Case 086Retail and portfolio creditCore
A housing finance company's mortgage book rolls 3% from current to 30 days, 25% from 30 to 60 and 40% from 60 to 90 days each month. Build a roll-rate delinquency model and say which borrower factors you would add to make it predictive.
1The situation
Dhanvira Housing Finance has a Rs 10,000 crore mortgage book, all current today. Its collections data show that each month 3% of current balances miss a payment and roll to 30 days past due, 25% of the 30-day bucket roll on to 60 days, and 40% of the 60-day bucket roll on to 90 days, where a loan is classed as non-performing. Balances that do not roll forward are assumed to cure back to current, a simplification.
New lending keeps the current book at about Rs 10,000 crore. The chief risk officer wants a first model of how much reaches 90 days each month and over the next year, and a plan for making it predictive rather than descriptive.
2Your task
How much reaches 90 days each month and over a year, which roll rate matters most, and what would you add to the model?
Quick check
At these roll rates, how much of the book reaches 90 days each month?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
About Rs 30 crore reaches 90 days each month, Rs 360 crore a year once the pipeline is full, or about Rs 300 crore in the first year from a clean book. The flow is the book times three roll rates chained together. The first rate is the most sensitive: one extra point takes the flow to Rs 40 crore. To make it predictive, model each roll rate from borrower data such as EMI to income, loan to value, bureau score, employment type and rate resets.
Step 1What is a roll-rate model, in one picture?
Think of a school where some pupils fall behind each term: a few slip one grade behind, a quarter of those slip two behind, and some of those drop out. Follow the chain and you can forecast dropouts without knowing any pupil's name. A roll rateThe share of balances in one delinquency bucket this month that move to the next, worse bucket next month. model does the same for loans: each month a share of each bucket moves one bucket worse, and the rest cure. Multiply along the chain: Rs 10,000 crore times 3% times 25% times 40% is Rs 30 crore a month arriving at 90 days.
Step 2How much reaches 90 days over a year?
Once the pipeline is full, twelve months of Rs 30 crore is Rs 360 crore, 3.6% of the book. From a book that is all current today, nothing can reach 90 days before month 3, so the first year sees ten months of arrivals, about Rs 300 crore. Saying that out loud shows the interviewer you know the model has a lag built in, which is also why a sudden rise in 30-day balances is an early warning worth two months.
Step 3Which roll rate matters most?
Each rate multiplies the others, so a proportional change in any one moves the answer by the same proportion. But in percentage points they differ enormously: one point on the first rate is a third more flow, Rs 40 crore, while one point on the last rate is 2.5% more, Rs 30.75 crore. The first rate describes the whole book, and it is also where collections effort is cheapest, a phone call before a missed EMI turns into two.
Step 4What would you add to make it predictive?
A roll-rate table describes the past average. To forecast, model each transition for each loan from what drives a missed payment, and train it on loan-level monthly history. Fit a model of the chance each loan rolls next month on borrower and loan factors, test it on a later period it has not seen, and check that predicted and actual rates match by segment.
| Factor | Why it predicts a missed EMI |
|---|---|
| EMI to income | Less room in the monthly budget to absorb a shock |
| Current loan to value | Less equity, less reason to keep paying when prices fall |
| Bureau score and recent enquiries | Past behaviour and new borrowing elsewhere |
| Salaried or self-employed | Income that stops at once against income that dips |
| Floating rate resets | A rise in EMI without a rise in income |
| Months on book | Early missed payments often signal fraud or poor underwriting |
| Local unemployment and house prices | The macro link that lets the model run scenarios |
Where candidates lose it
The usual slip is to apply each roll rate to the whole book, getting Rs 300 crore, Rs 2,500 crore and Rs 4,000 crore, or to add the rates instead of multiplying them. Each rate applies only to the bucket in front of it.
The second is listing borrower factors without saying how the model would be trained and tested. The interviewer asked how you would set it up; out-of-time testing and a check by segment are the answer to that part.
What the interviewer asks next
- The 30-day bucket jumps from Rs 300 crore to Rs 450 crore this month. What do you forecast for 90 days, and when?
- How would you turn the 90-day flow into an expected credit loss number?
- Why might roll rates understate risk in a book growing 40% a year?
Asked at Neuberger Berman, Risk, Chicago, 2024 (Wall Street Oasis): how i would approach building a delinquency model. This involved showing knowledge of the factors that contribute to mortgage loans failing to make a payment
Company names and figures are illustrative.