University of Cardiff
MAT012 Credit Risk Scoring (2015/16)
Lab Session 3
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1. Measuring scorecard performance
a) The following data describe the scores and Good/Bad status for 25 applicants.
Using this information to draw the scorecard
i) Calculate the statistic
ii) The Kolmogorov-Smirnov curve
iii) The Receiver Operating Characteristics (ROC) Curve
iv) The Cumulative Accuracy Profile (CAP) Curve
2. Building a scorecard by logistic regression and testing it on a holdout sample
In this task, you are required to build the same logistic regression model in Q3 in Lab session 1. But this time, you will do more tasks.
a. Test how the model performs on a different dataset – a holdout (or testing) sample – to the one it was built. This is because the scorecard will always perform better on the set which was already built on others for some of the special features would have been captured by the existing scorecard.
We use the same dataset as before but we have now split it into two sets: 1) training set with 700 borrowers; and 2) holdout sample with 300 borrowers.
You need to maintain the proportion of ‘Bad’ (or ‘Good’) in both sample sets. [Hint: using proc surveyselect].
Now, please set up a model to predict a ‘Good’ customer.
b. Find out how to 1) plot the ROC curve for the holdout sample; and 2) generate the classification table in SAS.
c. Using the training set, try to: 1) calculate a score for each observation; 2) calculate a score for each attribute (you could export your dataset to Excel for the analysis).
Note: there are some insignificant variables included in this model. Since the focus of this task is to practise how to build a logistic regression model, we will include all variables in the model. In real practice (or your coursework project), you will only select variables that are statistically significant and intuitive.
3. Markov chain models for customer behaviour.
a. The state of a customer is described by whether his repayments are up-to date (0 months overdue), 1-month, 2-months or 3 or more months overdue. The changes in state from month to month in a sample of customers over the last four years is given as follows:
Current state
Next month state
Using your common sense as well as mathematical expertise calculate a transition matrix that describes the probability of the changes from month to month in the state of the customer.
If you have 1000 new customers starting this month what do you expect the distribution of their states to be in 4 months’ time?
b. In fact more careful, analysis suggest that there is a difference in the movements in the first six months of the ear compared with the last six months (Why might this be?). The numbers of the monthly transitions are as follows for the first six months of the last four years
Current state
Next month state
For the second six months in the year, the number of transitions is as follows:
Current state
Next month state
Find the transition matrices for the monthly transitions in the two types of periods. Hence if 1000 new clients join in May, describe the distribution of their states four months later ( N.B, the first two months are in the first six months of the year and the second two months in the last six months).
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