Loan Workouts: Putting it All TogetherLoan WorkoutsSlide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Loan Work Out Tree DiagramLoan Workouts: Putting it All TogetherLoan WorkoutsSo far we’ve looked at:Probability of success and failure over the entire loan recordsP(S) = 0.464P(F) = 0.536Expected Value of WorkoutE(X) = (Full Loan) P(S) + (Default) P(F)Loan WorkoutsWe also looked at the conditional probabilities of success and failure based on Y, T, and CP(S|Y)P(F|Y)P(S|T)P(F|T)P(S|C)P(F|C)Loan WorkoutsWe also looked at the expected value of each of our borrowers characteristics:E(ZY)E(ZT)E(ZC)Unfortunately, none of these pieces of info helps for making a decision for our particular borrowerLoan WorkoutsWe would like to be able find out expected value and probabilities using all of our borrower’s characteristicsIn other words:P(S|Y&T&C) AND P(F|Y&T&C)E(Z)Loan WorkoutsUnfortunately our loan records do NOT contain enough information to computeP(S|Y&T&C) AND P(F|Y&T&C)Why?The loan records are incomplete across the three banks that were mergedCustomer #1 in the loan records has information with respect to education level onlyNo Info on Years of Business Experience or Economic TimesLoan WorkoutsBayes’ Theorem to rescueAllow us to find:If we know: CTYSP | SCTYP |Loan WorkoutsHow?But the numerator portion can be expressed as: CTYPCTYSPCTYSP| SPSCTYPCTYSP |Loan WorkoutsHow do we compute:One of the project assumptions is that Y, T, and C are all independent of each other event if we consider successes or failures SCTYP |Loan WorkoutsKnowing this we can say:We know need to find SCPSTPSYPSCTYP |||| SCPSTPSYP|||Loan WorkoutsLet’s look at one of these and figure out its probability. Computations will be similar for the other twoConsider:This is asking for the probability a borrower has the same # of years experience as your borrower given the workout was successful SYP |Loan WorkoutsBecause BR Bank was the only bank to keep records on borrowers years of experience, we only have their records to rely on:But since we can assume each bank made out loans to similar populations of borrowers, our estimation is a good one BRBRSYPSYP || Loan WorkoutsTo find BRBRBRS of#S with Yof #||BRBRBRBRBRSPSYPSYPSYPLoan WorkoutsSo if reproduce the same calculation for the other conditional probabilities we now know:From this we can also do similar calculations for: SCPSTPSYPSCTYP |||| FCPFTPFYPFCTYP |||| Loan Work Out Tree DiagramSF(Y T C)(Y T C)C(Y T C)(Y T C)CP(S)P(F)P(Y T C | S)P(Y T C | F)P(S Y T C) = P(S). P(Y T C | S) = P(S). P(Y|S). P(T|S). P(C|S)P(F Y T C) = P(F). P(Y T C | F) = P(F). P(Y|F). P(T|F).
View Full Document
Unlocking...