1. Presentations  For presentations: Bring 3 copies of slides, two to turn in (4 slides per page) and one copy in case of computer problems (1 slide per page)  Check website for general guidelines on presentations and papers  Check website for due dates on papers.  Bring to class for presentations: Copies of peer evaluation form, 6 forms, one for each presentation other than your own. These will be due each day following the presentations.

2. Scenario  You work at a bank and need to decide whether to foreclose on a loan for a borrower who is delinquent  Arcadia Bank has a set of records from 3 banks: 1.BR bank has records of # of years experience 2.Cajun Bank has records of educational level 3.DuPont bank has records on state of the economy  NOTE: Each bank has records only regarding ONE criteria and whether the loan was paid off or not

3. Data & Notation  The data set is a collection of successes and failures for loan workouts, divided into three categories, Y, T, C  Notation and variables: S=the set of all successful loan workouts F=the set of all failed workouts Y=the event that a borrower has y years experience T=the event that a borrower has educational level t C=the event that a borrower has economic condition c  NOTE: The information given on each of the borrowers satisfies one and only one of the events Y, T, or C.

4. Goal  The goal is to use all available information to compute the expected return on your borrowers loan workout  Let Z=the random variable giving the amount of money that Arcadia Bank will receive from a loan workout  Z can take on two values: 1.full value if loan is successful 2.default value if the loan is a failure

5. Expected Return  For your preliminary reports you calculated: E(Z)=full value*P(S)+default value*P(F)  This was just a simple calculation and did not take into account the specific data on your borrower  Now we can use all the tools we have learned in order to make a quantitative decision on whether to do a workout or foreclosure on your borrower  Why do we need to make a quantitative decision? Address this in your project.

6. Expected Value Using Y,T,C  E(Z)=full * P(S|Y∩T∩C) + default *P(F|Y∩T∩C) (By definition of conditional probability) (By definition of Bayes’ Theorem) Let’s look at P(S|Y ∩ T ∩ C)=

7. Expected Value Using Y,T,C, con’t  But we know that This is true because Y, T and C are independent events, which implies that are independent events Since they are independent, we can multiply their probabilities You need to explain why they are independent.

8. Expected Value Using Y,T,C, con’t  We can closely estimate the value of by using our database

9. E(Z YTC )  E(Z YTC )=full * P(S|Y∩T∩C) + default * P(F|Y∩T∩C)

10. E(Z YTC ), con’t So you must calculate this as part of your decision making process. When you talk about this calculation, do not beat the point to death!! In other words, do not tell me step by step what you did (i.e, multiply by this number and add it to this number, etc.)

11. E(Z YTC ), con’t  We just calculated part of our E(z YTC ) value  E(Z)=full * P(S|Y∩T∩C) + default * P(F|Y∩T∩C)  NOTE: P(S|Y∩T∩C) + P(F|Y∩T∩C)=1  Why?

12. E(Z Y’TC )  Just when you thought it was all over…  Now you go through the calculation again except this time, using Y’ and Y”  EX: if Y=4 years Y’=3-5 years ( a range of years) Y”=2-6 years

13. E(Z Y’TC )  Use the values of E(Z YTC ), E(Z Y’TC ), E(Z Y’TC ) to make your decision  NOTE that using Y’ or Y” does NOT require a totally new calculation. Only the probabilities dealing with the Y change, everything else stays the same

14. Things to consider  Why do we use Expected Value to make our decision?  Why are Y, T and C independent?  Where is independence used?  Why do you use Bayes’ Theorem?  Why can you use Bayes’ Theorem?

15. Further Analysis  The entire project has been laid out for you – you should now know exactly what to do so you can make a decision  I want you to do some further analysis on this project  Things to consider – What would happen if the economy changed? Education level?  Make your project be unique and stand out!