Case 011Retail and portfolio creditCore
You are given a lender's personal loan data by score band. Compute default rates, check that the score ranks risk, and set an approval cut-off from what a good loan earns and a bad loan loses.
1The situation
Mitravel Finance, a consumer lender, gives you two years of performance data on its personal loans, grouped into five application score bands from lowest to highest score. Loans booked: 4,000, 6,000, 8,000, 6,000 and 2,000. Loans that defaulted within twelve months: 360, 330, 240, 90 and 20.
Finance estimates that a loan that performs earns Rs 4,000 over its life after funding and operating costs, and a loan that defaults loses Rs 60,000 after recoveries. Mitravel currently approves every band.
2Your task
What is the default rate in each band, does the score rank borrowers correctly, and where would you set the cut-off?
Quick check
At what default rate does a band stop making money for Mitravel?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
Default rates run 9.0%, 5.5%, 3.0%, 1.5% and 1.0% from the lowest band up, so the score ranks correctly, and only band 1 is above the 6.25% breakeven. Band 1 loses about Rs 70 lakh; cutting it lifts profit from Rs 374 lakh to Rs 445 lakh. Band 2 at 5.5% is profitable but thin, so approve it with tighter limits and watch it.
Step 1What do you check first in a scorecard data set?
Divide defaults by loans in each band. A score is doing its job if the default rate falls steadily as the score rises; a band that breaks the pattern means the score is not separating risk there. Here it holds: 9.0%, 5.5%, 3.0%, 1.5%, 1.0%. The portfolio average is 4.00%, a number that hides a nine-fold difference between the bottom and top bands. Averages are where bad loans hide.
Step 2Where does a band stop paying for itself?
Think of a shopkeeper who gives credit to regulars: each customer who pays adds a small margin, and each who vanishes wipes out fifteen good ones. The cut-off sits where expected loss on the bad loans overtakes expected income on the good ones, not at a round score. With Rs 4,000 earned per good loan and Rs 60,000 lost per bad one, breakeven is 4,000 over 64,000, which is 6.25%. Band 1 at 9.0% loses money; band 2 at 5.5% makes a little.
| Band | Loans | Defaults | Default rate | Profit, Rs lakh |
|---|---|---|---|---|
| Band 1 (lowest) | 4,000 | 360 | 9.0% | -70.4 |
| Band 2 | 6,000 | 330 | 5.5% | 28.8 |
| Band 3 | 8,000 | 240 | 3.0% | 166.4 |
| Band 4 | 6,000 | 90 | 1.5% | 182.4 |
| Band 5 (highest) | 2,000 | 20 | 1.0% | 67.2 |
| All bands | 26,000 | 1,040 | 4.0% | 374.4 |
Step 3How confident are you about band 2?
Band 2's 5.5% is close to the 6.25% line, so check the noise. On 6,000 loans the standard error of a 5.5% rate is about 0.29 points, so a rough 95% range is 4.9% to 6.1%, just below breakeven. Band 2 is profitable on this evidence, but a small rise in defaults or a fall in recoveries would tip it. Approve it with smaller loan sizes, which cut the Rs 60,000 loss, and track its monthly default curve.
Say the two limitations before you finish. The data only covers loans Mitravel approved, so it cannot say how applicants it rejected would have behaved, which matters if the cut-off moves down. And twelve months may be too short for a personal loan book; defaults that arrive in month eighteen would push every rate up. Ask for vintage curves by band before the cut-off is fixed.
Where candidates lose it
Candidates compute breakeven as 4,000 over 60,000, 6.67%, forgetting that a bad loan earns nothing. That moves the line and, in a closer data set, would approve a losing band.
The second miss is judging the book on its 4.0% average. The whole value of the data is in the bands: the average says the book is fine while one band quietly loses money.
What the interviewer asks next
- Recoveries fall so a bad loan loses Rs 80,000. Which bands survive?
- How would you use pricing rather than a cut-off to make band 1 work?
- What is reject inference, and why does it matter if you lower the cut-off?
Asked at Jane Street, Credit Risk, London, 2025 (Wall Street Oasis): The case study consisted of credit risk data that I had to analyse using Excel or Python
Company names and figures are illustrative.