Reference no: EM133210410

Assignment - Lauderdale Lakes Quantitative Methods Worksheet

This final assignment focuses on Chapter 9, especially trees, as well as the start of Chapter 11. You should look at the practice problems for Chapter 9 to get ideas on how to construct probability trees. In this assignment, the trees extend to three levels of branching, rather than just 2 levels.

Stonehurst Credit Union (SCU) is trying to identify clients who are likely to get into financial difficulty and default on their loans. Their goal is to intervene early, before the debt situation gets out of control, so that not only do they limit their exposure to losses, but they may be able to salvage their relationship with a member (credit unions are owned by their members).

One of the first indicators of a deteriorating debt situation is a missed loan payment. That is, a payment was due on a certain date, but no payment was received on that date or during the subsequent weeks.

Missed credit card loan payments occur 6% of the time.

SCU has examined the records of over 1,000 customers over the last 2 years to examine the amount owing on their credit cards. Among those that missed last month's payment, the balance owing was over $3,000 for 60% of them. But, among those who made their payment on time, only 15% owed more than $3,000.

Among those with a balance over $3,000 and who missed their last payment, 80% paid less than 20% of the balance owing, the previous month. Among those owing less than $3,000 and who missed their last payment, 40% paid less than 20% of the balance owing.

Among those with a balance over $3,000 and who made their last payment on time, 30% paid less than 20% of the balance owing in the previous month. Among those owing less that $3,000 and who made their last payment on time, only 10% paid less than 20% of the balance owing in the previous month.

Clearly, those who missed the last payment and those who paid on time are different in many respects with respect to their previous borrowing and payment behaviours. Maybe these can be used as early indicators of deteriorating credit worthiness and SCU can make interventions to assist clients before they get into more trouble.

SCU would like to identify customers who are high risk to default and send them information about how having a good credit score reduces the cost of borrowing and makes it easier to borrow when you need to. They would explain factors that go into the determination of a credit score and the importance of making loan payments on time. They would offer assistance to clients who were concerned that their credit score may decline and what could SCU do to help them.

1. Construct a tree diagram to describe the events in terms of the sequence of information provided above (missed payment, balance, previous payment amount). Note that this sequence is actually going backwards in time, but we will reverse that later. Label each branch as to the event it represents as well as the probability of travelling down that branch. If you are using labels, then you must define them (e.g., M = Missed payment). You may try to create the tree in Word, but you may find it easier to draw the tree by hand, take a picture and paste the picture into your assignment.

2. Calculate the final probabilities at the end of each branch and summarize them in a table like the one below:

	Missed Payment	On Time	Total
Balance > $3,000 Last Payment < 20%
Balance >$3,000 Last Payment >20%
Balance <$3,000 Last Payment < 20%
Balance < $3,000 Last Payment > 20%
Total

You may prefer to explore the tree and summarize the outcome by assuming that you are looking at 100,000 payment cases and find the frequency of occurrence of each outcome, but these should then be translated into the appropriate probabilities for the above table.

3. What is the probability that a customer has a balance over $3,000?

4. What is the probability that the customer's previous payment was for more than 20% of the balance owing?

5. Among those with a balance exceeding $3,000, what proportion made their last payment on time?

6. Among those with a balance exceeding $3,000 and whose previous payment was for less than 20% of the balance owing, what proportion made their last payment on time?

7. SCU has decided to classify customers who owe more than $3,000 and whose previous payment was for less than 20% of the balance owing as "High Risk to Default" and all others as in "Good Standing". Assuming this decision rule is applied to 100,000 cases, construct a confusion matrix that summarizes the decision and truth outcome frequencies. You should be able to do this by multiplying 100,000 times the appropriate probabilities from question 2.

Decision\Truth	Missed Payment	On Time	Total
High Risk to Default
Good Standing
Total			100,000

8. What is the "Accuracy Rate" of this decision rule in terms of classifying those as High Risk who then Miss Payment or those as in Good Standing who make their payment On Time? Explain Accuracy Rate in this situation in terms that SCU can understand.

9. What is the "Sensitivity Rate" of this decision rule? Explain what you mean by "Sensitivity Rate" in this situation.

10. What is the "Specificity Rate" of this decision rule? Explain what you mean by "Specificity Rate" in this situation.

11. What is the "False Omission Rate" of this decision rule? Explain what you mean by "False Omission Rate" in this situation.

12. What is the "False Detection Rate" of this decision rule? Explain what you mean by "False Detection Rate" in this situation.

13. You may feel that this classifier has not performed very well, because so many Missed Payment cases were not correctly detected and so many of those classified as High Risk actually paid on time. But what if you had no classifier at all? The naïve strategy would be to classify every transaction as On Time since 94% of cases are On Time. What would be the Sensitivity Rate of this decision rule? What would be the False Detection Rate?

14. What could CSU do to improve the performance of their classifier used in question 7? There are numerous ways you can answer this question.