUSINESS REVIEW  |  VOL. 19  |  No. 3  |  2017
that generate market data and, consequently, make them objective and available on 
on-going basis (see for instance Flannery, 2001; Flannery 1998).
- The authors explicitly stress that accounting data cannot be completely replaced 
by market information, it should be rather viewed as complementary source to 
accounting data.
- The authors are aware of the limitations or deficiencies resulting from the direct 
application of the structural model introduced by Black-Scholes hence they try 
to correct it with methodological adaptations, i.e. by testing the plausibility of the 
assumptions on which the model is founded.
- The studies recommend complementary use of the discussed approach both for the 
analysis of risk sensitivity of individual credit institutions and at the aggregate level 
for the analysis of macrofinancial stability.
- Some studies explicitly conclude that asset variability (volatility) determined on the 
basis of market data is indeed the key component that contributes to the explanatory 
power of the dd indicator (see, for instance, Gapen et al., 2004; V assalou & Xing, 2004; 
Crosbie & Bohn, 2003).
2. THEORETICAL BASIS FOR APPLYING THE OPTION PRICING MODEL IN 
THE VALUATION OF COMPANY EQUITY AND LIABILITIES
The methodology for the calculation of the distance-to-default is derived from the Black-
Scholes-Merton option pricing model (Black & Scholes, 1973) that can also be used to 
determine a firm’s equity value and corporate liabilities (see also Merton, 1974). The 
assumption for the use of the model for equity valuation is that owners of companies have 
an option (call option)–the right to purchase all assets of the company by paying off all its 
liabilities. Having paid off all outstanding liabilities, only the equity holders have claim to 
the company’s assets, and the price for exercising such an option (exercise price) is equal 
to the value of total liabilities.
Shareholders’ equity has positive value only in the case that the value of the company’s 
assets exceeds the value of its liabilities. Should that not be the case, owners would never 
exercise their call option to buy assets, since they would have to pay for the assets more 
than their value. If that is the case, the company’s creditors could exercise the option they 
have (put option) and sell their claims on the company in exchange for taking over all its 
assets in order to minimise their loss.
Let us assume that a bank (or a company) is insolvent and unable to honour its obligations, 
meaning that the value of its assets is lower that the value of its liabilities. Under these 
circumstances, creditworthiness of banks (or any other company) can be measured with 
the difference between the value of its assets and the value of its liabilities (the distance to 
the default point). The smaller the difference is, the greater the probability of insolvency 
and vice versa. The distance-to-default (dd) as shown by the equation below measures how 
many standard deviations a bank is away from insolvency, i.e. the default point (Gapen et 
al., 2004, p. 34; Crosbie & Bohn, 2003, p. 18; Gropp et al., 2002, page 10):

305 B. JAŠOVIČ  |  TESTING THE HYPOTHESIS OF THE ADEQUACY OF THE DISTANCE-TO-DEFAULT ...
    (1) 
where:
S
a 
 = asset value,
O = amount of liabilities,
µ, σ
a
 = expected rate of return on assets and the volatility of returns, 
T = time to maturity.
   
According to some authors (e.g. Chan-Lau et al., 2004, p. 5; Gropp et al., 2004, p. 55), the 
distance-to-default is a complete and unbiased indicator of bank fragility, i.e. changes in its 
risk profile. The foundation for such a conclusion is the finding that the indicator captures 
the most significant determinants of insolvency risk: expectations regarding earnings i.e. 
return on assets, financial leverage (indebtedness) and risk associated with the volatility of 
assets. The expectations regarding rising returns decrease insolvency risk and, therefore, 
increase the value of the indicator dd. The value of the indicator dd also increases, if 
financial leverage (bank indebtedness) decreases and if asset volatility declines. Inverse 
processes have an impact on lowering the value of the indicator and consequently lead a 
bank (company) closer to the point of insolvency (Gropp et al., 2002, p. 10).
For the calculation of the indicator dd, the data on the market value of a bank’s assets 
and asset volatility are necessary. Since such data are not directly available, a direct 
calculation by using equation (1) is less appropriate for practical reasons. It is why most 
research studies have used the indirect approach to calculate implied asset value and their 
volatility by using the model developed by Black and Scholes (Black & Scholes, 1973). For 
the calculation it is necessary to have as input a series of market share prices and their 
volatility (standard deviation), market capitalisation, the size of debt and risk-free rate of 
return.
3
By following the Black-Scholes model (B-S model), we are in a position to estimate the 
value of capital as the value of the call option of the company where the exercise price is 
equal to the nominal value of its debt, by applying the following formula (Hull, 2005, p. 
295):
4
    (2)
where:
N(d..)  = cumulative density function of the standard normal distribution,
3 See for instance in Bukatarević, Jašovič, Košak and Šuler, 2008.
4 The derivation of the Black-Scholes-Merton model was carried out under the assumption that fluctuations 
in share prices follow the general Wiener process (stochastic share price movement process). (For more de-
tails see Hull (2005, p. 291– 295).
company’s assets, and the price for exercising such an option (exercise price) is equal to the 
value of total liabilities. 
 
Shareholders’ equity has positive value only in the case that the value of the company’s assets 
exceeds the value of its liabilities. Should that not be the case, owners would never exercise 
their call option to buy assets, since they would have to pay for the assets more than their 
value. If that is the case, the company’s creditors could exercise the option they have (put 
option) and sell their claims on the company in exchange for taking over all its assets in order 
to minimise their loss. 
 
Let us assume that a bank (or a company) is insolvent and unable to honour its obligations, 
meaning that the value of its assets is lower that the value of its liabilities. Under these 
circumstances, creditworthiness of banks (or any other company) can be measured with the 
difference between the value of its assets and the value of its liabilities (the distance to the 
default point). The smaller the difference is, the greater the probability of insolvency and vice 
versa. The distance-to-default (dd) as shown by the equation below measures how many 
standard deviations a bank is away from insolvency, i.e. the default point (Gapen et al., 2004, 
p. 34; Crosbie & Bohn, 2003, p. 18; Gropp et al., 2002, page 10): 
 
𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = 
𝑙𝑙𝑙𝑙 𝑙𝑙𝑙𝑙 𝑆𝑆𝑆𝑆 𝑎𝑎𝑎𝑎 𝑇𝑇𝑇𝑇 𝑂𝑂𝑂𝑂 𝑡𝑡𝑡𝑡 + � 𝜇𝜇𝜇𝜇𝜇 
𝜎𝜎𝜎𝜎 𝑎𝑎𝑎𝑎 2
2
�
𝜎𝜎𝜎𝜎 𝑎𝑎𝑎𝑎 √ 𝑇𝑇𝑇𝑇      (1) 
 
where: 
 
S
a 
 = asset value, 
O = amount of liabilities, 
µ, σ
a
 = expected rate of return on assets and the volatility of returns,  
T = time to maturity. 
    
According to some authors (e.g. Chan-Lau et al., 2004, p. 5; Gropp et al., 2004, p. 55), the 
distance-to-default is a complete and unbiased indicator of bank fragility, i.e. changes in its 
risk profile. The foundation for such a conclusion is the finding that the indicator captures the 
most significant determinants of insolvency risk: expectations regarding earnings i.e. return 
on assets, financial leverage (indebtedness) and risk associated with the volatility of assets. 
The expectations regarding rising returns decrease insolvency risk and, therefore, increase the 
value of the indicator dd. The value of the indicator dd also increases, if financial leverage 
(bank indebtedness) decreases and if asset volatility declines. Inverse processes have an 
impact on lowering the value of the indicator and consequently lead a bank (company) closer 
to the point of insolvency (Gropp et al., 2002, p. 10). 
 
For the calculation of the indicator dd, the data on the market value of a bank’s assets and 
asset volatility are necessary. Since such data are not directly available, a direct calculation by 
using equation (1) is less appropriate for practical reasons. It is why most research studies 
have used the indirect approach to calculate implied asset value and their volatility by using 
the model developed by Black and Scholes (Black & Scholes, 1973). For the calculation it is 
necessary to have as input a series of market share prices and their volatility (standard 
deviation), market capitalisation, the size of debt and risk-free rate of return.
2
 
 
                                                           
2
 See for instance in Bukatarević, Jašovič, Košak and Šuler, 2008. 
By following the Black-Scholes model (B-S model), we are in a position to estimate the value 
of capital as the value of the call option of the company where the exercise price is equal to 
the nominal value of its debt, by applying the following formula (Hull, 2005, p. 295):
3
 
 
𝐾𝐾𝐾𝐾 = 𝑆𝑆𝑆𝑆 𝑎𝑎𝑎𝑎 𝑁𝑁𝑁𝑁 ( 𝑑𝑑𝑑𝑑 1
) − 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂
− 𝑟𝑟𝑟𝑟 𝑇𝑇𝑇𝑇 𝑁𝑁𝑁𝑁 ( 𝑑𝑑𝑑𝑑 2
)    (2) 
 
where: 
 
N(d..)  = cumulative density function of the standard normal distribution, 
 
𝑑𝑑𝑑𝑑 1
=
𝑙𝑙𝑙𝑙 𝑙𝑙𝑙𝑙 𝑙 𝑆𝑆𝑆𝑆 𝑎𝑎𝑎𝑎 𝑂𝑂𝑂𝑂 �+ � 𝑟𝑟𝑟𝑟+ 
𝜎𝜎𝜎𝜎 𝑎𝑎𝑎𝑎 2
2
� 𝑇𝑇𝑇𝑇 𝜎𝜎𝜎𝜎 𝑎𝑎𝑎𝑎 √ 𝑇𝑇𝑇𝑇      (3) 
 
𝑑𝑑𝑑𝑑 2
= 𝑑𝑑𝑑𝑑 1
− 𝜎𝜎𝜎𝜎 𝑎𝑎𝑎𝑎 √ 𝑇𝑇𝑇𝑇      (4) 
 
r  = risk-free rate. 
 
A relationship between share price volatility and asset volatility is given with the following 
equality: 
 
𝜎𝜎𝜎𝜎 𝑘𝑘𝑘𝑘 = 
𝑆𝑆𝑆𝑆 𝑎𝑎𝑎𝑎 𝐾𝐾𝐾𝐾 𝜎𝜎𝜎𝜎 𝑎𝑎𝑎𝑎 𝑁𝑁𝑁𝑁 ( 𝑑𝑑𝑑𝑑 1
)      (5) 
 
where: 
 
K = capital, 
σ
k
  = volatility of share prices or returns. 
 
Given that market prices for listed bank shares traded on regulated markets are continuously 
available, and given that standard deviation of returns can be computed on the basis of those 
prices, it is possible to solve with the iterative method the system of simultaneous equations 
(3) and (5) so that we obtain the implied assets value S
a
 and their standard deviation σ
a
. We 
then use both variables for the calculation of the indicator dd following the equation (1).  
 
 
3. Methodological adjustment using indirect market data to calculate the distance-
to-default indicator  
 
Since bank shares traded on a regulated securities market are “in short supply” and also due to 
poor liquidity of the equity market in Slovenia in general, we have undertaken the calculation 
of the distance-to-default indicator with the use of “indirect” market data. Market expectations 
in the corporate sector are best reflected by share prices of companies listed on a stock 
exchange. As a rule, these are shares issued by larger companies whose pricing mostly 
reflects market sentiment in a particular sector as a whole (as, for instance, Persson & 
Blavarg, 2003, p. 24). Market expectations of investors who invested in shares of such 
companies have implied effects on the bank portfolio risk dynamics. That impact is direct and 
given that bank balance sheets tend to be non-transparent (investors are not informed of all 
                                                           
3
 The derivation of the Black-Scholes-Merton model was carried out under the assumption that fluctuations in 
share prices follow the general Wiener process (stochastic share price movement process). (For more details see 
Hull (2005, p. 291– 295). 

306 ECONOMIC AND BUSINESS REVIEW  |  VOL. 19  |  No. 3  |  2017
      (3)
      (4)
r  = risk-free rate.
A relationship between share price volatility and asset volatility is given with the following 
equality:
      (5)
where:
K = capital,
σ
k
  = volatility of share prices or returns.
Given that market prices for listed bank shares traded on regulated markets are 
continuously available, and given that standard deviation of returns can be computed on 
the basis of those prices, it is possible to solve with the iterative method the system of 
simultaneous equations (3) and (5) so that we obtain the implied assets value S
a
 and their 
standard deviation σ
a
. We then use both variables for the calculation of the indicator dd 
following the equation (1). 
3. METHODOLOGICAL ADJUSTMENT USING INDIRECT MARKET DATA 
TO CALCULATE THE DISTANCE-TO-DEFAULT INDICATOR 
Since bank shares traded on a regulated securities market are “in short supply” and also 
due to poor liquidity of the equity market in Slovenia in general, we have undertaken 
the calculation of the distance-to-default indicator with the use of “indirect” market 
data. Market expectations in the corporate sector are best reflected by share prices 
of companies listed on a stock exchange. As a rule, these are shares issued by larger 
companies whose pricing mostly reflects market sentiment in a particular sector as a 
whole (as, for instance, Persson & Blavarg, 2003, p. 24). Market expectations of investors 
who invested in shares of such companies have implied effects on the bank portfolio 
risk dynamics. That impact is direct and given that bank balance sheets tend to be 
non-transparent (investors are not informed of all bank’s investments), the described 
approach is more appropriate than the approach using market prices of bank shares 
used to calculate the implied value of assets and their volatility (by applying B-S model), 
which in such light actually is »indirect«. Moreover, we must not forget to emphasise 
that using indirect market data is more relevant for the sector-based distance-to-default 
indicator (for the entire banking sector) since it indicates changes in risk exposure 
By following the Black-Scholes model (B-S model), we are in a position to estimate the value 
of capital as the value of the call option of the company where the exercise price is equal to 
the nominal value of its debt, by applying the following formula (Hull, 2005, p. 295):
3
 
 
𝐾𝐾𝐾𝐾 = 𝑆𝑆𝑆𝑆 𝑎𝑎𝑎𝑎 𝑁𝑁𝑁𝑁 ( 𝑑𝑑𝑑𝑑 1
) − 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂
− 𝑟𝑟𝑟𝑟 𝑇𝑇𝑇𝑇 𝑁𝑁𝑁𝑁 ( 𝑑𝑑𝑑𝑑 2
)    (2) 
 
where: 
 
N(d..)  = cumulative density function of the standard normal distribution, 
 
𝑑𝑑𝑑𝑑 1
=
𝑙𝑙𝑙𝑙 𝑙𝑙𝑙𝑙 𝑙 𝑆𝑆𝑆𝑆 𝑎𝑎𝑎𝑎 𝑂𝑂𝑂𝑂 �+ � 𝑟𝑟𝑟𝑟+ 
𝜎𝜎𝜎𝜎 𝑎𝑎𝑎𝑎 2
2
� 𝑇𝑇𝑇𝑇 𝜎𝜎𝜎𝜎 𝑎𝑎𝑎𝑎 √ 𝑇𝑇𝑇𝑇      (3) 
 
𝑑𝑑𝑑𝑑 2
= 𝑑𝑑𝑑𝑑 1
− 𝜎𝜎𝜎𝜎 𝑎𝑎𝑎𝑎 √ 𝑇𝑇𝑇𝑇      (4) 
 
r  = risk-free rate. 
 
A relationship between share price volatility and asset volatility is given with the following 
equality: 
 
𝜎𝜎𝜎𝜎 𝑘𝑘𝑘𝑘 = 
𝑆𝑆𝑆𝑆 𝑎𝑎𝑎𝑎 𝐾𝐾𝐾𝐾 𝜎𝜎𝜎𝜎 𝑎𝑎𝑎𝑎 𝑁𝑁𝑁𝑁 ( 𝑑𝑑𝑑𝑑 1
)      (5) 
 
where: 
 
K = capital, 
σ
k
  = volatility of share prices or returns. 
 
Given that market prices for listed bank shares traded on regulated markets are continuously 
available, and given that standard deviation of returns can be computed on the basis of those 
prices, it is possible to solve with the iterative method the system of simultaneous equations 
(3) and (5) so that we obtain the implied assets value S
a
 and their standard deviation σ
a
. We 
then use both variables for the calculation of the indicator dd following the equation (1).  
 
 
3. Methodological adjustment using indirect market data to calculate the distance-
to-default indicator  
 
Since bank shares traded on a regulated securities market are “in short supply” and also due to 
poor liquidity of the equity market in Slovenia in general, we have undertaken the calculation 
of the distance-to-default indicator with the use of “indirect” market data. Market expectations 
in the corporate sector are best reflected by share prices of companies listed on a stock 
exchange. As a rule, these are shares issued by larger companies whose pricing mostly 
reflects market sentiment in a particular sector as a whole (as, for instance, Persson & 
Blavarg, 2003, p. 24). Market expectations of investors who invested in shares of such 
companies have implied effects on the bank portfolio risk dynamics. That impact is direct and 
given that bank balance sheets tend to be non-transparent (investors are not informed of all 
                                                           
3
 The derivation of the Black-Scholes-Merton model was carried out under the assumption that fluctuations in 
share prices follow the general Wiener process (stochastic share price movement process). (For more details see 
Hull (2005, p. 291– 295). 
By following the Black-Scholes model (B-S model), we are in a position to estimate the value 
of capital as the value of the call option of the company where the exercise price is equal to 
the nominal value of its debt, by applying the following formula (Hull, 2005, p. 295):
3
 
 
𝐾𝐾𝐾𝐾 = 𝑆𝑆𝑆𝑆 𝑎𝑎𝑎𝑎 𝑁𝑁𝑁𝑁 ( 𝑑𝑑𝑑𝑑 1
) − 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂
− 𝑟𝑟𝑟𝑟 𝑇𝑇𝑇𝑇 𝑁𝑁𝑁𝑁 ( 𝑑𝑑𝑑𝑑 2
)    (2) 
 
where: 
 
N(d..)  = cumulative density function of the standard normal distribution, 
 
𝑑𝑑𝑑𝑑 1
=
𝑙𝑙𝑙𝑙 𝑙𝑙𝑙𝑙 𝑙 𝑆𝑆𝑆𝑆 𝑎𝑎𝑎𝑎 𝑂𝑂𝑂𝑂 �+ � 𝑟𝑟𝑟𝑟+ 
𝜎𝜎𝜎𝜎 𝑎𝑎𝑎𝑎 2
2
� 𝑇𝑇𝑇𝑇 𝜎𝜎𝜎𝜎 𝑎𝑎𝑎𝑎 √ 𝑇𝑇𝑇𝑇      (3) 
 
𝑑𝑑𝑑𝑑 2
= 𝑑𝑑𝑑𝑑 1
− 𝜎𝜎𝜎𝜎 𝑎𝑎𝑎𝑎 √ 𝑇𝑇𝑇𝑇      (4) 
 
r  = risk-free rate. 
 
A relationship between share price volatility and asset volatility is given with the following 
equality: 
 
𝜎𝜎𝜎𝜎 𝑘𝑘𝑘𝑘 = 
𝑆𝑆𝑆𝑆 𝑎𝑎𝑎𝑎 𝐾𝐾𝐾𝐾 𝜎𝜎𝜎𝜎 𝑎𝑎𝑎𝑎 𝑁𝑁𝑁𝑁 ( 𝑑𝑑𝑑𝑑 1
)      (5) 
 
where: 
 
K = capital, 
σ
k
  = volatility of share prices or returns. 
 
Given that market prices for listed bank shares traded on regulated markets are continuously 
available, and given that standard deviation of returns can be computed on the basis of those 
prices, it is possible to solve with the iterative method the system of simultaneous equations 
(3) and (5) so that we obtain the implied assets value S
a
 and their standard deviation σ
a
. We 
then use both variables for the calculation of the indicator dd following the equation (1).  
 
 
3. Methodological adjustment using indirect market data to calculate the distance-
to-default indicator  
 
Since bank shares traded on a regulated securities market are “in short supply” and also due to 
poor liquidity of the equity market in Slovenia in general, we have undertaken the calculation 
of the distance-to-default indicator with the use of “indirect” market data. Market expectations 
in the corporate sector are best reflected by share prices of companies listed on a stock 
exchange. As a rule, these are shares issued by larger companies whose pricing mostly 
reflects market sentiment in a particular sector as a whole (as, for instance, Persson & 
Blavarg, 2003, p. 24). Market expectations of investors who invested in shares of such 
companies have implied effects on the bank portfolio risk dynamics. That impact is direct and 
given that bank balance sheets tend to be non-transparent (investors are not informed of all 
                                                           
3
 The derivation of the Black-Scholes-Merton model was carried out under the assumption that fluctuations in 
share prices follow the general Wiener process (stochastic share price movement process). (For more details see 
Hull (2005, p. 291– 295). 

307 B. JAŠOVIČ  |  TESTING THE HYPOTHESIS OF THE ADEQUACY OF THE DISTANCE-TO-DEFAULT ...
at the sectoral level. For a single bank risk analysis it is more appropriate to calculate 
dd indicator in line with traditional methodology (based on market share prices of 
a concrete bank) where we also capture specific expectations of market participants, 
which relate to that particular bank only. 
Willem van den End and Tabbae (2005, p. 9) have also pointed out that in the absence 
of market prices of financial instruments, other sources of market data can be used in 
order to apply the Black-Scholes model. It is the latter approach seen as a key guide to the 
adjustments on which this paper elaborates below.
We use the alternative, indirect approach to calculate the time series for the distance-
to-default indicator. By tapping different sources of market data we introduced market 
variability in the model. We assume that a bank portfolio is composed of the following 
segments:
1. w
1
 – cash and cash equivalents;
2. w
2
 – loans to banking and non-banking sector (retail and corporate, other  
  than items 4, 5 and 6) largely influenced by movement in variable  
  EURIBOR;
3. w
3
 – debt securities portfolio;
4. w
4
 – loans to companies from the manufacturing sector;
5. w
5
 – loans to companies from trading sector;
6. w
6
 – loans to companies from ‘other services’ sector;
7. w
7
 – equity securities, capital investments and derivatives;
8. w
8
 – other (fixed assets, accounting categories). 
In the equation (6), the shares of above portfolio segments are used as risk weights (w
it
) 
for the calculation of σ
at
 of bank assets (investments) at the end of every month during 
the observed period beginning January 1996 and ending June 2009. We present for an 
illustrative purposes time series of risk weights per each segment at year ends and at the 
end of observed period. 

308 ECONOMIC AND BUSINESS REVIEW  |  VOL. 19  |  No. 3  |  2017
Table 1: Time series of shares of bank portfolio segments (in %)
5
Source: Bank of Slovenia
For each of the described eight segments, we have assigned a source of “indirect” market 
data, which has most significant impact on the value of movements in that segment (in the 
same order as description of the segments above):
1. w
1–
movement in one-month LIBOR in EUR until the end of 1999, then the interbank 
interest rate EONIA for overnight deposits;
2. w
2–
movement in in six-month LIBOR in EUR until the end of 1999, then the 
interbank interest rates EURIBOR for 6-month period;
3. w
3–
movement in average return on bond indices composed of 5 European sovereign 
bond indices (GDBR5 Index, GECU10YR Index, GECU2YR Index, GECU30YR Index 
and GECU5YR Index), 4 U.S. sovereign bond indices (USGG10YR Index, USGG2YR 
Index, USGG30YR Index and USGG5YR Index) and BIO, Slovenian bond index;
4. w
4–
movement in average return on shares of the companies Gorenje, Krka, Pivovarna 
Laško and Žito (representatives of manufacturing sector);
5. w
5–
movement in average return on shares of the companies Mercator, Merkur and 
Petrol (representatives of trading sector);
6. w
6–
movement in average return on shares of the companies Helios, Intereuropa, 
Luka Koper, Sava and Terme Čatež (representatives of “other services” sector);
7. w
7–
movement in average return on equity indices composed of 9 European indices 
(AEX Index, ATX Index, BEL 20 Index, CAC Index, DAX Index, ISEQ Index, 
MIBTEL Index, UKX Index and SMI Index), 3 U.S. indices (CCMP Index, INDU 
Index and SPX Index) and SBI, Slovenian stock exchange index;
8. w
8–
movement in consumer price index.
5 Data series are available in Bank of Slovenia statistical publications. The segments on an aggregate level 
were grouped together with the help of Financial Stability Department. Data series are available from author 
upon a request.
 
Source: Bank of Slovenia 
 
For each of the described eight segments, we have assigned a source of “indirect” market 
data, which has most significant impact on the value of movements in that segment (in the 
same order as description of the segments above): 
1. w
1–
movement in one-month LIBOR in EUR until the end of 1999, then the interbank 
interest rate EONIA for overnight deposits; 
2. w
2–
movement in in six-month LIBOR in EUR until the end of 1999, then the interbank 
interest rates EURIBOR for 6-month period; 
3. w
3–
movement in average return on bond indices composed of 5 European sovereign 
bond indices (GDBR5 Index, GECU10YR Index, GECU2YR Index, GECU30YR 
Index and GECU5YR Index), 4 U.S. sovereign bond indices (USGG10YR Index, 
USGG2YR Index, USGG30YR Index and USGG5YR Index) and BIO, Slovenian 
bond index; 
4. w
4–
movement in average return on shares of the companies Gorenje, Krka, Pivovarna 
Laško and Žito (representatives of manufacturing sector); 
5. w
5–
movement in average return on shares of the companies Mercator, Merkur and 
Petrol (representatives of trading sector); 
6. w
6–
movement in average return on shares of the companies Helios, Intereuropa, Luka 
Koper, Sava and Terme Čatež (representatives of “other services” sector); 
7. w
7–
movement in average return on equity indices composed of 9 European indices 
(AEX Index, ATX Index, BEL 20 Index, CAC Index, DAX Index, ISEQ Index, 
MIBTEL Index, UKX Index and SMI Index), 3 U.S. indices (CCMP Index, INDU 
Index and SPX Index) and SBI, Slovenian stock exchange index; 
8. w
8–
movement in consumer price index. 
 
We have calculated from the above market sources on a daily frequency for the moving one-
year window the returns, variances and standard deviations at the annual level for the entire 
observed period from the beginning of 1997 until June 2009. Variances of returns of all 
variables were included in the calculation of variance-covariance matrix from equation (6): 
 
𝜎𝜎𝜎𝜎 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎
= � ∑ 𝑤𝑤𝑤𝑤 𝑖𝑖𝑖𝑖 𝑎𝑎𝑎𝑎 2 𝑙𝑙𝑙𝑙 𝑖𝑖𝑖𝑖 𝑖𝑖
𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 𝑣𝑣𝑣𝑣
𝑖𝑖𝑖𝑖 𝑎𝑎𝑎𝑎 + ∑∑ 𝑤𝑤𝑤𝑤 𝑖𝑖𝑖𝑖 𝑎𝑎𝑎𝑎 𝑤𝑤𝑤𝑤 𝑗𝑗𝑗𝑗 𝑎𝑎𝑎𝑎 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑣𝑣𝑣𝑣 𝑖𝑖𝑖𝑖 𝑗𝑗𝑗𝑗𝑎𝑎𝑎𝑎
𝑙𝑙𝑙𝑙 𝑗𝑗𝑗𝑗 𝑖𝑖
𝑙𝑙𝑙𝑙 𝑖𝑖𝑖𝑖 𝑖𝑖
  (6) 
 
where: 
w
..t,
 =
  
shares of individual segments (i = j = 1 –8) in the banking system portfolio at the end 
of the month t, 
Date w
1
w
2
w
3
w
4
w
5
w
6
w
7
w
8
31.12.1996 3,45% 1,96% 27,87% 35,81% 10,52% 5,07% 9,61% 5,70%
31.12.1997 3,72% 2,08% 34,26% 28,83% 9,34% 5,17% 10,89% 5,72%
31.12.1998 3,68% 3,30% 29,83% 30,27% 9,94% 6,23% 11,60% 5,14%
31.12.1999 3,38% 3,69% 25,56% 31,34% 10,15% 7,73% 13,22% 4,94%
31.12.2000 3,16% 3,61% 23,94% 32,33% 9,98% 8,03% 13,68% 5,27%
31.12.2001 5,32% 28,57% 27,09% 10,07% 7,87% 13,10% 3,34% 4,65%
31.12.2002 3,15% 26,67% 32,32% 9,85% 7,70% 12,05% 3,20% 5,07%
31.12.2003 2,80% 25,85% 32,59% 11,24% 7,88% 12,05% 3,05% 4,54%
31.12.2004 2,48% 29,83% 27,47% 12,04% 8,60% 12,53% 3,01% 4,02%
31.12.2005 2,05% 32,35% 26,15% 11,82% 8,69% 12,09% 3,66% 3,18%
31.12.2006 3,12% 36,57% 20,73% 11,53% 7,72% 13,51% 3,85% 2,97%
31.12.2007 1,43% 40,49% 15,50% 11,42% 8,13% 16,43% 4,19% 2,43%
31.12.2008 2,61% 41,95% 13,13% 11,75% 8,39% 16,77% 3,47% 1,93%
30.6.2009 2,35% 42,46% 13,83% 11,11% 7,84% 16,32% 3,88% 3,09%

309 B. JAŠOVIČ  |  TESTING THE HYPOTHESIS OF THE ADEQUACY OF THE DISTANCE-TO-DEFAULT ...
We have calculated from the above market sources on a daily frequency for the moving 
one-year window the returns, variances and standard deviations at the annual level for 
the entire observed period from the beginning of 1997 until June 2009. Variances of 
returns of all variables were included in the calculation of variance-covariance matrix 
from equation (6):
        (6)
where:
w
..t,
 =
  
shares of individual segments (i = j = 1–8) in the banking system portfolio at the 
end of the month t,
var
it
 = variance of selected returns,,
cov
it
 = covariance of returns.
The above calculated time series volatility σ
at
 on a daily basis was translated to a monthly 
series as the daily data average at the annual level in an individual month and then 
used for the calculation of the distance-to-default indicator at the aggregate level with 
monthly frequency. We have used the book values for assets, equity and liabilities at an 
aggregate level for the banking sector at the end of each month in the calculation of dd 
indicator.
The essential point of using market data is that they reflect investors’ expectations and 
uncertainty (volatility) in relation to the future price fluctuations. Asset volatility is the 
key parameter when calculating the indicator dd and without volatility (σ
a
), the Black-
Scholes model is useless, since in such a case we are dealing with a specific, deterministic 
situation typical of traditional, static analyses. In our modification to the methodology, 
we have ensured that by providing a large set of statistically processed market data, the 
volatility (uncertainty) has been introduced in the calculation, which impacts to a highest 
possible degree the fluctuation of the value of a selected bank’s portfolio segments. Similar 
conclusions have been presented also in some of the aforementioned studies, which 
explicitly state that asset variability (volatility), determined on the basis of market data, is 
indeed the key component that contributes to the indicator’s explanatory power (see, for 
instance, Gapen et al., 2004; Vassalou & Xing, 2004; Crosbie & Bohn, 2003).
Figure 1 shows a comparative movement of both calculated series of the distance-to-default 
indicator dd. Under the first approach–based on movement of bank share prices
6
–we have 
calculated implied asset value and asset volatility (by using the traditional B-S model) 
and then used the output in the calculation of the indicator dd for an individual bank; 
the aggregate indicator has been calculated based on risk-weighted average of individual 
indicators. In the second, adjusted approach, for the calculation of the indicator dd we 
6 To calculate the time series of indicator dd, we have used the movement in the price of shares in Probanka, 
NKBM and Abanka Vipa. In the greater part of the period observed only the shares of Probanka were listed 
on a stock exchange. Due to this the sample is not representative and we present it only for an illustrative 
purpose.
 
Source: Bank of Slovenia 
 
For each of the described eight segments, we have assigned a source of “indirect” market 
data, which has most significant impact on the value of movements in that segment (in the 
same order as description of the segments above): 
1. w
1–
movement in one-month LIBOR in EUR until the end of 1999, then the interbank 
interest rate EONIA for overnight deposits; 
2. w
2–
movement in in six-month LIBOR in EUR until the end of 1999, then the interbank 
interest rates EURIBOR for 6-month period; 
3. w
3–
movement in average return on bond indices composed of 5 European sovereign 
bond indices (GDBR5 Index, GECU10YR Index, GECU2YR Index, GECU30YR 
Index and GECU5YR Index), 4 U.S. sovereign bond indices (USGG10YR Index, 
USGG2YR Index, USGG30YR Index and USGG5YR Index) and BIO, Slovenian 
bond index; 
4. w
4–
movement in average return on shares of the companies Gorenje, Krka, Pivovarna 
Laško and Žito (representatives of manufacturing sector); 
5. w
5–
movement in average return on shares of the companies Mercator, Merkur and 
Petrol (representatives of trading sector); 
6. w
6–
movement in average return on shares of the companies Helios, Intereuropa, Luka 
Koper, Sava and Terme Čatež (representatives of “other services” sector); 
7. w
7–
movement in average return on equity indices composed of 9 European indices 
(AEX Index, ATX Index, BEL 20 Index, CAC Index, DAX Index, ISEQ Index, 
MIBTEL Index, UKX Index and SMI Index), 3 U.S. indices (CCMP Index, INDU 
Index and SPX Index) and SBI, Slovenian stock exchange index; 
8. w
8–
movement in consumer price index. 
 
We have calculated from the above market sources on a daily frequency for the moving one-
year window the returns, variances and standard deviations at the annual level for the entire 
observed period from the beginning of 1997 until June 2009. Variances of returns of all 
variables were included in the calculation of variance-covariance matrix from equation (6): 
 
𝜎𝜎𝜎𝜎 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎
= � ∑ 𝑤𝑤𝑤𝑤 𝑖𝑖𝑖𝑖 𝑎𝑎𝑎𝑎 2 𝑙𝑙𝑙𝑙 𝑖𝑖𝑖𝑖 𝑖𝑖
𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 𝑣𝑣𝑣𝑣
𝑖𝑖𝑖𝑖 𝑎𝑎𝑎𝑎 + ∑∑ 𝑤𝑤𝑤𝑤 𝑖𝑖𝑖𝑖 𝑎𝑎𝑎𝑎 𝑤𝑤𝑤𝑤 𝑗𝑗𝑗𝑗 𝑎𝑎𝑎𝑎 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑣𝑣𝑣𝑣 𝑖𝑖𝑖𝑖 𝑗𝑗𝑗𝑗𝑎𝑎𝑎𝑎
𝑙𝑙𝑙𝑙 𝑗𝑗𝑗𝑗 𝑖𝑖
𝑙𝑙𝑙𝑙 𝑖𝑖𝑖𝑖 𝑖𝑖
  (6) 
 
where: 
w
..t,
 =
  
shares of individual segments (i = j = 1 –8) in the banking system portfolio at the end 
of the month t, 
Date w
1
w
2
w
3
w
4
w
5
w
6
w
7
w
8
31.12.1996 3,45% 1,96% 27,87% 35,81% 10,52% 5,07% 9,61% 5,70%
31.12.1997 3,72% 2,08% 34,26% 28,83% 9,34% 5,17% 10,89% 5,72%
31.12.1998 3,68% 3,30% 29,83% 30,27% 9,94% 6,23% 11,60% 5,14%
31.12.1999 3,38% 3,69% 25,56% 31,34% 10,15% 7,73% 13,22% 4,94%
31.12.2000 3,16% 3,61% 23,94% 32,33% 9,98% 8,03% 13,68% 5,27%
31.12.2001 5,32% 28,57% 27,09% 10,07% 7,87% 13,10% 3,34% 4,65%
31.12.2002 3,15% 26,67% 32,32% 9,85% 7,70% 12,05% 3,20% 5,07%
31.12.2003 2,80% 25,85% 32,59% 11,24% 7,88% 12,05% 3,05% 4,54%
31.12.2004 2,48% 29,83% 27,47% 12,04% 8,60% 12,53% 3,01% 4,02%
31.12.2005 2,05% 32,35% 26,15% 11,82% 8,69% 12,09% 3,66% 3,18%
31.12.2006 3,12% 36,57% 20,73% 11,53% 7,72% 13,51% 3,85% 2,97%
31.12.2007 1,43% 40,49% 15,50% 11,42% 8,13% 16,43% 4,19% 2,43%
31.12.2008 2,61% 41,95% 13,13% 11,75% 8,39% 16,77% 3,47% 1,93%
30.6.2009 2,35% 42,46% 13,83% 11,11% 7,84% 16,32% 3,88% 3,09%
 
Source: Bank of Slovenia 
 
For each of the described eight segments, we have assigned a source of “indirect” market 
data, which has most significant impact on the value of movements in that segment (in the 
same order as description of the segments above): 
1. w
1–
movement in one-month LIBOR in EUR until the end of 1999, then the interbank 
interest rate EONIA for overnight deposits; 
2. w
2–
movement in in six-month LIBOR in EUR until the end of 1999, then the interbank 
interest rates EURIBOR for 6-month period; 
3. w
3–
movement in average return on bond indices composed of 5 European sovereign 
bond indices (GDBR5 Index, GECU10YR Index, GECU2YR Index, GECU30YR 
Index and GECU5YR Index), 4 U.S. sovereign bond indices (USGG10YR Index, 
USGG2YR Index, USGG30YR Index and USGG5YR Index) and BIO, Slovenian 
bond index; 
4. w
4–
movement in average return on shares of the companies Gorenje, Krka, Pivovarna 
Laško and Žito (representatives of manufacturing sector); 
5. w
5–
movement in average return on shares of the companies Mercator, Merkur and 
Petrol (representatives of trading sector); 
6. w
6–
movement in average return on shares of the companies Helios, Intereuropa, Luka 
Koper, Sava and Terme Čatež (representatives of “other services” sector); 
7. w
7–
movement in average return on equity indices composed of 9 European indices 
(AEX Index, ATX Index, BEL 20 Index, CAC Index, DAX Index, ISEQ Index, 
MIBTEL Index, UKX Index and SMI Index), 3 U.S. indices (CCMP Index, INDU 
Index and SPX Index) and SBI, Slovenian stock exchange index; 
8. w
8–
movement in consumer price index. 
 
We have calculated from the above market sources on a daily frequency for the moving one-
year window the returns, variances and standard deviations at the annual level for the entire 
observed period from the beginning of 1997 until June 2009. Variances of returns of all 
variables were included in the calculation of variance-covariance matrix from equation (6): 
 
𝜎𝜎𝜎𝜎 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎
= � ∑ 𝑤𝑤𝑤𝑤 𝑖𝑖𝑖𝑖 𝑎𝑎𝑎𝑎 2 𝑙𝑙𝑙𝑙 𝑖𝑖𝑖𝑖 𝑖𝑖
𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 𝑣𝑣𝑣𝑣
𝑖𝑖𝑖𝑖 𝑎𝑎𝑎𝑎 + ∑∑ 𝑤𝑤𝑤𝑤 𝑖𝑖𝑖𝑖 𝑎𝑎𝑎𝑎 𝑤𝑤𝑤𝑤 𝑗𝑗𝑗𝑗 𝑎𝑎𝑎𝑎 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑣𝑣𝑣𝑣 𝑖𝑖𝑖𝑖 𝑗𝑗𝑗𝑗𝑎𝑎𝑎𝑎
𝑙𝑙𝑙𝑙 𝑗𝑗𝑗𝑗 𝑖𝑖
𝑙𝑙𝑙𝑙 𝑖𝑖𝑖𝑖 𝑖𝑖
  (6) 
 
where: 
w
..t,
 =
  
shares of individual segments (i = j = 1 –8) in the banking system portfolio at the end 
of the month t, 
Date w
1
w
2
w
3
w
4
w
5
w
6
w
7
w
8
31.12.1996 3,45% 1,96% 27,87% 35,81% 10,52% 5,07% 9,61% 5,70%
31.12.1997 3,72% 2,08% 34,26% 28,83% 9,34% 5,17% 10,89% 5,72%
31.12.1998 3,68% 3,30% 29,83% 30,27% 9,94% 6,23% 11,60% 5,14%
31.12.1999 3,38% 3,69% 25,56% 31,34% 10,15% 7,73% 13,22% 4,94%
31.12.2000 3,16% 3,61% 23,94% 32,33% 9,98% 8,03% 13,68% 5,27%
31.12.2001 5,32% 28,57% 27,09% 10,07% 7,87% 13,10% 3,34% 4,65%
31.12.2002 3,15% 26,67% 32,32% 9,85% 7,70% 12,05% 3,20% 5,07%
31.12.2003 2,80% 25,85% 32,59% 11,24% 7,88% 12,05% 3,05% 4,54%
31.12.2004 2,48% 29,83% 27,47% 12,04% 8,60% 12,53% 3,01% 4,02%
31.12.2005 2,05% 32,35% 26,15% 11,82% 8,69% 12,09% 3,66% 3,18%
31.12.2006 3,12% 36,57% 20,73% 11,53% 7,72% 13,51% 3,85% 2,97%
31.12.2007 1,43% 40,49% 15,50% 11,42% 8,13% 16,43% 4,19% 2,43%
31.12.2008 2,61% 41,95% 13,13% 11,75% 8,39% 16,77% 3,47% 1,93%
30.6.2009 2,35% 42,46% 13,83% 11,11% 7,84% 16,32% 3,88% 3,09%

310 ECONOMIC AND BUSINESS REVIEW  |  VOL. 19  |  No. 3  |  2017
have used the assets book value and calculated the asset volatility on the basis of a large set 
of the market data that have the highest impact on certain bank asset segments.
Figure 1: Movement in distance-to-default indicator computed directly from prices of bank 
shares and indirectly from market data based on adjusted methodology during the period 
1997–June 2009 (number of standard deviations)
Legend: The shaded area shows the period in which the quarterly GDP growth was negative.
Source: Author’s calculations.
The indicator calculated directly from the bank share prices moves consistently at the 
higher level than the indirectly computed indicator; hence, it reflects banks’ lower risk 
profile. Based on the anecdotic evidence, we could argue that market optimism was 
reflected in high valuation of bank shares (we have to caution that for the greater part of 
the observed period, we dealt with one issuer only). The favourable market capitalisation 
of the banks was mirrored in a high implied asset value and, as a consequence, in the 
value of the dd indicator. Even in the first half of 2008 when the global financial crisis was 
already evident, the indicator was still moving at a relatively high level and it only started to 
decline in the second half of 2008. We may conclude that the series calculated on the basis 
of the bank share prices exhibits, contrary to expectations, a relatively delayed reaction to 
the crisis situation. One of plausible explanations for it is that bank shareholders, despite 
the turbulences on financial markets, valued the bank shares relatively high knowing that 
the Slovenian banks did not have toxic assets in their portfolios. Only later on, when the 
financial crisis spread to the real sector, the value of the indicator started to fall because of 
investors’ negative perception.
 
  Legend: The shaded area shows the period in which the quarterly GDP growth was negative. 
Source: Author’s calculations. 
 
The indicator calculated directly from the bank share prices moves consistently at the higher 
level than the indirectly computed indicator; hence, it reflects banks’ lower risk profile. Based 
on the anecdotic evidence, we could argue that market optimism was reflected in high 
valuation of bank shares (we have to caution that for the greater part of the observed period, 
we dealt with one issuer only). The favourable market capitalisation of the banks was 
mirrored in a high implied asset value and, as a consequence, in the value of the dd indicator. 
Even in the first half of 2008 when the global financial crisis was already evident, the 
indicator was still moving at a relatively high level and it only started to decline in the second 
half of 2008. We may conclude that the series calculated on the basis of the bank share prices 
exhibits, contrary to expectations, a relatively delayed reaction to the crisis situation. One of 
plausible explanations for it is that bank shareholders, despite the turbulences on financial 
markets, valued the bank shares relatively high knowing that the Slovenian banks did not 
have toxic assets in their portfolios. Only later on, when the financial crisis spread to the real 
sector, the value of the indicator started to fall because of investors’ negative perception. 
 
The movement in the indirectly calculated indicator corresponds more to the expectations. If 
we focus on the pre-crisis period, the value of the indicator was increasing from mid-2004 
onward all the time until the second half of 2006, and then the trend reversed and its value 
kept on decreasing. In mid-2009, the indicator value hit the rock-bottom. The indicator 
calculated in the indirect manner and by use of several different market data series reflects the 
perception of market instability in the eyes of different investor groups. The downward trend 
of the indicator’s value started as early as in second half of 2006 when the sub-prime 
mortgage crisis started to unfold in the United States and with the full-blown crisis in 2007 
and 2008 (the demise of the investment bank Lehman Brothers), that tendency only 
continued. Against that background, a movement in the indicator computed on the basis of 
“indirect” market information changes much more according to expectations and in line with 
0
2
4
6
8
10
12
1996M12
1997M06
1997M12
1998M06
1998M12
1999M06
1999M12
2000M06
2000M12
2001M06
2001M12
2002M06
2002M12
2003M06
2003M12
2004M06
2004M12
2005M06
2005M12
2006M06
2006M12
2007M06
2007M12
2008M06
2008M12
Direct calculation
Indirect calculation

311 B. JAŠOVIČ  |  TESTING THE HYPOTHESIS OF THE ADEQUACY OF THE DISTANCE-TO-DEFAULT ...
The movement in the indirectly calculated indicator corresponds more to the expectations. 
If we focus on the pre-crisis period, the value of the indicator was increasing from mid-2004 
onward all the time until the second half of 2006, and then the trend reversed and its value 
kept on decreasing. In mid-2009, the indicator value hit the rock-bottom. The indicator 
calculated in the indirect manner and by use of several different market data series reflects 
the perception of market instability in the eyes of different investor groups. The downward 
trend of the indicator’s value started as early as in second half of 2006 when the sub-prime 
mortgage crisis started to unfold in the United States and with the full-blown crisis in 
2007 and 2008 (the demise of the investment bank Lehman Brothers), that tendency only 
continued. Against that background, a movement in the indicator computed on the basis 
of “indirect” market information changes much more according to expectations and in 
line with anecdotal evidence on the evolution of the financial crisis. Market participants 
were recognising crisis impulses and valued their investments accordingly as reflected in 
the fluctuations of market categories we have used for the calculation of dd indicator.
4. EMPIRICAL TESTING OF ASSUMPTIONS OF THE ADEQUACY OF 
DISTANCE-TO-DEFAULT AS A PREDICTOR OF BANK RISK EXPOSURE
Our starting point is the basic assumption that market data (prices, indices, returns) are a 
valuable additional source of information for an analysis of financial stability. What is the 
grounding for making such an assumption? Market data have the following properties:
- they are a reflection of numerous market participants–less informed small investors, 
professional market analysts, institutional investors, credit rating agencies, investment 
advisors and others–and reflect their prevailing judgement;
- they are prospective, forward-looking, since they reflect prevailing expectations;
- they are continuously available without lengthy time lags, if not even in real time.
In comparison with official, accounting data and reports submitted by financial institutions 
to their supervisors, market-based data have several advantages. Official reports are 
published with a delay; they refer to the past and tend to disclose a limited scope of data. If 
we add the tendency sometimes displayed by reporting institution that makes the reporting 
entity look better than it actually is, then the usefulness of information obtained on the 
basis of market data is even more valuable. We are not arguing that official information 
should not be treated as reliable or that it might not be required. On the contrary, in the 
absence of official, accounting information, any serious analysis of the financial condition 
of an individual institution or the system made solely on the basis of market data would be 
all but credible. That said, we want to demonstrate that a traditional, static analysis based 
merely on official accounting data should be complemented by market information drawn 
from numerous market transactions (see for instance Curry et al., 2003; Krainer & Lopez, 
2003; Krainer & Lopez, 2002; Gunther et al., 2001; Berger et al., 2000).
In our case, we have calculated the indicator dd from the market data sets by applying two 
methodologically different approaches. Now we want to determine whether the fluctuations 
in the indicator by taking into account properties of market data communicates some 

312 ECONOMIC AND BUSINESS REVIEW  |  VOL. 19  |  No. 3  |  2017
information, even before it is disclosed in official reports. More specifically, we would like 
to establish whether a change in the dd indicator indicates in advance (precedes) a probable 
movement in certain variables (parameters) - before they appear also in accounting data 
after some time has passed. To this end we have selected such variables (parameters) of 
bank performance that to certain extent also indicate the changes in degree of riskiness in 
the banking system:
- C_DOB_SKM - profit before tax in the 12-month moving window;
- C_PLL_SKM - costs for net impairments and provisions in the 
    12-month moving window;
- K_DVP_SKM - share of debt securities in total assets;
- K_KAP_SKM - share of equity in total assets;
- P_KU_SKM - capital adequacy ratio in percentage;
- P_NPL_SKM - percentage of claims classified as D and E   
    (approximation for non-performing assets) in  
    classified assets;
- P_OSLAB_SKM - percentage of impairments and provisions in
    gross assets;
- P_ROA_SKM - return on assets in the 12-month moving window in  
    percentage;
- S_TA_SKM - total assets.
The selection of the variables from static accounting records proves the necessity to use 
both types of information, since in the absence of historical data, it would also be difficult 
to verify the reliability of market data, i.e. indicators, calculated on their basis. Moreover, 
static indicators reflect changes in institutions’ risk profiles and the question we can ask 
is how long a lag is between the realisation of risk to its identification and disclosure in 
reports.
If we go back to the above variables, each of them reflects in its own right the changed 
performance influenced by changed risk. Pre-tax profit starts to decline with the narrowing 
net interest margin and/or banks have to book increased impairments for credit risk due 
to deteriorating portfolio quality and vice versa. Credit risk costs (net impairments) grow, 
if the quality of credit portfolio deteriorates and, by contrast, banks form impairments at 
a slower pace and even decide to release accumulated impairments, if portfolio quality 
starts to improve in favourable economic conditions. The need for additional impairments 
arises, however, during the period of economic contraction and bank de-leveraging that 
follows the period of unsustainable credit growth. The share of debt securities in total 
assets is a specific indicator that directly reflects a change in the level of secondary liquidity 
reserves in banks: a fall in that share is a signal for sound economic conditions and vice 
versa–its rise indicates stressed financial conditions in which risk aversion rises and the 
aspiration to maintain stable liquidity is high.
The leverage ratio (capital to total assets) and the capital adequacy ratio may seem rather 
similar at first glance, but they differ both in their approach to on- and off-balance sheet 
items inclusion in terms of risk and the approach to the calculation of capital. The concept 

313 B. JAŠOVIČ  |  TESTING THE HYPOTHESIS OF THE ADEQUACY OF THE DISTANCE-TO-DEFAULT ...
of credit risk weights attributed to asset classes in accordance with Basel recommendations 
is often subject to a critical scrutiny for allegedly failing to reflect risk appropriately (see for 
instance Haldane, 2012). The conceptual differences in the calculation of both indicators, 
is precisely the reason for including both indicators in our analysis.
The share of assets classified as D and E categories can be used as an approximation for 
non-performing loans (bad assets). Otherwise, the number of days past due (more than 
90 days) is commonly used as a criterion for non-performing loans but given the fact that 
it was not consistently used in the past, we have chosen as its substitute the share of banks’ 
claims classified as D and E, which as a rule by their substance are non-performing, i.e. 
bad assets. It was our assumption that when the economic conditions deteriorate, the 
portion of non-performing exposures on banks’ balance sheets surges. At this point we 
should add that banks are usually rather late and start to apply a conservative assessment 
approach to their claims and form loan loss impairments with a delay. This practice is 
also attributable to the provisions of International Financial Reporting Standards that 
did not allow forming ex ante impairments for expected losses, which means that unless 
there was objective evidence of a customer’s financial difficulties meaning that such a 
customer would not be able to make the full repayment of the debt, no provisioning was 
allowed.
The return on assets is a combined ratio which may reflect deterioration in bank business/
operations: reduced profitability that impacts the numerator, and unsustainable bank 
assets growth, that impacts the denominator of that parameter. It is expected that the value 
of that indicator will start to decline when the economic conditions get tighter: profits 
that are in the numerator start to plunge, while total assets in the denominator after high 
unsustainable growth do not decrease at the same dynamics, but only after a breakout of 
a crisis when a deleveraging process starts. The latter parameter, total assets, was included 
in the denominator of the previous indicator: however, we also examine it independently 
as it exhibits a different correlation with other variables than return on assets. We assume 
that during the period before economic conditions tighten, banks’ total assets swelled 
driven by fast credit activities in a boom cycle. A surge in total assets growth is followed 
by a period of crisis and depressed economic conditions. As it is to be expected, total 
assets start to decline only in the post-crisis period with a contraction of credit activity, the 
diminished reliance on wholesale financing and when banks begin to adjust their business 
models to the changed situation (divestiture of non-core assets). 

314 ECONOMIC AND BUSINESS REVIEW  |  VOL. 19  |  No. 3  |  2017
Table 2: Descriptive statistics for selected variables for the period February 1997–June 2009
7
Source: Bank of Slovenia and author’s calculations.
Table 3: Correlation coefficients between the selected variables for the period February 1997–
June 2009
Source: Bank of Slovenia and author’s calculations.
We have gathered monthly series for the period from February 1997 to June 2009 and 
Tables 2 and 3 show some descriptive statistics and correlation coefficients for all the 
described variables of the bank operations. We find the observed period to be relevant 
for our research since it is sufficiently long and encompasses at least two peaks (cycles) in 
the fluctuation of the indicator dd. Furthermore, it is adequate from the view point of the 
evolution of the latest financial and economic crisis: the first signs emerged with the sub-
prime mortgage lending crisis in July 2007 in the United States to be followed by a full-
blown distrust in the financial markets and the collapse of the interbank market in autumn 
2008 when the investment bank Lehman Brothers failed (for more details of the unfolding 
of the financial crisis see De Larosiere et al., 2009, p. 11). Economic recession unfolded 
in the aftermath of those events and in 2009 all EU Member States with the exception of 
Poland had negative economic growth. In terms of the economic cycle, the second part 
of the period under review was the most dynamic one: a strong cyclical upswing coupled 
with unsustainable credit growth which ultimately tilted to a contraction period marked 
by credit crunch. The observed period ends in mid-2009 when Slovenia was already in 
the third quarter in a row of negative quarterly GDP growth (the shaded area in Figure 
1). From that time on, the strained situation in the financial markets and its consequences 
began to manifest in standard financial ratios for bank performance (banks posted losses 
7 Data series of selected variables are available from author upon a request.
that indicator will start to decline when the economic conditions get tighter: profits that are in 
the numerator start to plunge, while total assets in the denominator after high unsustainable 
growth do not decrease at the same dynamics, but only after a breakout of a crisis when a 
deleveraging process starts. The latter parameter, total assets, was included in the 
denominator of the previous indicator: however, we also examine it independently as it 
exhibits a different correlation with other variables than return on assets. We assume that 
during the period before economic conditions tighten, banks’ total assets swelled driven by 
fast credit activities in a boom cycle. A surge in total assets growth is followed by a period of 
crisis and depressed economic conditions. As it is to be expected, total assets start to decline 
only in the post-crisis period with a contraction of credit activity, the diminished reliance on 
wholesale financing and when banks begin to adjust their business models to the changed 
situation (divestiture of non-core assets).  
 
Table 2: Descriptive statistics for selected variables for the period February 1997–June 
2009
6
 
 
 
 
Source: Bank of Slovenia and author’s calculations. 
 
Table 3: Correlation coefficients between the selected variables for the period February 
1997–June 2009 
 
 
Source: Bank of Slovenia and author’s calculations. 
 
We have gathered monthly series for the period from February 1997 to June 2009 and Tables 
2 and 3 show some descriptive statistics and correlation coefficients for all the described 
variables of the bank operations. We find the observed period to be relevant for our research 
since it is sufficiently long and encompasses at least two peaks (cycles) in the fluctuation of 
the indicator dd. Furthermore, it is adequate from the view point of the evolution of the latest 
financial and economic crisis: the first signs emerged with the sub-prime mortgage lending 
crisis in July 2007 in the United States to be followed by a full-blown distrust in the financial 
markets and the collapse of the interbank market in autumn 2008 when the investment bank 
Lehman Brothers failed (for more details of the unfolding of the financial crisis see De 
Larosiere et al., 2009, p. 11). Economic recession unfolded in the aftermath of those events 
and in 2009 all EU Member States with the exception of Poland had negative economic 
growth. In terms of the economic cycle, the second part of the period under review was the 
most dynamic one: a strong cyclical upswing coupled with unsustainable credit growth which 
                                                           
6
 Data series of selected variables are available from author upon a request. 
C_DOB_SKM C_PLL_SKM K_DVP_SKM K_KAP_SKM P_KU_SKM P_NPL_SKM P_OSLAB_SKM P_ROA_SKM S_TA_SKM
EUR 000 EUR 000 ratio ratio percentage percentage perentage percentage EUR millions
Median 185.173,0 137.614,0 0,2295 0,0858 11,66% 3,71% 3,35% 0,98% 19.283,0 
Average 213.682,4 132.682,4 0,2147 0,0935 13,08% 3,39% 3,22% 0,95% 22.420,4 
Minimum 59.375,0 29.881,0 0,1058 0,0763 10,46% 1,56% 2,26% 0,35% 7.183,0 
Maksimum 538.368,0 420.663,0 0,3051 0,1200 20,07% 4,88% 3,78% 1,35% 49.682,3 
Standard deviation 136.373,5 64.111,0 0,0654 0,0135 2,82% 0,95% 0,40% 0,20% 12.600,6 
Number of observations 149 149 86 149 149 149 149 149 149 
C_DOB_SKM C_PLL_SKM K_DVP_SKM K_KAP_SKM P_KU_SKM P_NPL_SKM P_OSLAB_SKM P_ROA_SKM S_TA_SKM
C_DOB_SKM 1,000 0,262 -0,790 -0,682 -0,624 -0,879 -0,791 0,479 0,868
C_PLL_SKM 1,000 -0,228 -0,625 -0,607 -0,543 -0,250 -0,536 0,627
K_DVP_SKM 1,000 0,217 0,418 0,960 0,965 -0,131 -0,969
K_KAP_SKM 1,000 0,925 0,757 0,377 0,038 -0,771
P_KU_SKM 1,000 0,740 0,329 0,060 -0,697
P_NPL_SKM 1,000 0,846 -0,133 -0,955
P_OSLAB_SKM 1,000 -0,220 -0,830
P_ROA_SKM 1,000 0,039
S_TA_SKM 1,000
that indicator will start to decline when the economic conditions get tighter: profits that are in 
the numerator start to plunge, while total assets in the denominator after high unsustainable 
growth do not decrease at the same dynamics, but only after a breakout of a crisis when a 
deleveraging process starts. The latter parameter, total assets, was included in the 
denominator of the previous indicator: however, we also examine it independently as it 
exhibits a different correlation with other variables than return on assets. We assume that 
during the period before economic conditions tighten, banks’ total assets swelled driven by 
fast credit activities in a boom cycle. A surge in total assets growth is followed by a period of 
crisis and depressed economic conditions. As it is to be expected, total assets start to decline 
only in the post-crisis period with a contraction of credit activity, the diminished reliance on 
wholesale financing and when banks begin to adjust their business models to the changed 
situation (divestiture of non-core assets).  
 
Table 2: Descriptive statistics for selected variables for the period February 1997–June 
2009
6
 
 
 
 
Source: Bank of Slovenia and author’s calculations. 
 
Table 3: Correlation coefficients between the selected variables for the period February 
1997–June 2009 
 
 
Source: Bank of Slovenia and author’s calculations. 
 
We have gathered monthly series for the period from February 1997 to June 2009 and Tables 
2 and 3 show some descriptive statistics and correlation coefficients for all the described 
variables of the bank operations. We find the observed period to be relevant for our research 
since it is sufficiently long and encompasses at least two peaks (cycles) in the fluctuation of 
the indicator dd. Furthermore, it is adequate from the view point of the evolution of the latest 
financial and economic crisis: the first signs emerged with the sub-prime mortgage lending 
crisis in July 2007 in the United States to be followed by a full-blown distrust in the financial 
markets and the collapse of the interbank market in autumn 2008 when the investment bank 
Lehman Brothers failed (for more details of the unfolding of the financial crisis see De 
Larosiere et al., 2009, p. 11). Economic recession unfolded in the aftermath of those events 
and in 2009 all EU Member States with the exception of Poland had negative economic 
growth. In terms of the economic cycle, the second part of the period under review was the 
most dynamic one: a strong cyclical upswing coupled with unsustainable credit growth which 
                                                           
6
 Data series of selected variables are available from author upon a request. 
C_DOB_SKM C_PLL_SKM K_DVP_SKM K_KAP_SKM P_KU_SKM P_NPL_SKM P_OSLAB_SKM P_ROA_SKM S_TA_SKM
EUR 000 EUR 000 ratio ratio percentage percentage perentage percentage EUR millions
Median 185.173,0 137.614,0 0,2295 0,0858 11,66% 3,71% 3,35% 0,98% 19.283,0 
Average 213.682,4 132.682,4 0,2147 0,0935 13,08% 3,39% 3,22% 0,95% 22.420,4 
Minimum 59.375,0 29.881,0 0,1058 0,0763 10,46% 1,56% 2,26% 0,35% 7.183,0 
Maksimum 538.368,0 420.663,0 0,3051 0,1200 20,07% 4,88% 3,78% 1,35% 49.682,3 
Standard deviation 136.373,5 64.111,0 0,0654 0,0135 2,82% 0,95% 0,40% 0,20% 12.600,6 
Number of observations 149 149 86 149 149 149 149 149 149 
C_DOB_SKM C_PLL_SKM K_DVP_SKM K_KAP_SKM P_KU_SKM P_NPL_SKM P_OSLAB_SKM P_ROA_SKM S_TA_SKM
C_DOB_SKM 1,000 0,262 -0,790 -0,682 -0,624 -0,879 -0,791 0,479 0,868
C_PLL_SKM 1,000 -0,228 -0,625 -0,607 -0,543 -0,250 -0,536 0,627
K_DVP_SKM 1,000 0,217 0,418 0,960 0,965 -0,131 -0,969
K_KAP_SKM 1,000 0,925 0,757 0,377 0,038 -0,771
P_KU_SKM 1,000 0,740 0,329 0,060 -0,697
P_NPL_SKM 1,000 0,846 -0,133 -0,955
P_OSLAB_SKM 1,000 -0,220 -0,830
P_ROA_SKM 1,000 0,039
S_TA_SKM 1,000

315 B. JAŠOVIČ  |  TESTING THE HYPOTHESIS OF THE ADEQUACY OF THE DISTANCE-TO-DEFAULT ...
from operations, there was pressure to increase impairments for credit risk, credit activity 
contracted, etc.). Testing distance-to-default indicator under such circumstances would 
hardly be productive. The question we should ask is whether the information extracted 
from a large market data set, preceded the described dynamics of the economic cycle, 
even before it appeared in banks’ accounting data and business reports or standard bank 
performance ratios. Therefore, we continue by testing the hypothesis that the distance-to-
default indicator, points to stressed conditions and increasing risk associated with a bank’s 
operations even before it is reflected in the standard, static indicators of bank financial 
performance.
We have carried out our empirical test by applying the Granger causality test. The 
assumption underlying the test is that the future cannot predict the past, but it is the other 
way round. If changes in a particular variable predict changes in the other variable, then 
we are talking about Granger causality (Gujarati, 1995, p. 620; Asteriou & Hall, 2007, 
p. 281). Granger has developed a relatively simple test that defines causality by saying 
that the variable y
t 
Granger-causes x
t
, if x
t
 can be predicted more accurately by using 
past values of the y
t 
variable rather than not using such past values, while all other terms 
remain unchanged. Therefore, we are not to interpret causality in statistics as we would 
have done in everyday use, since it relates to a cause and effect relationship. By using the 
Granger causality test, we are able to prove that changes in one variable predict changes 
in the other variable.
The direct Granger causality test can be carried out only with the stationary time series. 
It is a commonplace in the time series that describe economic phenomena to be non-
stationary, since their mean value and/or variance change over time given the fact that 
they comprise trends or breakpoints. To that end, we have carried out the ADF test (ADF , 
Augmented Dickey-Fuller Test, see in Asteriou & Hall, 2007, p. 297) of stationarity for all-
time series of bank performance indicators and both time series of the distance-to-default. 
The results of the ADF unit root test are presented in Table 4.
Table 4: Results of the Augmented Dickey-Fuller Unit Root Test
Legend:
- Δ
1
 or Δ
2
 designate the first or the second difference of the baseline time series;
- *** designates the rejection of null hypothesis at the 1% level of significance.
Source: Author’s calculations.
ultimately tilted to a contraction period marked by credit crunch. The observed period ends in 
mid-2009 when Slovenia was already in the third quarter in a row of negative quarterly GDP 
growth (the shaded area in Figure 1). From that time on, the strained situation in the financial 
markets and its consequences began to manifest in standard financial ratios for bank 
performance (banks posted losses from operations, there was pressure to increase impairments 
for credit risk, credit activity contracted, etc.). Testing distance-to-default indicator under such 
circumstances would hardly be productive. The question we should ask is whether the 
information extracted from a large market data set, preceded the described dynamics of the 
economic cycle, even before it appeared in banks’ accounting data and business reports or 
standard bank performance ratios. Therefore, we continue by testing the hypothesis that the 
distance-to-default indicator, points to stressed conditions and increasing risk associated with 
a bank’s operations even before it is reflected in the standard, static indicators of bank 
financial performance. 
 
We have carried out our empirical test by applying the Granger causality test. The assumption 
underlying the test is that the future cannot predict the past, but it is the other way round. If 
changes in a particular variable predict changes in the other variable, then we are talking 
about Granger causality (Gujarati, 1995, p. 620; Asteriou & Hall, 2007, p. 281). Granger has 
developed a relatively simple test that defines causality by saying that the variable y
t 
Granger-
causes x
t
, if x
t
 can be predicted more accurately by using past values of the y
t 
variable rather 
than not using such past values, while all other terms remain unchanged. Therefore, we are 
not to interpret causality in statistics as we would have done in everyday use, since it relates 
to a cause and effect relationship. By using the Granger causality test, we are able to prove 
that changes in one variable predict changes in the other variable. 
 
The direct Granger causality test can be carried out only with the stationary time series. It is a 
commonplace in the time series that describe economic phenomena to be non-stationary, 
since their mean value and/or variance change over time given the fact that they comprise 
trends or breakpoints. To that end, we have carried out the ADF test (ADF, Augmented 
Dickey-Fuller Test, see in Asteriou & Hall, 2007, p. 297) of stationarity for all-time series of 
bank performance indicators and both time series of the distance-to-default. The results of the 
ADF unit root test are presented in Table 4. 
 
Table 4: Results of the Augmented Dickey-Fuller Unit Root Test 
 
 
Legend: 
- Δ
1
 or Δ
2
 designate the first or the second difference of the baseline time series; 
- *** designates the rejection of null hypothesis at the 1% level of significance. 
Source: Author’s calculations. 
 
By testing for stationarity, we have determined that all tested time series (both distance-to-
default indicator time series and all bank performance variables time series) are non-
stationary in levels of data (it was not possible to reject the null hypothesis). We have tested 
t - test Probability t - test Probability
Variable tp Variable tp
Δ
1
 C_DOB_SKM -10,4136 0,00*** Δ
1 
P_OSLAB_SKM -15,2170 0,00***
Δ
1 
C_PLL_SKM -11,4574 0,00*** Δ
1 
P_ROA_SKM -11,3207 0,00***
Δ
1 
K_DVP_SKM -8,3084 0,00*** Δ
1 
S_TA_SKM -1,8189 0,37010
Δ
1 
K_KAP_SKM -15,1904 0,00*** Δ
2
 
 
S_TA_SKM -9,2725 0,00***
Δ
1 
P_KU_SKM -11,0158 0,00*** Δ
1 
DTOD_PON_1L -9,5310 0,00***
Δ
1 
P_NPL_SKM -12,3422 0,00*** Δ
1 
DTOD_VAR_COV_1L -8,9714 0,00***

316 ECONOMIC AND BUSINESS REVIEW  |  VOL. 19  |  No. 3  |  2017
By testing for stationarity, we have determined that all tested time series (both distance-
to-default indicator time series and all bank performance variables time series) are non-
stationary in levels of data (it was not possible to reject the null hypothesis). W e have tested 
the first difference time series and rejected the null hypothesis at low level of significance 
and confirmed stationarity of the series of differences save for the variable total assets 
(S_TA_SKM) where we have been able to determine the stationarity only at the level of 
second differences.
The finding that all baseline time series in value levels are non-stationary has significant 
consequences when conducting the Granger casualty test. In such a case, it is not possible 
to use the Granger test directly, but the augmented Granger causality test should be 
performed (see for instance Toda & Yamamoto, 1995; Giles, 2011; Binh, 2010). Toda and 
Yamamoto have shown that the V AR model can be evaluated by applying a time series at 
the value levels and then tested for introduced restrictions in the model regardless of the 
different levels of integration or cointegration of time series (Toda & Yamamoto, 1995, p. 
225). They have developed an alternative causality test where the VAR model has to be 
evaluated with the number of lags n + d, or m + d, where d presents the additional number 
of lags, which equals the highest level of integration of the used variables. When testing for 
linear restrictions, we do not take into account the coefficients of the additional d lags, since 
they are introduced in the model in order to ensure the validity of the standard asymptotic 
theory. Therefore, additional lags appear in the model specification as exogenous variable 
(Giles, 2011, p. 5). The expanded Granger causality test requires the assessment of the 
V AR model specified with the following equations:
        (7)
        
(8)
We have carried out the augmented Granger causality test between the distance-to-
default indicator series and the selected banking performance ratios
8
. For each test we 
have chosen different monthly lagged variables, since the test is sensitive to the selected 
lag-length. It should be highlighted that the literature suggests using rather a higher 
number of lags than just a few, since thus the problem of autocorrelation is eliminated. 
We set in the test the null hypothesis that the coefficients of lag variable as a group are not 
different from zero. We test the assumption by applying the X
2
 (Chi Square) test and if the 
calculated value exceeds the critical value for the selected level of significance, then we can 
reject the fundamental assumption (null hypothesis) and conclude that the changes in the 
lagged variable (in our case: distance-to-default) precede (Granger cause) changes in the 
dependent variable (selected banking performance ratio). An overview of the test results 
is presented in Table 5. 
8 We have performed the Granger causality test also with a series dd calculated on the basis of bank share 
prices. Since the sample is not representative, we do not present the calculation.
the first difference time series and rejected the null hypothesis at low level of significance and 
confirmed stationarity of the series of differences save for the variable total assets 
(S_TA_SKM) where we have been able to determine the stationarity only at the level of 
second differences. 
 
The finding that all baseline time series in value levels are non-stationary has significant 
consequences when conducting the Granger casualty test. In such a case, it is not possible to 
use the Granger test directly, but the augmented Granger causality test should be performed 
(see for instance Toda & Yamamoto, 1995; Giles, 2011; Binh, 2010). Toda and Yamamoto 
have shown that the VAR model can be evaluated by applying a time series at the value levels 
and then tested for introduced restrictions in the model regardless of the different levels of 
integration or cointegration of time series (Toda & Yamamoto, 1995, p. 225). They have 
developed an alternative causality test where the VAR model has to be evaluated with the 
number of lags n + d, or m + d, where d presents the additional number of lags, which equals 
the highest level of integration of the used variables. When testing for linear restrictions, we 
do not take into account the coefficients of the additional d lags, since they are introduced in 
the model in order to ensure the validity of the standard asymptotic theory. Therefore, 
additional lags appear in the model specification as exogenous variable (Giles, 2011, p. 5). 
The expanded Granger causality test requires the assessment of the VAR model specified 
with the following equations: 
 
𝑦𝑦𝑦𝑦 𝑎𝑎𝑎𝑎 = 𝑣𝑣𝑣𝑣 1
+ ∑ 𝛽𝛽𝛽𝛽 𝑖𝑖𝑖𝑖 𝑥𝑥𝑥𝑥 𝑎𝑎𝑎𝑎 −1
𝑙𝑙𝑙𝑙 +𝒅𝒅𝒅𝒅
𝑖𝑖𝑖𝑖 𝑖 1
 + ∑ 𝛾𝛾𝛾𝛾 𝑗𝑗𝑗𝑗 𝑦𝑦𝑦𝑦 𝑎𝑎𝑎𝑎 −𝑗𝑗𝑗𝑗
𝑚𝑚𝑚𝑚 +𝒅𝒅𝒅𝒅
𝑗𝑗𝑗𝑗 𝑖1
+ 𝜀𝜀𝜀𝜀 𝑦𝑦𝑦𝑦 𝑎𝑎𝑎𝑎  (7) 
 
𝑥𝑥𝑥𝑥 𝑎𝑎𝑎𝑎 = 𝑣𝑣𝑣𝑣 2
+ ∑ 𝜃𝜃𝜃𝜃 𝑖𝑖𝑖𝑖 𝑥𝑥𝑥𝑥 𝑎𝑎𝑎𝑎 −1
𝑙𝑙𝑙𝑙 +𝒅𝒅𝒅𝒅
𝑖𝑖𝑖𝑖 𝑖 1
 + ∑ 𝛿𝛿𝛿𝛿 𝑗𝑗𝑗𝑗 𝑦𝑦𝑦𝑦 𝑎𝑎𝑎𝑎 −𝑗𝑗𝑗𝑗
𝑚𝑚𝑚𝑚 +𝒅𝒅𝒅𝒅
𝑗𝑗𝑗𝑗 𝑖1
+ 𝜀𝜀𝜀𝜀 𝑥𝑥𝑥𝑥 𝑎𝑎𝑎𝑎  (8) 
 
We have carried out the augmented Granger causality test between the distance-to-default 
indicator series and the selected banking performance ratios
7
. For each test we have chosen 
different monthly lagged variables, since the test is sensitive to the selected lag-length. It 
should be highlighted that the literature suggests using rather a higher number of lags than 
just a few, since thus the problem of autocorrelation is eliminated. We set in the test the null 
hypothesis that the coefficients of lag variable as a group are not different from zero. We test 
the assumption by applying the X
2
 (Chi Square) test and if the calculated value exceeds the 
critical value for the selected level of significance, then we can reject the fundamental 
assumption (null hypothesis) and conclude that the changes in the lagged variable (in our 
case: distance-to-default) precede (Granger cause) changes in the dependent variable (selected 
banking performance ratio). An overview of the test results is presented in Table 5.  
 
Table 5: The results of the Granger test–values X
2 
and corresponding probabilities (p) 
(dd, calculated by using adapted methodology, February 1997–June 2009, monthly 
series) 
 
  
Number of monthly lags 
 
Variable 
 
2 4 6 8 12 
C_DOB_SKM 
X
2
 
1,5150 2,0021 2,9495 3,1576 7,4933 
p 
0,4688 0,7354 0,8152 0,9241 0,8234 
C_PLL_SKM X
2
 
1,7982 3,2649 5,5101 5,6259 4,7317 
                                                           
7
 We have performed the Granger causality test also with a series dd calculated on the basis of bank share prices. 
Since the sample is not representative, we do not present the calculation. 

317 B. JAŠOVIČ  |  TESTING THE HYPOTHESIS OF THE ADEQUACY OF THE DISTANCE-TO-DEFAULT ...
Table 5: The results of the Granger test–values X
2 
and corresponding probabilities (p)
(dd, calculated by using adapted methodology, February 1997–June 2009, monthly series)
Number of monthly lags
Variable 2 4 6 8 12
C_DOB_SKM
X
2
1,5150 2,0021 2,9495 3,1576 7,4933
p
0,4688 0,7354 0,8152 0,9241 0,8234
C_PLL_SKM
X
2
1,7982 3,2649 5,5101 5,6259 4,7317
p 0,4069 0,5145 0,4802 0,6891 0,9663
K_DVP_SKM
X
2
1,3347 10,3139 10,9263 3,7109 10,6023
p 0,5131  0,0355** 0,0907* 0,8822 0,5633
K_KAP_SKM
X
2
4,7983 6,6886 14,8312 15,6122 20,6755
p 0,0908* 0,1533  0,0216**  0,0483**  0,0553*
P_KU_SKM
X
2
0,5162 4,1889 5,1531 7,5471 11,8765
p 0,7725 0,3810 0,5243 0,4789 0,4556
P_NPL_SKM
X
2
1,3958 3,0893 3,2725 4,6516 8,4581
p 0,4976 0,5430 0,7739 0,7941 0,7484
P_OSLAB_SKM
X
2
0,9807 2,3316 6,8204 7,7198 14,1308
p 0,6124 0,6750 0,3378 0,4613 0,2924
P_ROA_SKM
X
2
6,1574 5,2266 6,8483 7,1213 11,5871
p  0,0460** 0,2648 0,3351 0,5236 0,4794
S_TA_SKM
X
2
1,5763 2,2342 4,9274 5,1222 8,3780
p 0,4547 0,6928 0,5532 0,7444 0,7549
Legend:
*** designates the rejection of null hypothesis at the 1% level of significance;
** designates the rejection of null hypothesis at the 5% level of significance;
* designates the rejection of null hypothesis at the 10% level of significance.
Source: Author’s calculations.
The results in Table 5 show the value of X
2 
statistics and the corresponding probabilities, i.e. 
significance levels for the rejection of the null hypothesis on the non-existence of Granger 
causality. The results contradict the expectations that changes in the dd indicator precede 
changes in most indicators (ratios) of bank performance. The variables for which the 
null hypothesis may be rejected with a higher degree of probability (5% or 10% level of 
significance), are the share of debt securities and the share of capital in total assets. For these 
two variables we may assert that the indicator dd precedes their changes with the lead time 
of 4 months up to one year; the result for the share of debt securities in total assets should be 
interpreted with a caution given the fact that at a higher number of lags, it is not possible to 
prove the existence of Granger causality. A similar argument holds true also for the return 
on total assets ratio, where the null hypothesis is rejected only at the lowest number of lags.
 

318 ECONOMIC AND BUSINESS REVIEW  |  VOL. 19  |  No. 3  |  2017
Evidence for existence of Granger causality for the capital in total assets ratio (leverage 
ratio) does not come as a surprise. The market sentiment is also reflected in a number of 
market prices we have used for the calculation of the variability of bank assets. Some of the 
selected market parameters even have direct impact on movement in value of bank assets 
and, as a consequence, influence also the selected banking performance ratios. In this 
regard, we draw attention to the adjusted methodology we have used for the calculation 
of the indicator dd. The values of assets are entered in the calculation at their book value 
since the domestic equity market does not provide pricing information on bank shares 
for the calculation of the implied asset value. We have calculated the volatility that reflects 
market sentiment, i.e. prospective view of market participants on the developments in 
financial markets by using a large data set of market prices (indices) and use of variance-
covariance matrix and thus included the synthesised market data in the calculation of 
dd. With a certain time lag and in a limited scope, market changes are also reflected on 
the book value of bank assets that influence the modified dd value. In this process, the 
equity is a residual claim, which at a high financial leverage typical for credit institutions, 
becomes highly sensitive to the fluctuations in asset value, which are the consequences of 
the changed market situation. Consequently, the existence of Granger causality between 
dd and the leverage ratio does not come as a surprise, even though it was not possible 
to prove Granger causal relation between dd and total assets. Nevertheless, what does 
come as a surprise is the existence of causality also at shorter time lag, where the null 
hypothesis is rejected at a relatively low level of significance (10%). With longer time lags 
(6–12 months), the results are more reliable (at a 5% level of significance). 
Adrian and Shin (2010) warned of the changes in leverage where leverage is the inverse 
value of the share of capital in total assets. They claim that the net value of financial 
institutions (shareholders’ equity value), given high leverage, is particularly sensitive to 
changes in market pricing, i.e. asset valuation. Based on empirical evidence, they report 
that movement in leverage is procyclical, since it swells during boom cycles and plunges 
during busts (Adrian & Shin, 2010, p. 1). In an analogy with the capital in total assets 
(leverage ratio), it would mean that leverage ratio falls during booms and then starts to 
increase again during downturns. In the case that financial institutions would refrain from 
additional borrowing on the market during booms, they would have excess capital which 
the authors call »surplus capacity« in an analogy with non-financial companies (ibid, 
p. 29). Financial institutions (banks) borrow additional funds (and reduce the capital 
in total assets or leverage) and, consequently, »deploy« surplus capital. Should there be 
no additional borrowing, the leverage would drop, i.e. the equity in total assets (leverage 
ratio) would rise. In the conditions of an economic upswing, there are expectations 
regarding rising asset values and a fear that capital would end up idle; hence when looking 
for additional placements, credit standards decline and losses start to pile up. However, 
these losses will not surface until recession hits. The authors have concluded that such 
behaviour played a role in the development of sub-prime mortgage market in the United 
States where the financial crisis erupted (ibid, p. 30).
However, there are also other elements that drive changes in bank financial leverage. 
Baumann and Nier (2003) have explored the impact of market discipline, risk-related 

319 B. JAŠOVIČ  |  TESTING THE HYPOTHESIS OF THE ADEQUACY OF THE DISTANCE-TO-DEFAULT ...
elements and other impact on the share of capital in total assets (the leverage ratio we have 
used in our analysis). They found that the banks, which are subject to stronger market 
discipline, have on average higher shares of capital in total assets (Baumann & Nier, 2003, 
p. 137). That finding means that it is not possible to understand the mechanism of rising 
leverage in boom cycles in a mechanical sense, but we have to take into account other 
aspects as well. The authors represented market discipline in their model by means of 
different variables (government support, disclosure index, listing on a regulated securities 
market, deposit guarantee scheme, etc.).
The question that arises at this point is: why Granger causality between distance to default 
and capital adequacy ratio has not been demonstrated given the fact that in its substance 
it is similar to the leverage ratio. The key substantive reason is linked to the differences in 
the calculations of both indicators. The calculation of capital adequacy is based on risk-
weighted assets where bank’s assets are given a weighting that should reflect exposure 
to risk associated with a particular investment. The allocation of investments based on 
risk exposure can be, up to a point, also the result of judgement or national regulatory 
discretions. On the other hand, regulatory capital determined on the basis of special rules 
and regulations represents a broader concept than the book value of equity. With the 
new Basel standards, the regulatory framework for the calculation of risk-weighted assets 
and regulatory capital should have converged; nonetheless, there are still considerable 
differences in computations from one country to another and also among banks. In 
addition, the Basel standards give free hands to banks to choose different methodological 
approaches to the calculation of capital adequacy (standardised or advanced approach); 
hence there are differences in designating risk-weighted assets among banks that operate 
in the same country. These differences and, on top of that, the doubts as whether the given 
risk weights correctly reflect risk faced by banks, are the reason for making the concept for 
the capital adequacy calculation a popular target for criticism. And there are more reasons 
for concern: ever-increasingly complex rules for the calculation of risk-weighted assets 
and regulatory capital that are often changed. So it should not come as a surprise that 
criticism also comes from the ranks of regulators proposing more straightforward and 
clear regulation. They even produced empirical evidence that “...a straightforward metric 
of solvency, such as a leverage ratio, might do better at predicting failure than one, like a 
risk-weighted capital ratio, that banks could more easily game” (Haldane, 2012, p. 11).
5. CONCLUDING REMARKS
Based on the presented empirical testing by using the augmented Granger causality test, 
we may conclude the following:
- The adapted methodology for the calculation of the distance-to-default indicator dd 
is a proper tool to identify changes in exposure to risk of the entire banking system, 
since it uses as an input a large set of market data , which impact equally all banks; 
hence we talk about dd as a possible indicator of financial stability.
- The changes in the distance-to-default indicator whose value also depends on market 
sentiment and synthesised market data should, in accordance with our expectations, 

320 ECONOMIC AND BUSINESS REVIEW  |  VOL. 19  |  No. 3  |  2017
precede changes in those variables of the banking performance, which are most 
sensitive to the changed market conditions.
- In the case of our study, we can only confirm the existence of Granger causality from 
dd to the capital in total assets or leverage ratio.
- Furthermore, as reported in some other empirical studies, the capital in total assets 
ratio is a significant objective of market discipline and it better mirrors risk of bank 
insolvency than, for instance, capital adequacy ratio (see Haldane, 2012; Adrian & 
Shin, 2010 or Nier & Baumann, 2003).
- The existence of Granger causality was also confirmed for the debt securities in total 
assets ratio; nevertheless, caution is advised for the interpretation of the result due to 
specific conditions related to the functioning of foreign exchange market in Slovenia 
before euro adoption.
- In the case where bank performance variables are calculated on the basis of specific 
regulations and methodologies or are the result of management discretion, the 
existence of Granger causality between the indicator dd and the selected variable was 
not proved.
- The ultimate objective of further research would be to determine more precise 
(functional) links between dd and performance variables where Granger causality was 
identified, or compare the values of dd with particular critical values of performance 
variables given the fact that they are used to identify risk to financial stability.
Empirical research done so far still falls short of coming up with a methodologically 
finished analytical tool for a financial stability analysis, but merely corroborates the need 
for further research effort with the aim to work out an indicator that could be deployed for 
the identification of risk when the financial stability of the banking system is analysed. The 
described methodology adjustment would be more appropriate for a sectoral, systematic 
analysis of financial stability in the circumstances when no longer-term series of market 
prices of bank shares are available. The official supervision of financial institutions shall 
be complemented by market discipline or surveillance (see Flannery, 1998; Tarullo, 
2008). Market surveillance means that informative content of market messages (prices) 
will influence decision-making processes in banks and companies and, at the same time, 
these messages must be grasped also by bank supervisors in the analyses of banks’ risk 
exposures.
REFERENCES
Adrian, T., & Shin, H. S. (2008). Liquidity and Leverage. Staff Report no. 328. New York: 
Federal Reserve Bank of New Y ork.
Asteriou, D. & Hall, G. S. (2007). Applied Econometrics. A Modern Approach using EViews 
and Microfit. Revised Edition. New Y ork: Palgrave Macmillan.
Baumann, U. & Nier, E. (2003). Market discipline and financial stability: some empirical 
evidence. Financial Stability Review, June 2003, 134–141. London: Bank of England.

321 B. JAŠOVIČ  |  TESTING THE HYPOTHESIS OF THE ADEQUACY OF THE DISTANCE-TO-DEFAULT ...
Berger, A., Davies, S. & Flannery, M. (2000). Comparing Market and Supervisory 
Assessments of Bank Performance: Who Knows What When? Journal of Money, Credit, 
and Banking, vol. 32 (3), 641–667.
Binh, P. T. (2010). Toda–Yamamoto Version of Granger Causality. (Augmented Granger 
Causality).Time Series Analysis. http://www.slideshare.net/QuangHoang1/7-toda-
yamamotogranger-causality (accessed October 20, 2013).
Black, F. & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal 
of Political Economy, 81(3), 637–654.
Bukatarević, V ., Jašovič, B., Košak, T. & Šuler, T. (2008). The Use of Market Information 
in the Analysis of the Financial Stability of Banks. Financial Stabilty Review–Expert 
Papers on Financial Stability, May 2008, 1–12. https://www.bsi.si/iskalniki/reports.
asp?MapaId=1698 (accessed April 17, 2010).
Chan-Lau, J. & Sy, A. (2006) Distance-to-Default in Banking: A Bridge Too Far? IMF 
Working Paper, WP/06/215. Washington, D.C.: Intenational Monetary Fund.
Chan-Lau, J., Jobert, A. & Kong, J. (2004). An Option-Based Approach to Bank 
Vulnerabilities in Emerging Markets. IMF Working Paper, WP/04/33. Washington, D.C.: 
Intenational Monetary Fund.
Crosbie, P. & Bohn, J. (2003). Modeling Deafult Risk. White Papers, 18. december 
2003. Moody's KMV Research. http://www.moodysanalytics.com/~/media/Insight/
Quantitative-Research/Default-and-Recovery/03-18-12-Modeling-Default-Risk.ashx 
(accessed October 8, 2008).
Curry, T., Elmer, P. & Fissel, G. (2003). Using Market Information to Help Identify 
Distressed Institutions. A Regulatory Perspective. FDIC Banking Review, Vol. 15(3), 
Washington, D.C.: Federal Deposit Insurance Corporation.
De Larosiere, J., Balcerowicz, L., Issing, O., Masera, R., Mc Carthy, C., Nyberg, L., Perez, 
J. & Ruding, O. (2009). Report of the High Level Group on Financial Supervision in the EU. 
Brussels: European Commission.
European Central Bank. (2005). Financial Stability Review, June 2005. Frankfurt: European 
Central Bank.
Flannery, M. (2001). The Faces of »Market Discipline«. Journal of Financial Services 
Research, 20(2/3), 107–119.
Flannery, M. (1998). Using Market Information in Prudential Bank Supervision: A Review 
of the U.S. Empirical Evidence. Journal of Money, Credit and Banking, 30(3), 273–305.

322 ECONOMIC AND BUSINESS REVIEW  |  VOL. 19  |  No. 3  |  2017
Gapen, T. M., Dale, F . G., Lim, C. H., & Xiao, Y . (2004). The Contingent Claims Approach 
to Corporate Vulnerability Analysis: Estimating Default Risk and Economy-Wide Risk 
Transfer. IMF Working Paper, WP/04/121. Washington, D.C.: Intenational Monetary 
Fund.
Giles, D. (2011). Testing for Granger Causality. Econometrics Beat: Dave Gile's Blog. http://
davegiles.blogspot.ca/2011/04/testing-for-granger-causality.html (accessed November 14, 
2013).
Gray, D. & Walsh, P . J. (2008). Factor Model for Stress-testing with a Contingent Claims 
Model of the Chilean Banking System. IMF Working Paper, WP/08/89. Washington, D.C.: 
Intenational Monetary Fund.
Gropp, R., Vesala, J. & Vulpes, G. (2004). Market Indicators, Bank Fragility, and Indirect 
Market Discipline. FRBNY Economic Policy Review, September 2004, 53–62. New York: 
Federal Reserve Bank of New Y ork.
Gropp, R., Vesala, J. & Vulpes, G. (2002). Equity and Bond Market Signals as Leading 
Indicators of Bank Fragility. Working Paper Series No. 150. Frankfurt: European Central 
Bank.
Gujarati, N. D. (1995). Basic Econometrics. Third Edition. New Y ork: McGraw Hill.
Gunther, J., Levonian, M. & Moore, R. (2001). Can the Stock Market T ell Bank Supervisors 
Anything They Don't Already Know? Economic and Financial Review, Second Quarter 
2001, 2- 9. Dallas: Federal Reserve Bank of Dallas.
Haldane, A. G. (2012). The dog and the frisbee. In Jacksone Hole Economic Policy 
Symposium. The Changing Policy Landscape (pp. 109–159). Kansas City: Federal Reserve 
Bank of Kansas City.
Hull, J. (2005). Options, Futures, and Other Derivatives. Sixth Edition. New Jersey: Prentice 
Hall.
Krainer, J. & Lopez, J. (2003a). How Might Financial Market Information Be Used for 
Supervisory Purposes? FRBSF Economic Review, 29–45. San Francisco: Federal Reserve 
Bank of San Francisco.
Krainer, J. & Lopez, J. (2002). Incorporating Equity Market Information into Supervisory 
Monitoring Models. Federal Reserve Bank of San Francisco. http://www.frbsf.org/
publications/economics/papers/2001/wp01-14bk.pdf (accessed June 10, 2008).
Merton, C. R. (1974). On the Pricing of Corporate Debt: The Risk Structure of Interest 
Rates. The Journal of Finance, 29(4), 449–470.

323 B. JAŠOVIČ  |  TESTING THE HYPOTHESIS OF THE ADEQUACY OF THE DISTANCE-TO-DEFAULT ...
Persson, M. & Blavarg, M. (2003). The use of market indicators in financial stability 
analysis. Economic review, 2/2003. Stockholm: Sveriges Riksbank.
Tarullo, D. (2008). Banking on Basel. The Future of International Financial Regulation. 
Washington D. C.: Peterson Institute for International Economics.
Todda, Y. H., & Yamamoto, T. (1995). Statistical inference in vector autoregressions with 
possibly integrated processes. Journal of Econometrics, 66(1/2), 225–250.
Vassalou, M. & Xing, Y. (2004). Default Risk and Equity Returns. The Journal of Finance, 
59(2), 831–868.
Willem van den End, J. & Tabbae, M. (2005). Measuring financial stability: applying the 
MfRisk model to the Netherlands. DNB Working Paper, No. 30/March 2005. Amsterdam: 
Dutch National Bank.