Journal of Applied Finance & Banking, vol. 9, no. 4, 2019, 167-178
ISSN: 1792-6580 (print version), 1792-6599 (online)
Scienpress Ltd, 2019
Study of endogenous and exogenous factors
impact’s on the default probability of listed
companies on the Casablanca Stock Exchange
Abdessamad TOUIMER1 and Lahsen OUBDI2
Abstract
This paper aims to study the impact of endogenous and exogenous factors on the
default probability through the structural approach (Internal Ratings-Based IRB).
The study is conducted using data from listed companies on the Stock Exchange
of Casablanca (BVMC); it covers the period from the beginning to the end of 2017.
In this paper, we propose a numerical method, based on Monte Carlo simulation,
to estimate the default probabilities using the Black & Scholes (1973) model. Our
focus was on determining the most influential factors among the internal or
external ones that impact the default probability of the listed non-financial
companies on BVMC.
JEL classification numbers: D81
Keywords: Default probability, credit risk, IRB approach, Monte Carlo
simulation.
1 Introduction
Computing the default probability (DP) is a cornerstone in credit risk analysis and
management. In fact, DP is an important entry in many approaches of credit risk
management; at the portfolio level, in pricing and credit risk hedging. The default
of a company is usually associated with its bankruptcy.
1
2
National School of Applied Sciences, Morocco, e-mail: Adessamad.touimer@edu.uiz.ac.ma
National School of Applied Sciences, Morocco, e-mail: l.oubdi@uiz.ac.ma
Article Info: Received: January 29, 2019. Revised: February 23, 2019
Published online: May 10, 2019
168
Abdessamad TOUIMER and Lahsen OUBDI
Due to the fact that the DP is the major variable of the IRBF approach, this paper
is dedicated to computing the DP. In practice, predicting the failure of a company
can only be assessed when there is a probability even if it is small. In the event of
default, it will cause financial losses to the lender; so identifying DP is a critical
issue (Kollar b., 2014) [1]. People and businesses have predicted the DP for
decades (Allen & Saunders, 2002) [2]. It can be modeled in different ways and
using different models. These models evaluate probability by using market data
and can basically be divided into two groups based on assumptions they make.
Thus we can distinguish between structural and reduced models (Lehutová, 2011)
[3]. In the other hand, hybrid models have also been developed to try to combine
the assumptions of the two previously mentioned models (Cisko & Kliestik, 2013)
[4].
The roots of structural models go back to the work of Black and Scholes (1973)
[5] and Merton (1974) [6]. Geske (1977) [7] extended Merton's assumptions by
considering that several default options for coupons, sinking funds, subordinated
debt, security covenants or other payment obligations could be treated as
composite options (Majerčák & Majerčáková, 2013) [8].
The overall objective of our work is to evaluate and analyze the impact of internal
and external factors on credit risk of the listed companies on the BVMC. In order
to achieve our objectives, we have formulated two hypotheses:
Hypothesis 1: A same variation in the DP will result from the same
variation of the factors across listed companies on the BVMC.
Hypothesis 2: The standard deviation of assets is the major factor
influencing the probability of default for firms listed on the BVMC.
To verify these hypotheses we apply risk assessment methods to a sample of 12
listed companies over the period from January the 2nd to December the 31st of the
year 2017.
The remaining of this paper will be organized on two sections. The first will be
devoted to the theoretical approach of measuring credit risk. The second part will
focus on the evaluation of credit risk of listed companies on the BVMC.
2 Theoretical credit risk assessment models
Credit risk is one of the most important risks faced by credit institutions. Its
mastery rests on setting up clear identification, assessment and hedging
procedures. Credit risk can be handled using various methods among which we
find the structural approach (IRBF).
2.1 Basle requirements for credit risk
Study of endogenous and exogenous factors impact’s on the default probability…
169
The recent subprime crisis has once again shown that credit risk remains the major
risk for financial institutions. "At the heart of a global and complex crisis, credit
risk has been a powerful catalyst" (Zelenko & De Servigny, 2010) [9]. In this
perspective, the relative weight of credits is a primary criterion for judging the
health of the banking sector. Credit risk is one of the indicators of financial
stability on which the International Monetary Fund (IMF) and the World Bank
(WB) rely to assess the fragility of the financial sectors. Therefore, effective credit
risk management seems essential for the long-term survival of banking institutions
and for global financial stability.
In July 1988, the Basle Committee developed the international solvency ratio,
known as the COOKE ratio (Basle I) . It defines the capital requirements that
banks must meet according to the taken risks. This ratio relates regulatory capital
to weighted assets which must be at least 8%.
Due to the evolution of credit risks, the Cooke ratio scheme showed its limits. In
2004, the Basle Committee proposed a new set of recommendations that defines a
more effective measure of credit risk, through a system of internal ratings that is
specific to each institution (Internal Rating Based) as well as the new solvency
ratio, namely McDonough's ratio. This latter considers also the operational risk.
In 2010, After the Subprime crisis, the Basle Committee focused on strengthening
the regulation, control and risk management of banks through issuing the
recommendations under the name of Basle III. This latter sets-up harmonized
global liquidity standards by developing two minimum standards for liquidity
financing. The first is the liquidity coverage ratio (LCR) which promotes the
resilience of banks in the short-term through the provision of high quality liquid
assets in order to overcome a severe crisis that would last for one month. The
second ratio is the long-term net stable funding ratio (NSFR), with a 1-year
horizon, to provide a sustainable maturity structure.
2.2 Probability of default on the basis of share prices
Generally, the default probabilities are estimated from the issued data by rating
agencies which list the evolution of default rates according to a time horizon.
Unfortunately, the frequency of ratings’ review is low. For this reason, analysts
have turned to the stock price, since it is available on the financial market.
This ability to obtain information facilitates proportionally and indirectly the
calculation of values and the volatilities of assets, since the two variables
(volatility and value of assets) are not observable. To solve this complexity, we
used the model of (Black & Scholes, 1973) [5]. Let’s note:
: The value of the firm’s assets
: Variations in the firm’s assets
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Abdessamad TOUIMER and Lahsen OUBDI
: The average value of the firm’s assets
: The volatility of the firm’s assets
: The value of the firm’s shares
: The variations of the firm’s shares value
: Stock volatility
: A Wiener process
D: The value of the debt to be repaid at the date “T”
Let the value of the assets vary according to the following equation:
The market value of the shares and the market value of the assets are ultimately
linked by the Call formula (equation 2):
and
Where :
The “
.
” denotes the risk-free rate and N (.) is the standard normal
cumulative distribution function.
To compute
(2). The
on
and
and
(they are not directly observable) we use the equation
is known since the company is listed; this offers the first condition
. The lemma of Itô (1940) offers the second constraint imposed on
the two variables. We can establish that the volatilities of stocks and assets are
linked by equation (3):
The solution of the two nonlinear equations (2) and (3) makes it possible to
determine the value and the volatility of the assets.
Study of endogenous and exogenous factors impact’s on the default probability…
171
3 Data and Methodology
The nature of this study requires us to use quantitative research methods for data
collection and analysis. In fact, the management of credit risk, and in particular the
assessment of DP, is based on the measurement and, therefore, quantification.
Methods involve the forms of data collection, analysis, and interpretation that
researchers propose for their studies (Creswell, 2009) [10]. Calculation procedures
are particularly important in the context of DP.
The inputs of DP analysis are usually past performance, probabilistic beliefs of
specialists. The results of this analysis are only logical consequences and
reprocessing of these inputs. The data used in this study are in the form of
financial time series.
The target sample is composed of Moroccan non-financial companies
listed on BVMC's three compartments. Our final sample is made up of 12
non-financial Moroccan companies.
We used the annual financial statements of the five previous financial
years from 2013 to 2017, with a daily change in the stock price over the period
from the beginning to the end of 2017.
Within the structural models, initiated by Black-Scholes (1973) [5] and
Merton (1974) [6], the value of the debt is evaluated using the theory of options.
Thus, the company’s stock and its debt appear as derivatives on the total value of
its assets.
The structural approach to credit risk (also called the firm's model) is
generally used for the determination of DP. This probability depends on the
quality of the initial credit, the longevity of the debtor and, above all, its current
and future financial capacity.
The basic hypothesis of the Black-Scholes-Merton model is that the assets
of a firm X0 follow a stochastic process in continuous time (Geometric Brownian
Motion) and that the defect is realized if
crosses the fault barrier.
3.1 Modeling
The frequency of changes in the rating of financial assets has led financiers
to consider continuous stochastic processes to model share price variations. The
fluctuation of financial asset prices, both upwards and downwards; can be
modeled using a geometric Brownian motion or Weiner process. Equation (1)
admits as a solution:
As a result, the return on assets between “t” and
“t+dt” is:
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Abdessamad TOUIMER and Lahsen OUBDI
Moreover, since
and
difference
follows
deviation
and are standard Brownian motions, the
a
normal
distribution
with
a
standard
. This brings us to:
From equation (6), we can draw:
A first step before starting the study is to identify the statistical and stochastic
properties of the sample. These properties condition the models and estimation
methods.
3.2 Calculation method
To calculate the DP, Monte-Carlo method will be used. This method allows
generating default scenarios that are required for the calculation of DP. The
default occurs if
For “n” scenarios :
According to Oubdi & Touimer (2017) [11], the two parameters "dt" and "n" are
chosen so that their variations do not affect the calculated DP. From our tests we
can conclude that the pair (0.005, 10000) remains optimal.
3.3 Descriptive statistics of the sample
The choice of the concept of failure is not sufficient. We must add a temporal
horizon. A credit rating cannot be given without specifying a time horizon. We
know that every business can go bankrupt one day. The whole question for credit
evaluation is: when? This is why there is often an aspect of implicit anticipation in
the creation of a credit rating. This anticipation is linked to the choice of a time
horizon that makes it possible to determine a palette of reasonable scenarios for
the evolution of the variables of interest. It is not simple to make short-term
Study of endogenous and exogenous factors impact’s on the default probability…
173
expectations neither to make long-term ones. It is possible, however, to predict
short-term bankruptcy more accurately than long-term bankruptcy because credit
risk is increasing over time. Serious credit rating agencies issue both short-term
(12-month) credit notes and long-term credit ratings. Insofar as short-term
forecasting uses a narrower range of changes in interest variables, short-term
rating scales contain fewer steps than long-term ones. Thus, banks need to
estimate the probability of default of one year for each risk category. This is why,
in our case, we choose a time horizon from January the 2nd to December 31st.
Table 1 summarizes the descriptive statistics of the companies in our sample.
Table 1: Descriptive statistics
Value label
AFRIQUIA GAZ
C MINIERE
TOUISSIT
DLM
DOUJA PROM
ADDOHA
FENIE
BROSSETTE
MANAGEM
Mean (Stock return) %
-0,08
2,92
5,82
-8,16
-2,58
1,85
S.D (Stock return) %
1,95
2,01
1,56
1,84
3,37
2,20
1 649 994
720,00
13 079 281
598,33
Debt in MAD
20 582 524,41
224 420 000,00
50 664 502,31
44 600 000,00
10 066 594,08
Market Value in MAD
9 526 783 750,00
2 502 535 495,30
231 208 000,00
14 815 319 377,72
210 214 265,44
Shapiro-Wilk*
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
Anderson Darling*
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
Lilliefors*
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
Jarque-Bera*
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
Skewness (Pearson)
0,41
-0,93
0,46
0,899
0,421
0,601
Skewness (Fisher)
0,412
-0,936
0,463
0,904
0,423
0,604
Kurtosis (Pearson)
3,744
6,417
1,139
7,499
1,679
4,157
Kurtosis (Fisher)
3,845
6,572
1,186
7,677
1,737
4,266
ADF**
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
PP**
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
Value label
MED
PAPER
RES DAR
SAADA
SODEP
Marsa-Maroc
SOTHEMA
TAQA
MOROCCO
TOTAL
MAROC
Mean (Stock return) %
-4,70%
-5,68%
0,003%
-0,50%
0,00%
-2,03%
S.D (Stock return) %
3,95
1,97
1,53
1,60
1,43
2,04
Debt in MAD
839 199 000,00
6 355 416,53
22 379 636,97
398 692 810,36
57 142 857,16
Market Value in MAD
8 591 759,86
83
685
112,22
4 691 457 534,78
10 403 107 023,12
2 364 465 600,00
19 735 400 841,38
14 103 255 040,00
Shapiro-Wilk*
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
Anderson Darling*
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
Lilliefors*
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
Jarque-Bera*
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
Skewness (Pearson)
-1,442
-0,204
0,088
0,813
-0,282
-0,424
Skewness (Fisher)
-1,45
-0,205
0,089
0,818
-0,284
-0,426
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Abdessamad TOUIMER and Lahsen OUBDI
Kurtosis (Pearson)
16,471
4,43
8,227
7,848
1,752
4,155
Kurtosis (Fisher)
16,831
4,545
8,419
8,032
1,812
4,264
ADF**
< 0,0001
0,001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
PP**
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
< 0,0001
* H0: The financial series of price changes follows a Normal law. The tests performed are with a
level of significance alpha = 0.05. The results of the "p-value" are shown in the table.
** H0 : The series has a unit root.
It is worth noting that the number of data points is 250 and the average of the price
variations is almost zero. This is mainly due to the luck of transparency of the
companies. Indeed, many companies meet only minimum requirement in terms of
financial communication according to the Moroccan Authority of the capital
market (AMMC, May 2017). The second problem of attractiveness is the
classification of listed companies according to the activity sector rather than the
performance.
The Shapiro-Wilk, Anderson Darling, Lilliefors and Jarque-Bera tests reject the
null hypothesis of normality for all values (since the calculated "p-value" is below
the level of significance alpha = 0, 05). The non-normality of financial series is a
well-known fact in finance, especially for financial assets (Goodhart & O'Hara,
1997) [12].
The analysis of the thick tails (Fat tails) confirms the non-normality and that the
distribution of the prices does not follow a Gaussian as predicts the EMH
(Efficient Market Hypothesis). Finally, the D'Agostino [13]and Jarque-Bera tests,
based on the asymmetry and kurtosis coefficients, accept the hypothesis of
non-normality. Given that the calculated p-value of the financial values is less
than the level of significance alpha = 0.05, therefore one must reject the null
hypothesis H0, and retain the alternative hypothesis H1 (The series is stationary).
4 Results and discussion
The table 2 reports the estimates of the two parameters
using equations 3
and 4 with a risk-free rate of 2.37%3 .
3
According to Bank Al Maghrib, the risk-free rate over the period of study is 2.37%.
Study of endogenous and exogenous factors impact’s on the default probability…
175
Table 2: Calculation of volatility and market value of assets listed on the BVMC
Name
AFRIQUIA GAZ
C MINIERE TOUISSIT
DELATTRE LEVIVIER MAROC
DOUJA PROM ADDOHA
FENIE BROSSETTE
MANAGEM
MED PAPER
RES DAR SAADA
SODEP-Marsa Maroc
SOTHEMA
TAQA MOROCCO
TOTAL MAROC
1,95%
1,85%
2,03%
1,83%
3,22%
1,96%
3,59%
1,68%
1,53%
1,58%
1,40%
2,03%
9 546 884 203,68
2 721 699 273,55
280 685 870,73
14 858 874 785,04
220 045 086,19
14 690 631 197,02
92 075 641,37
5 511 001 352,39
10 409 313 587,15
2 386 321 075,42
20 124 755 723,67
14 159 059 533,70
Now we will study the DP using Monte Carlo simulation method. This method
consists in using the strong law of large numbers to estimate the DP. Table 3
summarizes the results obtained on the 10,000 simulations with 200 steps in time
(See methodology section for more details).
Table 3: The probability of default of companies in the sample
Company
DP
AFRIQUIA GAZ
1,49%
C M TOUISSIT
34,64%
DLM
59,32%
DOUJJA ADOHA
1,37%
FENIE
74,93%
MANAGEM
46,53%
MED PAPER
88,02%
SAADA
44,03%
MARSA MAROC
0,00%
SOTHEMA
1,56%
TAQA
1,85%
TOTAL
4,45%
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Abdessamad TOUIMER and Lahsen OUBDI
At the first glance, it is impossible to infer the most important factor impacting the
DP. In order to measure the relationship between DP and structural factors, we
have to test for each factor.
The high probability of default of Med PAPER, the sole national paper
manufacturer is justified primarily by the dumping strategy that was practiced by
paper exporters from Portugal and Secondly by the waiver of a claim of 4.3
million MAD. From the historical data retrieved from annual financial statements
closed since 31 December 2013, we can see that the net worth of this company is
less than one quarter of the share capital. An EGM was held on June 20, 2014 and
decided that the company would not be wound up early. The company was
required at the latest by the end of December 2016 to reconstitute equity up to a
value equal to at least one quarter of the share capital. An EGM was held on
September 19, 2017 and gave power to the Board of Directors to regularize the
company's net position by raising capital by capitalizing reserves, share premiums,
merger premiums and amortization. The commitments made in the framework of
the memorandum of understanding signed between the company and the CDG
group on December 24, 2013, and the agreements with its banks, the effect of
which has been recorded by the company during the 2017 financial year with the
CDG Group and some of its banks.
For FENNIE, the high probability of default is explained by the decline in its
turnover due to the gradual abandonment of low-margin trades, the difficulties of
the sector.
Our study consists of identifying the variables that have the strongest influence on
the DP by supposing a variation of each of them. This will allow as computing
new DP for each change in variables. Table 4 summarizes the results.
Table 4: The variation of the probability of default according to each factor
Name
AFRIQUIA GAZ
C M TOUISSIT
DLM
DOUJJA ADOHA
FENIE
MANAGEM
MARSA MAROC
MED PAPER
SAADA
SOTHEMA
TAQA
TOTAL
MAD
4%
5,27%
-4%
4,42%
100%
4%
1,95%
-4%
2,05%
100%
4%
1,54%
-4%
1,33%
100%
4%
2,70%
-4%
4,93%
100%
20%
0,58%
-4%
0,60%
100%
4%
1,71%
-4%
1,80%
100%
4%
36,36%
-4%
81,82%
100%
20%
0,22%
-4%
0,30%
100%
4%
1,92%
-4%
2,19%
100%
4%
6,26%
-4%
6,41%
100%
4%
6,50%
-4%
5,22%
4%
5,13%
-4%
5,85%
-0,83%
0,80%
8,90%
-1,90%
0,80%
1,06%
-1,72%
0,80%
1,06%
-11,64%
0,80%
5,66%
-0,14%
0,80%
0,93%
-2,38%
0,80%
1,38%
0,00%
0,80%
90,91%
-0,37%
0,80%
0,42%
-3,06%
0,80%
1,13%
0,80%
4,86%
100%
-1,03%
-0,65%
0,80%
3,57%
100%
4,17%
0,80%
7,52%
Study of endogenous and exogenous factors impact’s on the default probability…
177
From table 4, we can see that the variation of factors starts having a significant
impact on DP at a threshold of 4% for the debt and the asset value for the
companies AFRIQUIA GAZ, CM TOUISSIT, DLM, DOHHA , MANAGEM,
MARSA MOROCCO, SAADA, SOTHEMA, TAQA and TOTAL . This threshold
is only of 0.80% fpr σE, while it jumps to 100% for μ. Thus, we can infer that the
standard deviation of assets is the major factor influencing the DP of listed firms
on the BVMC (i.e H1 is retained).
In order to have a significant variation in the probability of default for the two
companies FENNIE and MED PAPER, the total debt factor must increase by
20%. Thus, the impact of variations in factor on DP varies across companies in
our sample (i.e., H2 is rejected).
For the sample as a whole, when the risk of default is very high, the variation in
the probability of default according to the debt criterion is very small but with the
same direction of variation. On the other hand, the value of the asset and the
probability of default are negatively correlated with a weak correlation. This may
be due, in one hand, to the value of the asset and, in other hand, to the debt level.
Finally, its influence of firms’ asset mean on DP is negligible, while the volatility
is found to be a key and significant element that strongly influences the
probability of default.
5
Conclusion
The results of the research study were presented, analyzed and discussed. An
initial analysis of the data shows the non-normality of the data in our sample. In
fact, the unconditional density of financial series generally has thicker tails than
the normal one since extreme values are relatively common.
The study of the DP shows that the credit universe offers an estimate of the risk in
order to make a reasonable study of credit applicants' ratings.
For the study of the DP, according to the IRB model, the results show the trend
that non-financial companies with low volatility have a lower default rate than
companies with higher volatility.
On the other hand, the study of the weight of each factor indicates the tendency for
debt and asset value to be less influencing than the volatility of the asset and that
both parameters (debt and market value) have almost the same impact weight on
DP. The assignment of the average asset factor to the probability of default is
almost zero.
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