Case 074Stress testing and scenariosHard

An NBFC has capital of Rs 1,500 crore on loans of Rs 9,000 crore, all at a 100% risk weight, and must hold at least 15%. Loss given default is 50%. Run a reverse stress test: what portfolio default rate takes it to the minimum, and how plausible is that?

The situation

Pradhik Finance lends to small businesses and truck operators. It has capital of Rs 1,500 crore against loans of Rs 9,000 crore, all risk-weighted at 100%, a capital ratio of 16.7%. Its minimum requirement, used here as an illustration, is 15%. About 30% of the book is commercial vehicle loans.

Instead of asking what a given recession would do, the board asks the reverse question: how bad would defaults have to be to take Pradhik to its minimum? Assume loss given default of 50%, losses written off against both capital and loans, and no profit earned in the stress year.

Your task

Find the portfolio default rate that takes Pradhik to 15%, show how sensitive it is to LGD, and judge how plausible that scenario is.

Quick check

Roughly what share of the loan book must default to take Pradhik to 15%?

Worked solution

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

30-second answerThe answer to give first

A portfolio default rate of about 3.9% takes Pradhik to its 15% minimum. It has only Rs 150 crore above the line, and each 1% of defaults costs Rs 45 crore at 50% LGD. That is plausible, not remote: a downturn in which its commercial vehicle loans, 30% of the book, default at 10% while the rest default at 1.3% gets there. At 60% LGD the breaking point falls to 3.3%.

Step 1Why run the stress test backwards?

A bridge engineer does not only ask whether the bridge holds a hundred lorries; she asks how many lorries would bring it down, and then whether that many could ever be on it at once. A reverse stress test finds the breaking point first and asks how plausible it is second, which exposes weaknesses that a pre-chosen scenario can miss. For Pradhik the question is: what default rate d brings the capital ratio to 15%?

The relationship
1,500−9,000×d×0.59,000−9,000×d×0.5=15%  ⇒  d=1503,825=3.92%\frac{1{,}500 - 9{,}000 \times d \times 0.5}{9{,}000 - 9{,}000 \times d \times 0.5} = 15\% \;\Rightarrow\; d = \frac{150}{3{,}825} = 3.92\%
1,500capital, Rs crore
9,000loans, Rs crore, all at a 100% risk weight
dthe share of the book that defaults
0.5loss given default
What it says in wordsLosses come off capital and off the loan book; solve for the default rate that leaves the ratio exactly at 15%.
Step 2How do you solve for the breaking point?

Losses of 4,500 x d come off capital, and the written-off amount also leaves the loan book, which lowers the RWA the minimum is measured against. Solving the ratio for 15% gives d of 3.92%, a loss of about Rs 176 crore. If you ignore the shrinking RWA, the break comes at 3.33%, a slightly harsher and quicker estimate; say which one you are using. The curve below shows how little room there is: the ratio starts only 1.7 points above the line.

Capital ratio against portfolio default rate, LGD 50%10%12%14%16%18%minimum 15%today 16.7%breaking point: 3.9% of loans default13.2% at 8%0%2%4%6%8%Share of the loan book that defaults
Pradhik's capital ratio falls from 16.7% to the 15% minimum when 3.9% of its loan book defaults at 50% LGD, and to about 13.2% at an 8% default rate.
Step 3How sensitive is the answer, and how plausible is it?

LGD matters as much as the default rate. At 40% LGD the breaking point is 4.9%; at 70% it is 2.8%. Commercial vehicle loans are secured, but in a freight downturn many trucks come to market at once and recoveries fall, so a 60% LGD is not extreme. Now build the story that reaches 3.9%. The commercial vehicle book is 30% of loans. If a freight slump pushes its default rate to 10% while the rest of the book defaults at 1.3%, the portfolio rate is 0.3 x 10% + 0.7 x 1.3% = 3.91%, right at the breaking point. One sector downturn, not a national crisis, takes Pradhik to its minimum.

Breaking-point default rate by loss given defaultLGD 40%4.90%LGD 50% (base)3.92%LGD 60%3.27%LGD 70%2.80%CV downturn scenario: 3.91%Worse recoveries lower the breaking point; the CV scenario reaches the base case line.
The default rate that takes Pradhik to 15% falls from 4.9% at 40% LGD to 2.8% at 70%, and a downturn confined to its commercial vehicle loans produces a 3.91% portfolio default rate, reaching the base case breaking point.
Step 4What should the board do with the answer?

Treat the breaking point as a limit input. A 3.9% breaking point with a plausible single-sector route to it means the buffer above the minimum is too thin for the concentration Pradhik carries. Options: hold more capital, cap the commercial vehicle share of the book, or buy protection through tighter collateral terms that lift recoveries. Then say the assumptions: no earnings in the year, which is harsh, since pre-provision profit of even 2% of loans, Rs 180 crore, would more than double the room, but earnings also fall in a downturn; all loans at a 100% risk weight; and a regulatory minimum the reader should confirm against the current RBI framework for NBFCs.

Where candidates lose it

Candidates often divide the buffer by the loan book and forget LGD, or forget that capital must stay above 15% of the remaining loans rather than drop to zero. Both give answers several times too large and make Pradhik look far safer than it is.

The second miss is stopping at the number. A reverse stress test is only useful once you say what scenario would produce the breaking point and whether that scenario could happen.

What the interviewer asks next

  • Pradhik earns pre-provision profit of 2% of loans in the stress year. What is the new breaking point?
  • How would a regulator use a reverse stress test differently from the board?
  • Which is more dangerous for Pradhik: LGD rising to 60% or the commercial vehicle share rising to 40%?

Company names and figures are illustrative.