Case 024Retail and portfolio creditWarm up

A bank has 2 lakh credit cards with Rs 1 lakh limits, each 40% used on average. Compute exposure at default and expected loss for the portfolio, allowing for borrowers drawing more before they default.

The situation

Pallavik Bank has 2 lakh credit cards outstanding, each with a Rs 1 lakh limit. Average utilisation is 40%, so the typical card carries a Rs 40,000 balance.

The bank's data shows that cardholders who default draw, on average, 60% of their unused limit in the months before default. The annual probability of default is 5% and loss given default is 85%. These parameters are the bank's own illustrative estimates.

Your task

What is the exposure at default per card and for the portfolio, and what is the expected annual loss?

Quick check

What is the exposure at default on a typical card?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

Exposure at default is Rs 76,000 a card, Rs 1,520 crore for the portfolio, and expected loss is about Rs 64.6 crore a year. Today's Rs 40,000 balance plus 60% of the Rs 60,000 unused limit gives the exposure; times a 5% default rate and 85% loss gives the expected loss. Using today's balances alone would show Rs 34 crore, understating the loss by Rs 30.6 crore.

Step 1Why is today's balance the wrong exposure?

Think of a friend who is struggling financially and has an unused overdraft. Before things collapse, they use it: rent, school fees, groceries. Borrowers heading for default draw down their open limits, so a revolving line is measured at the balance expected on the day of default, not today's. The share of the unused limit they draw is the credit conversion factorThe share of an unused credit limit expected to be drawn by the time a borrower defaults, used to turn a limit into exposure., here 60%.

Step 2How do the numbers work?

Per card: Rs 40,000 drawn plus 60% of the Rs 60,000 unused, Rs 36,000, gives exposure at default of Rs 76,000. Across 2 lakh cards that is Rs 1,520 crore, against Rs 800 crore drawn today and Rs 2,000 crore of limits. Expected loss is exposure times the chance of default times the loss when it happens: Rs 1,520 crore times 5% times 85%, Rs 64.6 crore a year.

A card is measured at the balance on the day it defaultsRs 40,000Drawn today+ Rs 36,000Drawn before defaultRs 24,000Never drawnOne card, Rs 1 lakh limitExposure at default Rs 76,000 = 40,000 + 60% of 60,000Using today's balanceRs 800 cr x 5% x 85% = Rs 34.0 crUsing exposure at defaultRs 1,520 cr x 5% x 85% = Rs 64.6 cr
Each Pallavik card carries Rs 40,000 today, but borrowers draw about Rs 36,000 more before defaulting, so exposure at default is Rs 76,000 a card and expected loss is Rs 64.6 crore a year, not the Rs 34 crore today's balances imply.
The relationship
EL=PD×LGD×EAD=0.05×0.85×1,520=64.6EL = PD \times LGD \times EAD = 0.05 \times 0.85 \times 1{,}520 = 64.6
PDchance a card defaults within the year, 5%
LGDshare of the exposure lost after recoveries, 85%
EADexposure at default, Rs crore: drawn balance plus 60% of the unused limit
What it says in wordsExpected loss is the chance of default times the share lost times the amount outstanding when default happens.
MeasurePer card, RsPortfolio, Rs croreExpected loss, Rs crore
Limit100,0002,00085.0
Today's balance40,00080034.0
Exposure at default76,0001,52064.6
Measuring at today's balance understates Pallavik's expected loss by Rs 30.6 crore; measuring at the full limit would overstate it; the exposure at default sits between them at Rs 1,520 crore.
Step 3What would you check behind the 60%?

The 60% is the number doing the work, so test it. It varies by segment: cardholders already near their limit have little left to draw, while low-utilisation cardholders can draw a lot. It rises in a downturn, when more borrowers are stretched. And the bank can manage it: cutting limits on cards showing early signs of stress reduces the unused amount before it is drawn. The limitation: a single portfolio average hides these differences, so the estimate should be built by utilisation band.

Where candidates lose it

Candidates multiply PD and LGD by today's Rs 800 crore of balances and report Rs 34 crore. That ignores the drawdown before default, which is the defining behaviour of revolving credit.

The opposite miss is using the full Rs 2,000 crore of limits, which assumes every defaulter maxes out. The conversion factor exists to sit between the two.

What the interviewer asks next

  • Pallavik cuts limits by 20% on cards showing early stress. How does that change the expected loss?
  • Why might the conversion factor be higher for low-utilisation cards?
  • How would you estimate the conversion factor from the bank's own default data?

Company names and figures are illustrative.