Risk Management puzzles, solved step by step
- Puzzles
- 100
- Traced to a firm
- 17
- Topics
- 13
- Hard
- 30
008What is the angle between the hour hand and the minute hand of a clock at 3:15?Bank market riskRisk GCC
Try it first
Answer inside five seconds.
Show the worked solution
7.5 degrees. The minute hand at 15 minutes points straight at the 3, 90 degrees from 12. The hour hand moves 30 degrees an hour, so half a degree a minute; at 3:15 it sits at 90 plus 7.5, which is 97.5 degrees. The gap is 7.5 degrees, not zero.
Why is zero the wrong answer?
Picture a train that leaves at 3 o'clock and a car that starts after it. If you only check where the train was at 3 o'clock, you will think the car has caught up when it reaches that station. The hour hand never waits at a number; it moves half a degree every minute, so at a quarter past it has already moved a quarter of the way to the next number. Most people see the static clock face of a child's drawing, where the hour hand points exactly at the 3.
At 3:15 the minute hand points at the 3, 90 degrees from 12, while the hour hand has moved a quarter of the way towards the 4, to 97.5 degrees, leaving a 7.5 degree gap between them. The relationshipH the hour, here 3 M the minutes past the hour, here 15 30H + 0.5M the hour hand's angle from 12 6M the minute hand's angle from 12 What it says in wordsWork out each hand's angle from 12, then take the difference.Why would a risk interviewer ask a clock question?
Because it tests one habit that matters on a risk desk. The question is designed so that the static picture gives a confident wrong answer, and the interviewer is watching whether you check what moves. A risk number is full of the same trap: a position that looks hedged at the close can drift out of balance intraday, a limit measured at month end can be breached in between. Getting 7.5 is fine; saying why the answer is not zero is what earns the point.
Have the general formula ready, because the follow-up usually asks for another time. At 9:45, the minute hand is at 270 degrees and the hour hand at 270 plus 22.5, a gap of 22.5 degrees. The hands overlap eleven times in twelve hours, roughly every 65.45 minutes, and working that out is the usual second question.
Where candidates lose it
The trap is answering zero, fast. The question is short, the picture feels obvious, and the hour hand's drift is exactly the detail the static picture hides.
If you catch yourself, say so: both hands look as if they point at the 3, but the hour hand has moved a quarter of the way on. Correcting out loud is almost as good as getting it right first time.
What the interviewer asks next
- What is the angle at 9:45?
- How many times a day do the hands overlap, and when is the first overlap after 12:00?
- At what time between 3 and 4 are the hands exactly opposite each other?
033A price rises 20% and then falls 20%. Separately, a bank's gross NPA ratio moves from 2% to 3%. What is the net price change, and how would you describe the NPA move, both in percentage points and in percent?Risk GCCAsset manager risk
Try it first
The gross NPA ratio went from 2% to 3%. Which description is wrong?
Show the worked solution
The price ends 4% lower, and the NPA ratio rose by 1 percentage point, which is a 50% increase. 100 up 20% is 120, and 20% off 120 is 24, leaving 96. The ratio moved from 2% to 3%: the gap is 1 percentage point, and 1 over the starting 2 is 50%. Saying it rose 1% would be wrong on both counts.
Why does up 20% then down 20% lose money?
A shopkeeper marks a shirt up 20% from Rs 100 to Rs 120, then runs a 20% off sale. The discount is taken on Rs 120, so it is Rs 24, and the shirt sells for Rs 96. Each percentage is measured on whatever base exists at the time, and the fall happens on a bigger base than the rise. The two moves multiply rather than add: 1.2 x 0.8 is 0.96. In general, up x then down x leaves you down x squared, here 0.2 x 0.2, or 4%.
A price that rises 20% from 100 to 120 and then falls 20% ends at 96, a 4% loss; a gross NPA ratio that moves from 2% to 3% has risen by 1 percentage point, which is a 50% increase on its starting level. What is the difference between a percentage point and a percent?
When the quantity is itself a percentage, there are two honest ways to describe a change. Percentage points measure the gap between two rates by subtraction; percent measures that gap relative to where you started. From 2% to 3% is +1 point by subtraction and +50% relative to 2. A gross NPA ratioNon-performing assets, loans on which the borrower has stopped paying for a set period, as a share of total loans before provisions. is a rate, so a risk report must say which one it means, and the two carry different messages: one point sounds mild; half as many bad loans again sounds serious.
In a risk committee, both descriptions are used and both can mislead. A desk that wants to play down deterioration quotes points; one that wants attention quotes percent. The disciplined habit is to quote the level and the change in points together, 3% from 2%, and let the reader see the relative move for themselves.
Where candidates lose it
On the price, the trap is answering zero because plus 20 and minus 20 seem to cancel. They cancel only when percentages are added, and returns multiply.
On the ratio, the trap is saying it rose by 1%. That phrase means 2.02%, a rounding-level change, and a risk manager who uses it in a committee has understated a 50% jump in bad loans.
What the interviewer asks next
- A price falls 20% and then rises 20%. Where does it end?
- A 10% default rate rises to 12%. Describe the change both ways.
- Why do regulators and banks prefer basis points when quoting changes in rates?
058A bank's loan book grows from Rs 4,000 crore to Rs 5,000 crore in a year, while its bad loans grow from Rs 120 crore to Rs 140 crore. Did asset quality improve?Bank credit riskRisk GCC
Try it first
The bad loan ratio fell from 3.0% to 2.8%. What is the best reading?
Show the worked solution
Probably not: the ratio improved only because the book grew. The bad loan ratio fell from 3.0% to 2.8%, but the bad loans themselves rose 16.7%, from Rs 120 crore to Rs 140 crore. The Rs 1,000 crore of new lending is too young to have defaulted. Set against last year's book, bad loans are 3.5% of the loans that could have gone bad.
How can a ratio fall while the problem grows?
A school with 40 failing students out of 1,000 has a 4% failure rate. Admit 500 new students in April, before any exams, and the rate drops to 2.7% without a single student improving. Any ratio can fall because its denominator grew, and a fast-growing loan book dilutes its bad loan ratio with loans that have not yet had time to fail. Here bad loans rose Rs 20 crore while the book rose Rs 1,000 crore.
Bad loans rose from Rs 120 crore to Rs 140 crore, up 16.7%, yet the bad loan ratio fell from 3.0% to 2.8% because the book grew 25%. Against last year's Rs 4,000 crore book, the same Rs 140 crore is 3.5%, which is worse. What would you check before calling it either way?
Loans take time to go bad, a process lenders call seasoningThe time a loan needs before its true default rate shows, because few borrowers default in the first months after taking a loan.. The fair test compares bad loans with the book that was old enough to produce them, which is why risk teams track lagged ratios and default rates by the year a loan was written. A lagged ratio of 3.5% against 3.0% says the old book is getting worse, not better.
The relationship140 this year's bad loans, Rs crore 5,000 and 4,000 this year's and last year's loan book, Rs crore What it says in wordsMeasured against the loans old enough to default, the bad loan ratio rose.The limitation: the lagged ratio assumes the new loans added nothing to the Rs 140 crore. Some of the extra Rs 20 crore could come from new loans that failed fast, which would itself be a warning about how they were underwritten. Either way, the headline ratio is the weakest of the three readings.
Where candidates lose it
The trap is reading the headline ratio and saying yes, asset quality improved. Interviewers use this exact set-up because a fast-growing lender often reports a falling bad loan ratio just before its problems surface.
The other miss is saying no without a number. Give the rupee growth in bad loans, 16.7%, and the lagged ratio, 3.5%, so the answer rests on arithmetic rather than suspicion.
What the interviewer asks next
- What growth in the book would have kept the ratio flat at 3.0%?
- How would you build a vintage table to settle the question?
- Why does fast loan growth often come before a rise in bad loans?