The documentation describes the use of various machine learning techniques used in estimation of credit risk. The analysis is done using SAS.

1. Estimating the probability
of default: Credit Risk
Mohamed Arsalan Qadri
Sarvesh Saurabh
Mohit Ravi

2. Summary
• Credit risk – The probability of default
• Data Cleansing
• Logistic Regression
• Linear Discriminant Analysis
• Comparison of the LR and LDA
• Factor Analysis

3. Credit Risk
What is it?
• The risk of default on a debt that may arise from a borrower failing to make
required payments.
Impact on the lender?
• Lost principal and interest, disruption to cash flows, and increased collection
costs.
How to estimate it?
• Credit risk arises from the potential that a borrower or counterparty will fail to perform
on an obligation

4. Sources of risk?
• For most banks, loans are the largest and most obvious source of credit risk.
• There are other sources of credit risk both on and off the balance sheet including
letters of credit unfunded loan commitments, and lines of credit.
• Other products, activities, and services that expose a bank to credit risk are credit
derivatives, foreign exchange, and cash management services.
Credit Risk

5. Credit Scoring vs Risk
Estimation of risk?
• The risk posed by the borrower is inversely proportional to the credit score.
• A statistically derived numeric expression of a person's creditworthiness that is used by
lenders to access the likelihood that a person will repay his or her debts.
• A credit score is based on, among other things, a person's past credit history (300-850)

6. Credit Scoring
• Consumers can typically keep their credit scores high by maintaining a long history of
always paying their bills on time and not having too much debt.
• A FICO score is the most widely used credit scoring system.
• A credit score is primarily based on a credit report information typically sourced from
credit bureaus.

7. Data Cleaning

8. Data Cleaning
• Serious Delinquency in two years. (Make a Pi chart for this)

9. • Revolving Utilization Of Unsecured Lines
Data Cleaning

10. • Age
Data Cleaning

11. • Number Of Time 30-59 Days Past Due Not Worse
Data Cleaning

12. • Number Of Time 60-89 Days Past Due Not Worse
Data Cleaning

13. • Number Of Times 90 Days Late
Data Cleaning

14. • Monthly Income
• Replaced with Mean
Data Cleaning

15. Data Cleaning
• Monthly Income
• Ran Multiple Linear Regression
on Missing Values

16. Data Cleaning
• Monthly Income
• The Histogram after running
Multiple Linear Regression
on Missing Values

17. Data Cleaning
• Debt Ratio
• We found that the Debt Ratio was extremely high in many cases.
• Upon Closer inspection, we found out that high debt ratio was present for those records
whose Monthly Income was unknown.
• From this we inferred that the Debt Ratio could most probably be the Debt.

18. Data Cleaning
• Debt Ratio
• We replaced the high values of debt ratio by dividing it by the predicted values of the
monthly income.
• The new mean after replacement was 0.67

19. Data Cleaning
• Number of Dependents

20. Data Modelling
• Split the dataset into Training data (70%) and Test Data (30%).
• Computed Co-relation Matrix among Independent variables.
• The variables had very less Co-relation amongst themselves.
• Ran Logistic Regression by using Stepwise selection.
• Ran Linear Discriminant Analysis.
• Compared both the models by measuring their accuracy of prediction.
• Ran both models on significant Factors using Factor Analysis.

21. Logistic Regression

22. Logistic Regression
• Ran Logistic Regression separately for each variable.
• Computed the ROC curve for each variable and compared the AUC value.

23. Stepwise Selection
• Overall Model was Significant.
• All the variables were included in the
model.
• The model built on the Training data
was tested on the Test data.
• Probability of default > 0.7 was coded
as 1, and Probability of default <0.7
was coded as 0.

24. Logistic Regression on Test Data
Overall Accuracy = (41374+291)/(41374+291+175+2661)
= 93.6 %
True Positive Rate = TP / (TP+FN)
= 9.85%
True Negative Rate = TN / (TN+FP)
= 99.5%
Predicted Values Actual Values
Confusion Matrix

25. ROC curve for Test Data
• AUC Value = 0.8557

26. Discriminant Analysis

27. Discriminant Analysis
Overall accuracy =(38134+1717)/Total
=89.5 %
True Positive Rate = TP / (TP+FN)
= 58%
True Negative Rate = TN / (TN+FP)
= 91.7%
Predicted Predicted
0 1
Actual
0
Actual
1
38134 3415
1235 1717
Serious
Deliquen

28. Comparison of Models
Linear Discriminant Analysis
Overall accuracy =89.5 %
Predicted Predicted
0 1
Actual
0
Actual
1
38134 3415
1235 1717
Serious
Deliquen
Logistic Regression
Overall Accuracy = 93.6 %

29. Normality of variables

30. Factor Analysis

31. Factor Analysis
Factor Pattern
Factor1 Factor2 Factor3 Factor4
NumberOfTimes90DaysLate 0.54684 0.28062 0.26286 -0.0429
Factor 1 NumberOfTime60_89DaysPastDueNot 0.50016 0.3943 0.37949 -0.0015
RevolvingUtilizationOfUnsecured 0.60945 0.24942 -0.1861 -0.0285
NumberOfOpenCreditLinesAndLoans -0.5203 0.5275 0.1922 0.15051
NumberRealEstateLoansOrLines -0.4698 0.61529 -0.0292 0.09694
Factor 2 NumberOfDependents_num 0.03058 0.46357 -0.6034 -0.008
Monthlyincome_debt -0.4298 0.5044 -0.09 -0.1628
NumberOfTime30_59DaysPastDueNot 0.40861 0.49901 0.31943 0.05977
Factor 3 age -0.4301 -0.1476 0.65733 -0.0396
Factor 4 DebtRatio 0.05584 -0.0712 -0.0331 0.97112

32. Conclusion
• 80% time spent on Data cleaning
• Logistic Regression gives better results when data is not normal as compared to LDA
• Factors can be grouped for a logical understanding, with Debt Ratio and age explaining high
variance.

33. Thank you