Delopment and testing of a credit scoring model

Seminario
MATLAB per il Computational Finance
Milano, March 22nd 2011

Implementazione e test di un
modello di credit scoring
Mattia Ciprian, PhD
CEO @ modeFinance

• modeFinance is one Italian company active in financial consulting and creditworthiness
research; thanks to its own rating methodology, MORE, modeFinance provides credit rating
reports on international markets with companies’ business details, creditworthiness
evaluations, credit limit values, financial strengths & weaknesses analysis.

Mission

• Every day millions of people around the world are wondering what is the real creditworthiness
of the companies with which they are in business. Every day, these questions remain
unanswered. modeFinance every day aims to answer these questions in a simple, complete
and immediate way.

Products

• modeFinance is specialized in the analysis and evaluation of credit risk assessed to every
company operating in the world and it supplies different products for helping the customer in
the financial monitoring of their portfolios (dealers, suppliers, clients, partners, vendors,
competitors, etc)

modeFinance and Mathworks

• modeFinance has been accepted into The MathWorks Connections Program with its product,
MORE (Multi Objective Rating Evaluation).
www.modefinance.com
3/22/2011 2
info@modefinance.com

CREDIT REPORT STATISTICAL ANALYSIS MARKET SEARCH INTERNAL CREDIT RISK
The companies who would Public institutions The companies who PLATFORM
like to monitor: search the best suppliers, The companies and the
customers, suppliers and customers, partnerships. banks who want to use
competitors Research organizations internal data for the credit
risk assessment
Banks
Banks, financial consulting Associations
companies

Insurance companies

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3/22/2011 3

Delopment and testing of a credit
scoring model
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• The term credit scoring refers to quantitative methods for evaluating the credit
quality of companies. Credit scoring is a quantitative exercise that is refreshingly
productive. A good scoring system can save lenders money and time, and can be a
first-order competitive advantage.
(Source: Falkenstein)

• The credit score is the first step for a rating assessment.

Good credit score = good rating

Bad credit score = bad rating

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1. Z-Score Model: the pioneer predictive tool
1. Dataset selection
2. Ratio definition
3. Credit scoring model selection
4. Discriminant analysis (in sample – out of sample)
2. Credit scoring models
3. Model development:
1. Choosing inputs;
2. Transforming inputs;
3. Combining transformed inputs;
4. PD evaluation
4. Validating techniques
5. Conclusions

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• •

•

•

• •

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2. Ratio definition
1. Choosing inputs;
4. PD evaluation
5. Conclusions

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2. Ratio definition
1. Choosing inputs;
4. PD evaluation
5. Conclusions

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Database
Validation with
techniques financial
figures

PD Ratio
evaluation definition

Ratio
selection

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•
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Z = zscore(A);
Dist = pdist(Z,'seuclidean');
Dist2Matrix = squareform(Dist);
Link = linkage(Dist,'ward');
Cluster = cluster(Link,'maxclust',15);
C = cophenet(Link,Dist);
Err = inconsistent(Link);
figure
[H,T,perm]=dendrogram(Link,'colorthreshold','default');
set(H,'LineWidth',2)

–

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It is possible to define thousands of ratios; in order to avoid redundancy, a first
simplification can be done by eliminating highly correlated variables.

50

45
c=corrcoef(database);
figure; pcolor (c); figure(gcf) 40

35

30

By their nature, most ratios are 25

correlated each other. The objective 20

should not be selecting completely 15

uncorrelated factors 10

5

5 10 15 20 25 30 35 40 45 50

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• The selection of the best set of ratios is the first step in the
development of a credit scoring model. The set should change
according to the sector in which the companies are active.
The selection include both statistical approaches and
analytical reviews.
• Statistical selection tools suggested:
– Distribution Analysis;
– F-test and t-Student;
– Default Frequencies;
– CAP plots;
– Etc.
• We’ll apply these tools in the following slides to 2 ratios:
– CAP = (Shareholders Founds)/(Total Assets);
– STK = (Stocks)/(Total Assets);

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Simple Statistical Analysis

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• Default Frequency
– The x-axis shows the percentile in which a particular ratio value lies and the y-
axis shows the default frequency that is observed for firms with ratios in that
percentile (Moody’s def).
– The relation between a financial statement ratio and default is generally
monotonic and “non-linear”

CAP STK

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• CAP Plot (Gini Index)
– The primary performance measure used by academics was measuring the percentage of
misclassifications. This was calculated based on the percentage of defaulting firms that
were accepted, and the percentage of non-defaulting firms that were rejected (Type I
and Type II errors). Essentially, power curves extend this analysis by plotting the
cumulative percentage of defaults excluded at each possible cut-off point for a given
model (Source: Moody’s)

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CAP STK

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2. Ratio definition
1. Choosing inputs;
4. PD evaluation
5. Conclusions

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• Transformation of this sort are essential because financial ratios are highly
skewed and fat-tailed, which causes a few observations to overly influence
the output if not transformed. Transformation methods include:
– Replacing the ratio with its percentile;
– Turning the ratio into a standard Gaussian variable;
– Applying a variety of sigmoidal functions;
– Using a nonparametric univariate default estimate generated by each variable
Source: Eric Falkenstein studies

z = (x-mean(x))./std(x);
s = 1 ./ (1 + exp(-z));
plot(x,s,'o')

CAP STK

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2. Ratio definition
1. Choosing inputs;
4. PD evaluation
5. Conclusions

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• If you follow the previous suggestions (reliable data and info, default info,
representative DB, ratio selection, ratio transformation, etc.), doesn’t matter which
kind of scoring technique you select.
• You can choose among:
– Discriminant analysis
– Logit and Probit
– Kernel density estimators (e.g. SVM)
– Neural Networks
– Genetic Algorithms
– Etc.

Maximum Likelihood – Logit function
In the training sample T, L is probability
(likelihood) of the observed situation (if the
π(i) is the probability of observations are independent)
observation i being in set B
or in set G

The problem is that the range of π(i) is [0,1] whereas the
predictors can take any real value. Therefore the right-
hand side is transformed using a monotonous function.

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2. Ratio definition
1. Choosing inputs;
4. PD evaluation
5. Conclusions

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EBITDA interest coverage ratio

ROE Return on equity

ROS Return on sales

Total Shareholders Founds / Total Assets

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2. Ratio definition
1. Choosing inputs;
4. PD evaluation
5. Conclusions

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3/22/2011 27

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2. Ratio definition
1. Choosing inputs;
4. PD evaluation
5. Conclusions

www.modefinance.com
3/22/2011 29

Delopment and testing of a credit scoring model

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