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CREDIT RISK UNDER THE NEW BASEL CAPITAL ACCORD: A
METHODOLOGICAL PROPOSAL.
By: Cristina Ruza and
Fernando Pampilln.
1. INTRODUCTION
Perhaps no industry has been subject to high degree of configuration during the last
three decades like banking, and it focuses the attention of academics and supervisors since
it is continuously facing new challenges. In this context it has been suggested the necessityof an appropriate prudential regulation in order to foster the banking solvency, as a key
area of concern. After a period of intense preliminary work, on June 2004 the Basle
Committee published the text of the New Capital Accord or Basle II. In spite of several
changes that have been introduced in the text, we will primary be focused on the new
treatment of credit risk, because banks are now allowed to use their own internal rating
systems in classifying their customers according to their real risk profile.
On these grounds, we will further the analysisof the scope and possibilities of those
internal rating systems which are a relevant and contemporary issue.
2. METHODOLOGY OF STUDY: ARTIFICAL NEURAL NETWORKS.
The recent financial trends are playing a major role in reshaping the operations and
structure of the financial institutions, and in turn the nature of credit risk. Hence, the
development of new tools for systematically assessing credit risk has become a major
priority for many banking institutions1. In this study we will apply artificial neural
networks (NN) for assessing the credit risk of a saving banks customers, because it has
obtained very good results as compared to other linear classification techniques.
1Two decades ago lending institutions resisted to rely upon credit risk predictions using numerical formulas
because of a reluctance to replace the expertise of loan officers and the absence of credit management
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2.1. Concept and elements of neural networks.
A neural network is a computerised system that tries to emulate the way in which
the information is processed by the biological neurons of the brain. The basic element of a
networks architecture is the "artificial neuron" that is a simple calculating device, which
from an input vector of external information will provide a unique response. In Figure 1
there are shown the different elements of a generic artificial neuron:
1- Set of inputs .)(tjX
2- Set of synapses or connecting links connected to neuron i ( w ) indicates the
strength or weight at the input of a neuron, and controls the strength of the
incoming signal from a sending (presynaptic) neuron j and a receiving
(postsynaptic) neuron i.
ij
3- An adder gives the value of the postsynaptic signal depending on the weights
and inputs (the more usual one is the weighted sum of inputs and synaptic
weights).
4- An activation or transfer function provides the current activity level of neuron i
depending upon its previous activity level and its postsynaptic signal. This acts
as a squashing function since it limits the amplitude of the postsynaptic signal
to some limited value.5- The output function gives the actual response of neuron i depending on its
activity level.
schooled in quantitative techniques. Nowadays, the grim reality is rather different and most financialinstitutions recognise their applicability to the credit-granting process.
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Figure 1. Generic Model of an artificial neuron.
Source: Adapted from Rumelhart et al(1986).
Output yj
Output Function
Transfer Function
yi = f(ai)
ai = f(hi)
Adder
Synapses Wij
Inputs Xj
hi=f(xj;wij)
However, a NN is not only one artificial neuron but a system of layers of
interconnected neurons, each of which is connected with the previous and the following
ones (when exist). Therefore, the whole architecture of a NN is characterised by features
such as the number of layers, the number of nodes within each layer (depending on the
kind of inputs and the expected response), and the direction of information propagation2.
One of the main properties of a NN is its capability of learning from its
environment and storing associations in order to improve its performance. The learning
procedure is an iterative process consisting of modifying the connections strengths in a
manner that emulate rule-like behaviour. We should bear in mind that those adjustments
make the NN more knowledgeable after each iteration, to a point when the learning
process is interrupted according to some optimisation criterion.
In the next section we will analyse the type of NN that will be applied in this study:
the multilayer perception or back-propagation network.
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2.2.The back-propagation neural network
A back-propagation neural network is a feedforward multilayer model whose
principal feature is that it uses a back-propagation algorithm as a mechanism of error-
correction within a supervised scheme. Here, the input vector proceeds through the
network in the forward pass emerging at the output end as the "actual response". These
resulting values are compared to the values of the output facts so if they agree no action is
taken, and if they differ the error signal is calculated. In the backward pass, this error
signal propagates backward in the network in such a way that all connections are modified
following the error-correction rule, as to make the "actual response" move closer to the
"target or desired response" in subsequent iterations.
Figure 2 depicts the network architecture organised into one input layer of source
nodes, one or more hidden layers of computation nodes and, finally, one output or exit
layer of computation nodes as well. The introduction of a hidden layer gives degrees of
freedom to the net and it permits to capture more complex features of the environment to
model. Going further, the hidden layer introduces non-linearity to the system since the
transfer function more commonly used is sigmoid, continuous, differentiable and
exhibiting asymptotic properties.
2The analysis of different types of NN exceeds the aim and scope of this study. For more information see
Martn del bro y Sanz (1997).
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Figure 2. Multilayer perceptron and the Transfer funtion of the neuron.
Input layer
x
f(x)
Hidden layer Exit layer
The learning procedure consists of repeatedly presenting related input- output sets
so the back- propagation algorithm can incrementally adjust the connection weights for
each neuron. This is strictly an optimisation problem and the cost function is defined in
terms of the mean-square-error-criterion.
To adjust the connecting weights there are two types: 1) those weights connecting
the input layer to the hidden layer ( ), and 2) those weights connecting the hidden layer
to the output layer (
ijw
jk ). To minimise the sum of squared errors the method of "gradient
descent" will be used. This method tries to identify in the multidimensional error surface
(with the shape of mountains and valleys)3 the direction of steepest descent (i.e. where the
error reduces more abruptly) by making adjustments to connecting weights proportional to
the product of the error signal and the input signal (see Figure 3).
5
3When dealing with non linear transfer functions the error surface has a global minimum and perhaps some
local minima to which the algorithm would converge.
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Figure 3. Error surface.
Source: Own elaboration.
The back-propagation algorithm will start from an arbitrary point of the error
surface (the initially assigned synaptic weights) and moves down successively toward a
minimum point.
The error signal is the sum of squared errors over all neurons in the output layer
and is defined by:
)2Yk-Ydk
(K
1=k
2
1=ECM (1)
where Ykd represents the desired response at the output neuron k, and Yk represents its
actual response (or fact).
The formulae for adjusting the connections are obtained by firstly differentiating
with respect to weights connecting the output layer to the hidden layer ( ), andjk
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thereafter with respect to weights connecting the hidden layer to the input layer ( ). On
the first stage we get
ij
4:
)3(
)2(
jk
NskNsk
Y k)Y k-Ydk
(K
1=k
-=jk
ECM
jk
Y k)Y k-Ydk
(K
1=k
-=jk
ECM
Z jNsk
Y k)Y k-Ydk
(-=jk
ECM
(4)
Once the error variation has been calculated, the connecting weights will be
updated according to the "delta rule", and using a sigmoid function (with range from 0 to
+1) as the output function:
( )
Ze+1
e
)Y-Y(--(t)=1)+(t jN- 2
N-
k
d
kjkjk sk
sk
(5)
where is the learning-rate5.
On the second stage the "chain rule" will be applied for modifying the synaptic
weights connecting the input layer to the hidden layer as follows:
4 Following Haykin (1994:145) "the gradient represents a sensitivity factor determining the
direction of search in weight space for the synaptic weight ".
jkECM /
jk5 The introduction of a learning rate will impact the performance of the back-propagation algorithm and the
rate of convergence to a stable solution.
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)6(XiNoj
Zj
J
1=j
jkNsk
Yk)Yk-Ydk
(K
1=k
-=wij
ECM
wij
Noj
Noj
ZjJ
1=j
jkNsk
Yk)Yk-Y
dk
(K
1=kij
wij
Zj
J
1=jjk
Nsk
Yk)Yk-Ydk
(K
1=k
-=wij
ECM
wij
Zjjk
J
1=j
Nsk
Yk)Yk-Y
dk
(K
1=k
-=wij
ECM
wij
NskNsk
Yk)Yk-Yk(K
K=k
-=wij
ECM
wij
Yk)Yk-Y
dk(
K
1=k-=wij
ECM
wij
YkYk
ECM=
wij
ECM
-=w
ECM
d
Proceeding as previously, the adjustments to be made to wij are:
N
Y)Y-Y(XN
Z+(t)w=1)+(tw jksk
kk
dk
K
=1k
i
j
j
ijij (7)
Among the different procedures for interrupting the training process of the network
in this study we have applied the cross validation. It simply consists of separately
calculating both the "learning error" and the "generalisation error". As it can be appreciated
in Figure 4, we can reduce the learning error to almost zero by increasing the number ofiterations. Then, after any iteration we will apply the new connecting weights to the
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generalisation set of examples until the point of minimum generalisation error, when the
learning process is interrupted (see the Figure 4 below). Once this point is reached we may
let the network deal with the environment by itself, which means that the network will
thereafter operate in an unsupervised fashion.
Figure 4. Learning error and generalisation error.
Fuente: Elaboracin propia.
Source: Own elaboration.
Error
Generalisation error
Learning error
N iterationsMinimum
Lastly, it is necessary to make clear that the back-propagation algorithm does not
always reach the global minimum of the error surface, but a local minimum instead.
Consequently, in spite any improvement of the learning process (defining an adaptative
learning rate, introducing a momentum term6 and so forth) we cannot assure whether the
point is a local or global minimum7.
3. EMPIRICAL APPLICATION.
For carrying out an empirical application of credit risk assessment, a Spanish
Saving Bank has provided us with information about its credits to small and medium sized
enterprises covering the period from December 1995 up to December 2002. The size of the
6 The momentum term is introduced in order to increase the algorithm rate of learning and to avoid thedanger of instability. Accordingly, the algorithm will accelerate descent in steady downhill directions,
whereas having an stabilisation effect when correlative changes in weights present different signs.
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initial sample comprises information from 4.229 good customers and 537 delinquent
customers.
With the purpose of appraising the credit quality of these customers we have
followed the criteria of Hale (1983), Toms et al (2002) and Checkley (2003), among
others. The financial ratios selected as good predictors of credit risk are:
1. - Capital borrowing = Long-term liabilities / Equity
2. - Interest coverage= Profit before taxes / Financial expenses
3. - Return on equity = Net profit / Equity
4. - Profitability = Net profit / Total assets
5. - Liquidity = (Inventory + Receivables + Cash assets) / Long-term liabilities
6. - Loan repayment capacity = (Net profit + Charge-offs) / Short-term liabilities
7. - Fixed assets turnover = Sales / Fixed assets
8. - Working assets turnover= Sales / Working assets
9. - Analysis of net interest income = Net interest income / Sales
10. - Self-financing capacity = (Net profit + Charge-offs) / Total assets
11. - Total sales revenue = Sales revenue / Total assets
The information has been divided into different samples following a chronological
criterion. For the group of good customers we have used the number of years from the
financing date, whereas for delinquent customers the criterion is the number of years in
advance to the date of delinquency.
Afterwards, an exploratory analysis of the financial ratios has been carried out, and
we found evidence of a high dispersion of data as a consequence of the presence of outliers
into the sample. Due to that, financial ratios have been codified according to the following
ranges (Table 1).
7 Sometimes the learning algorithm gets trapped at a local minimum and is unable to reach the global
minimum itself. This problem is known as a premature saturation of neurons or "flat spot effect".
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TABLE 1. VARIABLES RANGES.
RATIO VERY GOOD GOOD BAD VERY BAD
Variables codes 1 2 3 4
Capital borrowing 0- 0,50 0,50-1,25 1,25-2,50 + 2,50
Interest coverage > 10 5 - 10 2 -5 < 2
Return on equity > 20% 8 20 % 2 - 8 % < 2%
Profitability > 5% 2 - 5 % 0,5 2 % < 0,5%
Liquidity 1,5 0,75 1,5 0,50 -0,75 < 0,50
Loan repaymentcapacity
> 20% 10 20% 5 - 10 % < 5%
Fixed assetsturnover
> 8 4 - 8 2 - 4 < 2
Working assetsturnover
> 4 2 - 4 1 - 2 < 1
Analysis of netinterest income
> 25% 10 25% 0 10% < 0%
Self-financingcapacity
> 12 % 5 12 % 2 5 % < 2%
Total salesrevenue
> 3 1,5 - 3 0,75 1,5
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Figure 5. Self -organised Kohonen maps.
Source: From Olmeda and Barba - Romero (1993: 91).
Synapses
Presynaptic
layer
Postsynaptic
layer
The computer package that has been used is SAS System (8 th version), particularly
the module "Enterprise MinerTM" (4.1th version). It has been specified 2x1 nodes as the
map dimension; the neighbourhood radio is set equal 1, both during the ordering phase and
the convergence phase; the neighbourhood function is gaussian; the grouping procedure is
the batch-self organising map; and 100 the number of iterations carried out.
From the classification results (Table 2), we can assign each customer to an initial
rating category, which will be considered as the "target or desired responses" of the
network. The nodes interpretation are as follows: node 1 of good customers initial
rating of 1; node 2 of good customers initial rating of 2; node 1 of delinquent customers
initial rating of 3, and node 2 of delinquent customers initial rating of 4.
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TABLE 2. KOHONEN MAP RESULTS (2X1, r=1).
Group N of
Cases
Dist
Group
CLUSTER SEEDS*
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11
Delin
quent
0
1
2
120
150
0.887 0.443
0.545
0.549
0.459
0.386
0.590
0.262
0.690
0.495
0.504
0.248
0.699
0.494
0.505
0.391
0.587
0.343
0.627
0.246
0.704
0.441
0.547
Delin
quent
-1
1
2
139
194
0.844 0.435
0.546
0.401
0.570
0.432
0.549
0.276
0.660
0.467
0.523
0.228
0.694
0.546
0.467
0.437
0.545
0.337
0.604
0.232
0.691
0.485
0.511
Delin
quent-2
1
2
195
220
0.884 0.455
0.540
0.407
0.581
0.368
0.617
0.264
0.709
0.517
0.485
0.275
0.699
0.504
0.496
0.405
0.583
0.375
0613
0.257
0.714
0.454
0.540
Delin
quent
-3
1
2
133
185
0.736 0.496
0.502
0.393
0.574
0.358
0.601
0.239
0.687
0.483
0.511
0.248
0.680
0.534
0.475
0.505
0.495
0.362
0.600
0.471
0.520
0.498
0.501
Delin
quent
-4
1
2
79
84
0.863 0.512
0.488
0.408
0.583
0.413
0.581
0.287
0.700
0.478
0.520
0.257
0.727
0.518
0.482
0.412
0.581
0.399
0.594
0.265
0.720
0.432
0.563
Delin
quent
-5
1
2
40
41
0.825 0.548
0.452
0.475
0.525
0.368
0.627
0.342
0.653
0.551
0.448
0.280
0.719
0.584
0.417
0.368
0.628
0.489
0.579
0.272
0.722
0.464
0.535
Delin
quent
-6
1
2
10
10
0.824 0.507
0.494
0.497
0.502
0.487
0.512
0.335
0.665
0.5
0.5
0.29
0.71
0.502
0.497
0.335
0.665
0.43
0.57
0.26
0.74
0.407
0.592
Good
1
1
2
2025
2182
0.919 0.454
0.542
0.367
0.633
0.354
0.634
0.260
0.721
0.479
0.519
0.279
0.703
0.486
0.512
0.410
0.582
0.386
0.610
0.269
0.713
0.433
0.561
Good
2
1
2
1905
2287
0.907 0.438
0.551
0.337
0.641
0.339
0.633
0.249
0.708
0.474
0.521
0.278
0.684
0.487
0.510
0.424
0562
0.387
0.594
0.269
0.692
0.441
0.548
Good
3
1
2
2122
1899
1.01 0.442
0.564
0.305
0.724
0.344
0.673
0.275
0.750
0.474
0.528
0.303
0.719
0.485
0.515
0.461
0.542
0.346
0.672
0.288
0.736
0.462
0.541
Good
4
1
2
1797
1987
0.911 0.433
0.559
0.321
0.665
0.342
0642
0.259
0.717
0.471
0.525
0.291
0.688
0.506
0.494
0.429
0.563
0.403
0.588
0.280
0.698
0.457
0.543
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TABLE 2. KOHONEN MAP RESULTS (2X1, r=1). Continuation.
God
5
1
2
1601
1704
0.899 0.430
0.565
0.328
0.667
0.349
0.641
0.266
0.719
0.473
0.524
0.296
0.691
0.506
0.493
0.427
0.568
0.414
0.580
0.288
0.698
0.450
0.546
Good
6
1
2
1313
1435
0.896 0.441
0.553
0.316
0.672
0.339
0.647
0.261
0.717
0.450
0.545
0.294
0.687
0.512
0.488
0.449
0.546
0.408
0.584
0.294
0.688
0.468
0.528
Good
7
1
2
986
1101
0.887 0.441
0.552
0.315
0.669
0.324
0.656
0.259
0.714
0.459
0.536
0.299
0.674
0.516
0.484
0.453
0.541
0.415
0.576
0.297
0.681
0.477
0.520
Good
8
1
2
259
255
0.888 0.434
0.566
0.333
0.676
0.336
0.665
0.274
0.728
0.466
0.533
0.309
0.693
0.526
0.473
0.443
0.558
0.415
0.586
0.314
0.688
0.469
0.530
Source: Own elaboration.
* The variables are the following: V1: capital borrowing, V2: interest coverage, V3: return on equity, V4:profitability, V5: liquidity, V6: loan repayment capacity, V7: fixed asset turnover, V8: working assets
turnover, V9: analysis of net interest income, V10: self- financing capacity, V11: total sales revenue.
With this information we start the learning process of the back-propagation
network, for which we use the software Trajan Neural Networks 4.0 version. The network
architecture will be designed with 11 nodes in the input layer, 6 nodes in the hidden layer
and 4 nodes in the output layer. The transfer functions are the followings:
- Input layer: identity linear function a with pre-processing(t)h=(t) ii8.
- Hidden layer: sigmoid functione+1
1=(t)a (t)h-i i
with a range from 0 to +1.
- Output layer: sigmoid functione+1
1=(t)a (t)h-i i
with a range from 0 to +1 and with
post-processing summing up to 1.
Customers assignment to the different sets of examples is random and the final
composition is: training set = 12.558 cases; generalisation set = 6.279 cases and the
verification set = 6.278 cases.
8
The pre-processing consists of changing the scale and origin of the inputs in order to avoid a potentialproblem of neuron saturation that sometimes appears when using logistic transfer functions. Variables values
was multiplied by a factor equal to 0,1111 (scale) and then added a shift equal to -0,1111.
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Learning was carried out fixing an adaptive learning rate of an initial value of 0,7 and
a final value of 0,01, and a momentum term set equal to 0,6 was also introduced. The error
measure is the mean-square-error. The maximum number of iterations to be performed was
limited to 5.000 and we have interrupted the learning process at iteration 3.561, which
corresponds to the minimum generalisation error.
Table 3 shows the estimated synaptic weights connecting the input layer and the hidden
layer (wij) as well as the thresholds for each of the presynaptic neurons. Table 4 shows the
estimated synaptic weights connecting the hidden layer and the output layer ( ) and the
thresholds values.
jk
Finally, Table 5 presents the classification results obtained by applying the back-
propagation network are presented. For the training set we have that the percentage of
cases correctly classified is about 96%. Distinguishing by types of customers, the better
performance corresponds to "very good customers" (96.95%), closely followed by "good
customers" (95.8%). In general, the financial profile of those customers can be clearly
distinguished from the delinquent customers group, which in itself is an important finding.
Regarding the delinquent customers, the back-propagation network properly classifies the
92.29% of "very bad customers" and the 86.21% of "bad customers".
Even though the performance of the net is not perfectly balanced between good and
delinquent customers, such result is reasonable because the sample contains more
customers belonging from the first group rather than the second one.
If we focus the attention on the generalisation set, results are quite similar to the
previous ones with the following percentages of customers correctly classified: "very
good", 97.2%; "good ", 96.3%; "bad", 83.8% and "very bad", 92.4%.
Also, the verification or holdout set is composed by cases that are only used once the
learning process has finished completely. The primary aim of this set is to externally
validate the estimated weights of the network for cases completely unknown. Due to the
fact that the percentage of customers well classified are the following: "very good", 97.1%;
"good", 95.4%; "bad", 84.4% and "very bad", 90.3%, there is enough empirical support for
the external validation of the network. This is especially important if we take into account
that banking institutions concerns are to implement a credit assessment technique with a
good capacity for ex ante prediction, with the objective of constructing an efficient credit
portfolio according to a solvency criterion (regulatory capital) and risk aversion behaviour
(economic capital).
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TABLE 3. MATRIX OF ESTIMATED THRESOHOLDS AND SYNAPTIC WEIGHTS CONNECTING THE
INPUT LAYER AND THE HIDDEN LAYER.
\Hidden layer
Input layer\Neuron 1 Neuron 2 Neuron 3 Neuron 4 Neuron 5 Neuron 6
Threshold -87,39711 51,591670 -62,85674 -95,83867 -49,36286 -82,98805
Capital
borrowing
-4,793041 19,56604 -93,18329 -13,17544 -71,4148 -45,03547
Interest
coverage
-15,66782 4,480033 -59,78461 -101,8611 -8,164654 16,98045
Return on
equity
-0,7059 46,93832 -45,6084 -61,79653 6,422741 15,70674
Profitability -2,461284 55,59102 -53,55524 -90,0604 6,529964 9,363676
Liquidity -4,578899 9,875433 -29,25736 -3,746445 -13,38025 -19,67534
Loan repaym.capacity
-9,094162 52,29752 -42,85632 -74,79896 -66,47169 -45,37585
Fixed assets
turnover
-12,37476 -0,3004 7,001947 -8,315231 71,36565 15,49148
Wking assets
turnover
-17,39107 16,5868 -27,84732 -34,05244 41,20108 37,27043
Net interest
income
-38,54687 20,1122 -49,82619 -59,61193 7,768953 -64,00431
Self-financing
capacity
-24,49053 62,35182 -44,21426 -93,12161 67,64085 -61,60878
Total sales
revenue
6,737722 16,88155 -6,899281 -8,396957 -160,6237 -55,27595
Source: Own elaboration.
TABLE 4. MATRIX OF ESTIMATED THRESHOLDS AND SYNAPTIC
WEIGHTS CONNECTING THE HIDDEN LAYER AND THE OUTPUT
LAYER.
\Output layer
Hidden layer\Neuron 1
(Very good)
Neuron 2
(Good)
Neuron 3
(Bad)
Neuron 4
(Very bad)
Threshold -0,7622 15,14503 61,3072 -0,584034
Neuron 1 3,665215 3,739193 71,86225 -7,404866
Neuron 2 -9,151066 9,179011 -8,307265 3,171639
Neuron 3 5,235971 -5,265758 -2,605748 -0,219881
Neuron 4 4,183186 -4,218764 -5,989688 -1,066168
Neuron 5 -3,698388 3,556096 -3,190971 0,854727
Neuron 6 -2,448638 9,701068 -13,52736 -11,83772
Source: Own elaboration.
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TABLE 5. CLASSIFICATION RESULTS OF THEBACK-PROPAGATION NETWTRAINING SET GENERALISATION SET
Very
good
Good Bad Very bad Very
good
Good Bad Very bad
Total 5.807 5.914 370 467 2.942 2.953 173 211
Correct
cases
5.630 5.666 319 431 2.860 2.844 145 195 Targetresponse
Wrong
cases
177 248 51 36 82 109 28 16
Very good 5.630 224 0 0 2.860 101 0 0
Good 174 5.666 40 23 82 2.844 22 10
Bad 3 24 319 13 0 8 145 6 Actual
response
Very bad 0 0 11 431 0 0 6 195
% Correctly
classified96,95 95,80 86,21 92,29 97,21 96,30 83,81 92,41
Error % 3,05 4,20 13,79 7,71 2,79 3,70 16,19 7,59
Global % 95,93 96,26
Source: Own elaboration.
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Finally, we have carried out a sensitivity analysis aiming to determine which
variables contribute to improve the network classification performance to a higher
extent. The procedure consists of comparing the error incurred when omitting one
variable and the error incurred when all variables are jointly considered. For doing so
we will construct the following ratio:
Ratio RvariablestheallError with
Xleout variabError with j=
where:
if R 1; variable contribution is negligible jX
if R> 1; variable contributes to improve the overall performance.jX
Thus, an R ratio will be calculated for each of the 11 variables initially
considered in order to set out a ranking of variables from higher to lower contribution.
Table 6 presents the sensitivity analysis results. In regard of the training set, the first
five variables are: Self-financing capacity, Loan repayment capacity,Profitability, Net interest income and Return on equity. For the generalisation set
the results match the previous ones with the exception of Net interest income that
now occupies the sixth place after the Working assets turnover. However, the
interpretation of those results should be limited to establish a ranking of variables and
not for removing any of them from the analysis.
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TABLE 6. SENSIBILITY ANALYSIS.
TRAINING SET GENERALISATION SET
Errorwithout 1
variable
Ratio R Ranking Errorwithout 1
variable
Ratio R Ranking
Capital
borrowing
0,17208 1,284134 7 0,16293 1,277401 7
Interest coverage 0,16599 1,238737 9 0,162004 1,270069 8
Return on equity 0,17766 1,325828 5 0,17354 1,360578 4
Profitability 0,18192 1,357588 3 0,17955 1,407661 3
Liquidity 0,14584 1,088374 11 0,13609 1,066958 11
Loan repayment
capacity.
0,19034 1,420403 2 0.181009 1,419061 2
Fixed assets
turnover
0,16311 1,217261 10 0,15672 1,228695 10
Working assets
turnover
0,17677 1,319148 6 0,16626 1,303434 5
Analysis of net
income
0,17797 1,328122 4 0,16563 1,298545 6
Self-financing
capacity
0,19838 1,480466 1 0,18689 1,465207 1
Total sales
revenue
0,16865 1,258584 8 0,15918 1,247978 9
Source: Own elaboration.
4. DISCUSSION AND CONCLUSIONS.
The first conclusion that can be drawn from the empirical analysis carried out is
that the classification performance of the network is an improvement compared to
alternative linear techniques. Since artificial neural networks yields very satisfactory
results it should be recommended to apply this sort of technique, directly imported from
the Biology, onto this research field.
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In addition, the flexibility of NN is an important advantage taking into account the
dynamic nature of the credit risk. Then, it will be necessary to update the estimation of
weights on a frequent basis in order to assure that customers profile in terms of credit
risk, will be properly captured at different points in time. On these grounds, we can feel
confident about the possibilities of validating this model under the Basel II Capital
Accord dictates, in particular under the internal- rating based foundation approach.
Nevertheless, we cannot conclude this study without recognising the primary
shortcomings of this empirical analysis. In first place it should be noted that credit risk
is directly related to the financial situation of a firm, but also is influenced by the
external environment, which is not reflected in the accounting states. As a consequence,
it is absolutely necessary to widen the scope of analysis by including variables related to
the economic environment in a broader sense. Other aspects that deserve to be
mentioned are qualitative ratios such as customers concentration, diversification
degree, senior executives experience and age of the company, among others.
A final comment is that, despite the better results of the NN compared to
alternative linear techniques, these can also be improved by refining the sample of data
to be more balanced between good and delinquent customers. Indeed, the databases
currently available only store information about the bank customers considered to be
appropriate at the time of their credit application. Therefore, those customers whose
credit applications had been denied should be monitored in order to see whether they
comply with their financial obligations or they incurred in a delinquency with another
financial institution.
To do so, it will be required a joint effort from banking institutions to put
together their information and then benefit from a more precise classification of
customers according to their real risk profile. The extent to which the internal rating
systems of banks become more accurate, it will have a direct impact in terms of the
regulatory capital that banks have to hold to comply with the New Basel Capital
Accord.
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