Risk Management puzzles, solved step by step
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051A bank has CET1 capital of Rs 900 crore and risk-weighted assets of Rs 8,000 crore. It takes a Rs 200 crore loss. What happens to its CET1 ratio?Bank credit riskRisk GCC
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Before you divide anything: roughly where does the ratio land?
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The CET1 ratio falls from 11.25% to 8.75%, a drop of 2.5 percentage points. The Rs 200 crore loss comes straight out of CET1, taking it from Rs 900 crore to Rs 700 crore, while risk-weighted assets stay close to Rs 8,000 crore. A loss equal to 2.5% of risk-weighted assets wipes out 22% of the capital.
Why does a loss that looks small against the balance sheet hurt so much?
Think of a family with a Rs 80 lakh home loan and Rs 9 lakh in savings. A Rs 2 lakh medical bill is a rounding error against the loan and a painful bite out of the savings, because the savings are what pay for it. A bank works the same way. The CET1Common equity tier 1: the shareholders money and retained profits a bank can use to absorb losses while it keeps operating. ratio is capital over risk-weighted assetsThe bank assets, each scaled by a weight that reflects how risky it is, so a safe government bond counts for little and an unsecured loan counts in full.. Losses are paid from the numerator rupee for rupee, while the denominator moves only a little, so a ratio of 11% can lose a quarter of its height in one hit.
CET1 of Rs 900 crore over risk-weighted assets of Rs 8,000 crore is 11.25%. A Rs 200 crore loss takes CET1 to Rs 700 crore over the same Rs 8,000 crore, which is 8.75%, so the ratio loses 2.5 points. Is there a shortcut for the size of the drop?
Yes. With the denominator fixed, the ratio falls by the loss divided by risk-weighted assets: 200 over 8,000 is 2.5 points. Every Rs 80 crore of loss costs this bank one full point of CET1 ratio. That is the number a risk manager keeps in their head, because it turns a loss estimate from a stress test straight into a capital headline.
The relationshiploss the post-tax loss that reduces CET1, here Rs 200 crore RWA risk-weighted assets, held at Rs 8,000 crore What it says in wordsWith the denominator unchanged, the ratio drops by the loss as a share of risk-weighted assets.Say the limitation in one line. The written-off loans do leave the balance sheet, so risk-weighted assets fall a little too, and a tax credit on the loss can soften the hit. Both effects are small next to the Rs 200 crore coming out of capital. Where the result lands against the bank's minimum depends on the current regulatory figure and any buffers, which you would confirm rather than quote from memory.
Where candidates lose it
The common slip is to compare the loss with the balance sheet, call it 2.5%, and then shave 2.5% off the ratio to get about 11%. That confuses a fall of 2.5 percentage points with a fall of 2.5 per cent of the ratio, and it misses that the loss lands entirely on the capital line.
Say 11.25% to 8.75%, then add the shortcut: loss over risk-weighted assets gives the drop in points. It shows you can run a stress number in your head.
What the interviewer asks next
- How big a loss takes this bank to an 8% CET1 ratio?
- The written-off loans carried Rs 300 crore of risk-weighted assets. What is the ratio now?
- Why do regulators use a risk-weighted denominator rather than total assets?
052An asset has an arithmetic average return of 10% a year and a volatility of 30%. Roughly what is its compound annual growth rate?Asset manager risk
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Pick the closest before you calculate.
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About 5.5% a year. Compound growth is roughly the arithmetic mean minus half the variance. The variance is 0.30 squared, 0.09, and half of it is 4.5 points, so 10% becomes about 5.5%. A quick check: +40% then -20% averages 10% with a 30% spread, and Rs 100 ends at Rs 112, which is 5.8% a year.
Why is the average return not the growth rate?
A shopkeeper who marks a shirt up 40% and later cuts it 20% has not made 20% on the pair of moves. He has made 12%, because the cut is taken from the higher price. Returns work the same way. A loss is always taken from whatever the gain left you, so ups and downs of the same average size leave you with less than steady growth at that average. The more the returns swing, the bigger the shortfall.
Rs 100 rising 40% and then falling 20% ends at Rs 112, a compound 5.8% a year, even though the two returns average 10%. The rule of thumb puts compound growth at the 10% average less half the variance of 0.09, which is about 5.5%. Where does half the variance come from, and how good is it?
Take logs. The log of one plus a return is roughly the return minus half its square, so averaging the logs knocks off about half the variance. The drag grows with the square of volatility: at 15% volatility it is about 1.1 points, at 30% it is 4.5. The rule is an approximation that works best for small returns. The two-year example lands at 5.8%, and other return patterns with the same average and spread give slightly different answers.
The relationshipg the compound annual growth rate \mu the arithmetic average annual return, 10% \sigma the annual volatility, 30% What it says in wordsCompound growth is the average return less half the variance.For a risk manager this is why two funds with the same average return are not the same fund. The one with double the volatility has four times the drag, and its investors end up with less money even though the average looks identical.
Where candidates lose it
The trap is answering 10% because the question gave you 10%. The interviewer is checking whether you know that averages of returns overstate what an investor compounds, and that the gap is driven by volatility.
The second slip is subtracting the whole variance, or subtracting half the volatility, and landing at 1% or -5%. Square first, then halve: 0.09 over 2 is 4.5 points.
What the interviewer asks next
- What volatility would make the compound growth zero with a 10% average?
- If you lever this asset 2x, what happens to the average and to the compound growth?
- Which number should a fund report to investors, and why?
053A hedge instrument has a correlation of 0.8 with your position. If you put on the best possible hedge, what share of the position's variance does it remove, and how much of the volatility is left?Bank market riskQuant risk
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Your gut first: how much of the volatility does a 0.8 correlated hedge leave behind?
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The best hedge removes 64% of the variance and leaves 60% of the volatility. With the minimum variance hedge ratio, the share of variance removed is the correlation squared, 0.8 squared or 0.64. That leaves 36% of the variance, and because volatility is its square root, 60% of the original volatility is still there.
Why does a correlation of 0.8 leave so much behind?
Two friends walk home along roughly the same road. Most of the time they are close, but each takes a detour now and then, and the gap between them on those days is what a hedge cannot touch. A hedge only cancels the part of your position that moves with the instrument. The part it cancels is rho squared of the variance, and whatever is left, called basis riskThe risk that the hedge and the position do not move together, so the hedge gains or loses a different amount from the position., is all yours. At 0.8 that residual is 36% of variance.
A hedge with a 0.8 correlation removes 64 of every 100 units of variance and leaves 36. Because volatility is the square root of variance, the same hedge leaves 60 of every 100 units of volatility, so most of the swing you feel day to day survives. How do you get from variance left to volatility left?
Take the square root. Risk managers quote variance when they add risks and volatility when they talk about losses, and the square root between them is where candidates lose the answer. A hedge that removes 64% of variance sounds impressive; saying it leaves 60% of the volatility is the honest version, and it is the number that matters for a VaR limit, which scales with volatility.
The relationship\sigma_P the volatility of the unhedged position \rho the correlation between position and hedge, 0.8 What it says in wordsThe best hedge leaves the position's volatility times the square root of one minus the correlation squared.The limitation: the 0.8 was measured on past data. In a stress the correlation can fall, and the residual grows just when you need the hedge most. That is why desks watch the stability of a hedge correlation as closely as its level.
Where candidates lose it
The fast wrong answer is 20% of the risk left, one minus the correlation. It treats correlation as the share of risk removed, which it is not. Squaring the correlation gives the share of variance explained.
The second trap is stopping at 36% and forgetting that volatility is the square root. Give both numbers, 64% of variance removed and 60% of volatility left, and say which one a VaR limit sees.
What the interviewer asks next
- What correlation do you need to cut volatility in half?
- What hedge ratio achieves this if the position has twice the hedge instrument's volatility?
- Why might a proxy hedge's correlation drop in a crisis?
054A bank has four derivative trades with one counterparty, currently valued at plus 30, minus 20, plus 15 and minus 10 crore from the bank's side. What is the bank's exposure if the counterparty defaults, with and without an enforceable netting agreement?Counterparty riskBank credit risk
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Without netting, what does the bank stand to lose if the counterparty defaults today?
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Rs 45 crore without netting and Rs 15 crore with it. Without netting, each trade stands alone, so the bank is exposed to every trade in its favour, 30 plus 15, and must still pay the 30 it owes. With an enforceable netting agreement all four collapse into one net claim: 30 minus 20 plus 15 minus 10, which is Rs 15 crore.
Why does netting cut the exposure by two thirds?
Two flatmates keep a running tab: one owes the other Rs 3,000 for rent, the other owes Rs 2,000 for groceries. If they settle as one tab, Rs 1,000 changes hands. If one of them walks out, the other would want the tab settled as one, not to pay the grocery bill in full while chasing the rent. A netting agreementA legal contract under which all trades between two parties are combined into a single net amount if one of them defaults. turns many trades into one claim, so money you owe the defaulter is set against money it owes you.
Four trades worth plus 30, minus 20, plus 15 and minus 10 crore give an exposure of Rs 45 crore if each is treated alone, because only positive values are at risk. An enforceable netting agreement collapses them into a single claim of Rs 15 crore. What happens to the negative trades without netting?
They still get paid, by the bank. The administrator of a failed counterparty will collect every trade where the bank owes money and join the queue of creditors for every trade where the bank is owed. That asymmetry is called cherry-picking, and it is why exposure without netting is the sum of the positive values, never the net. Here the bank pays Rs 30 crore out and recovers only whatever the estate pays on Rs 45 crore.
The relationshipV_i the current value of trade i from the bank's side \max(\cdot,0) only amounts owed to the bank count as exposure What it says in wordsWithout netting take the positive part of each trade; with netting take the positive part of the total.The limitation to say out loud: netting only helps where it is enforceable in the counterparty's jurisdiction, which is why banks obtain legal opinions before counting it. Where that is uncertain, the risk system should fall back to the gross number.
Where candidates lose it
The most common error is answering Rs 15 crore for both cases, because the trades feel as if they offset. Without a legal right to set them off, they do not.
The other slip is adding all four absolute values to get Rs 75 crore. Money the bank owes is not exposure; it is an obligation it pays in full. Exposure counts only what the counterparty owes you.
What the interviewer asks next
- The counterparty posts Rs 10 crore of collateral under the netting agreement. What is the exposure now?
- How does netting change the potential future exposure, not just today's?
- Why would a regulator want a legal opinion before a bank counts netting?
055A Rs 80 crore credit line is 60% drawn. The credit conversion factor on the undrawn part is 50%, the probability of default is 2% and the loss given default is 45%. What is the expected loss?Bank credit riskNBFC credit risk
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Which exposure number goes into the expected loss formula?
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About Rs 57.6 lakh, or Rs 0.576 crore. The line is Rs 48 crore drawn and Rs 32 crore undrawn. Exposure at default adds half the undrawn part, Rs 16 crore, for Rs 64 crore. Expected loss is exposure times default probability times loss given default: 64 x 2% x 45% = Rs 0.576 crore.
Why is today's drawn balance the wrong exposure?
Think of a friend with a credit card who is quietly losing his job. In the months before he stops paying, the card balance climbs, because he is using the card to cover what his salary no longer does. Companies behave the same way with bank lines. Borrowers draw down their undrawn limits on the way to default, so exposure at default is the drawn balance plus a credit conversion factorThe share of an undrawn limit a bank assumes will be drawn by the time the borrower defaults. share of what is still undrawn.
The Rs 80 crore line has Rs 48 crore drawn and Rs 32 crore undrawn. Adding half the undrawn part gives exposure at default of Rs 64 crore, and 64 times 2% times 45% gives an expected loss of Rs 0.576 crore, about Rs 57.6 lakh. How much does the conversion factor change the answer?
A lot. Using only the drawn balance gives Rs 43.2 lakh; using the full limit gives Rs 72 lakh. The 50% conversion factor moves the expected loss by a third over the drawn-only figure, with no change in the borrower's credit quality. That is why the conversion factor is estimated from the bank's own default history on committed lines, not guessed.
The relationshipPD probability of default over the year, 2% LGD the share of exposure lost if default happens, 45% CCF the share of the undrawn limit assumed drawn at default, 50% What it says in wordsExpected loss is the chance of default times the share lost times the amount out on the day of default.Say the limitation plainly. Expected loss is an average, the amount the bank should price into the loan's spread and provide for, not the loss it would face if this borrower actually defaulted, which would be 45% of Rs 64 crore, or Rs 28.8 crore.
Where candidates lose it
Most candidates multiply the three inputs by Rs 48 crore, the drawn balance, and give Rs 43.2 lakh. They have read the conversion factor in the question and not used it.
The other trap is the unit. The answer is Rs 0.576 crore, which is Rs 57.6 lakh; saying Rs 57.6 crore is off by a factor of a hundred and loses the room fast.
What the interviewer asks next
- If the conversion factor were 75%, what would the expected loss be?
- What is the loss if this borrower actually defaults tomorrow?
- Why might a bank's conversion factor for a working capital line differ from one for a project finance facility?
056Two stocks both have a 10% cost of equity. One grows its dividends at 8% a year, the other at 2%. Using the Gordon growth model, how much does each price fall if the discount rate rises by 50 basis points?BlackRockNew York · 2026
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Which stock falls more when the discount rate rises half a point?
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The 8% grower falls 20%; the 2% grower falls about 5.9%. Under Gordon growth, price is next year's dividend over r minus g. For the fast grower that gap widens from 2% to 2.5%, so the price falls to 0.02 over 0.025, or 80% of what it was. For the slow grower the gap goes from 8% to 8.5%, and the price keeps 0.08 over 0.085 of its value.
Why does the fast grower react so much more?
Think of two ways to be paid Rs 10 lakh: most of it next year, or a trickle that grows for decades. If someone doubles the rate at which you discount the future, the trickle loses far more, because most of its money is far away. A fast-growing dividend is that trickle: its value sits in cash flows many years out. A stock whose value rests on distant cash flows behaves like a long bond, so the same rise in the discount rate cuts its price far more.
Both stocks are priced at 100 with a 10% cost of equity. A rise to 10.5% takes the 8% grower to 80, a fall of 20%, and the 2% grower to 94.1, a fall of 5.9%, because the fast grower's price rests on a gap of only 2 points between r and g. How do you turn this into a duration number?
Differentiate the price with respect to r and divide by price: the answer is 1 over (r minus g). That gives the fast grower an equity duration of 50 years and the slow grower 12.5 years. Duration times 0.5% predicts falls of 25% and 6.25%; the exact falls are a little smaller, 20% and 5.9%, because the price curve bends, the same convexity a bond has.
The relationshipD_1 next year's dividend r the cost of equity, 10% g the constant dividend growth rate, 8% or 2% What it says in wordsAn equity's sensitivity to the discount rate is one over the gap between the discount rate and growth.The limitation is that Gordon growth assumes growth never changes and runs for ever, which exaggerates duration for a fast grower that will slow. The direction survives any sensible model: growth stocks carry more rate risk than stocks priced on today's cash.
Where candidates lose it
The trap is answering that both fall by about the same amount because the rate change is the same. The rate change is the same; the base it lands on is not. The fast grower's r minus g is a quarter of the slow grower's, so the same half point is four times as large relative to it.
The second slip is quoting the duration answer, 25%, as exact. Give 20% and say duration overstates it because the price curve bends.
What the interviewer asks next
- What happens to each price if growth expectations for the fast grower fall to 7% at the same time?
- Why might a portfolio of growth stocks behave like a long-duration bond fund?
- What does equity duration mean for a pension fund that holds equities against long liabilities?
Asked at BlackRock, Risk and Quantitative Analysis, New York, 2026 (Wall Street Oasis):
Which equities have duration? Technical and behavioural on VaR, market views and stock valuation.
057A bank has loans of Rs 95 crore and deposits of Rs 100 crore. Deposits fall 10%. If the bank keeps its loan-to-deposit ratio at 95%, by how much must its loans shrink?Treasury and ALMBank credit risk
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Quick answer: how much lending goes?
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Loans must shrink by Rs 9.5 crore, from Rs 95 crore to Rs 85.5 crore. Deposits fall 10% to Rs 90 crore, and 95% of Rs 90 crore is Rs 85.5 crore. The Rs 10 crore that leaves is met by Rs 9.5 crore of loans running off and Rs 0.5 crore of liquid assets, so the bank's lending falls by the same 10% as its deposits.
Why does a deposit outflow become a lending cut?
A household that lives on its salary and lends a cousin money every month has to stop lending if the salary is cut. The cousin has done nothing wrong; the money simply is not there. A bank funding its loans from deposits is in the same position. Holding the loan-to-deposit ratio fixed means every rupee of deposit flight passes straight into less lending, scaled by the ratio.
Deposits fall from Rs 100 crore to Rs 90 crore. Keeping loans at 95% of deposits takes loans from Rs 95 crore to Rs 85.5 crore, so Rs 9.5 crore of lending runs off and liquid assets fall by Rs 0.5 crore to cover the rest of the outflow. What makes this harder in practice than on paper?
Loans do not shrink on command. Term loans run off only as they repay, and calling them early harms the borrower and the bank's franchise. In the short run the bank has to meet the outflow from liquid assets or new funding, and a buffer of Rs 5 crore against a Rs 10 crore outflow is not enough. That gap is why liquidity rules ask banks to hold enough high quality liquid assets to survive a stressed outflow without selling loans.
The relationship\Delta L the change in loans, Rs crore \text{LDR} the loan-to-deposit ratio held fixed at 95% \Delta D the change in deposits, a fall of Rs 10 crore What it says in wordsWith the ratio fixed, loans change by the ratio times the change in deposits.Say the limitation: a real bank also has equity and wholesale funding on the liability side, and it could replace lost deposits with borrowing at a higher cost. The puzzle shuts that door deliberately, to show how directly a deposit run reaches lending when no other funding is available.
Where candidates lose it
The quick wrong answer is Rs 10 crore, matching the deposit fall one for one. That ignores that the ratio is 95%, not 100%, so only 95 paise of lending goes for every rupee of deposits.
The more costly miss is stopping at the arithmetic. The interviewer wants to hear that loans cannot shrink overnight, so the outflow is met first from liquid assets, which is what a liquidity buffer is for.
What the interviewer asks next
- If the bank instead keeps loans unchanged, what does its ratio become?
- How much liquid asset buffer would it need to meet a 20% outflow without shrinking loans?
- Why do regulators care about the speed at which different deposits can leave?
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
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The bad loan ratio fell from 3.0% to 2.8%. What is the best reading?
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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?
059Failed trades on a settlement desk average 12 a day with a standard deviation of 3. An amber alert fires at 18. If nothing about the process has changed, how many false amber alerts should you expect in a 250-day year?Operational risk
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Your instinct first: how many false ambers a year?
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About 6 false ambers a year. The threshold of 18 is two standard deviations above the mean of 12. If daily fails are roughly normal, about 2.3% of days land above two standard deviations on the high side, and 2.28% of 250 days is 5.7. Roughly one quiet day in every 44 will trip the alert with nothing wrong.
Why does a sensible threshold still fire when nothing is wrong?
A smoke alarm set sensitive enough to catch every real fire also goes off when someone burns toast. Set it deaf enough never to react to toast, and it may miss a real fire. Operational alerts face the same trade. Any threshold drawn on a noisy count carries a false alarm rate you can compute in advance, and the only way to cut it is to accept missing more real problems.
Daily fails centred on 12 with a standard deviation of 3 put the amber line at 18, two standard deviations up. The shaded tail holds 2.3% of days, which over a 250-day year means about 5.7 false ambers with the process unchanged. How precise is the answer of about six?
It rests on two assumptions worth saying. First, fails are whole numbers: if a count of exactly 18 triggers the alert, a continuity correction moves the tail to about 3.3% and the count to about 8. Second, real operational counts often have fatter tails than a bell curve, with bad days clustering around month ends and system changes. Both push the true false alarm count up, so six is a floor, not a ceiling.
The relationshipz how many standard deviations the threshold sits above the mean P(Z>2) the share of a normal distribution beyond two standard deviations on one side What it says in wordsConvert the threshold to standard deviations, read off the tail, and multiply by the number of days.In the room, close with what you would do: tell the operations team to expect about one amber every two months from noise alone, so that a cluster of ambers in one week, not a single one, is what triggers an investigation.
Where candidates lose it
The trap is answering none, or close to none, because 18 looks far from 12. Six fails is only two standard deviations, and two standard deviations is not rare over 250 tries.
The second slip is using the two-sided 5% and getting 12 or 13 a year. Only the high side triggers an amber, so the tail is about 2.3%, not about 5%.
What the interviewer asks next
- Where would you set the threshold to get about one false amber a year?
- Three ambers arrive in one week. How surprised should you be if nothing has changed?
- Why might failed trade counts not follow a normal distribution?
060A one-year European call and put on a non-dividend stock, both struck at 100, trade at 12 and 7. The stock is at 100. What interest rate does put-call parity imply?Bank market risk
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Which relationship do you use?
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About 5.26% a year with annual compounding, or 5.13% continuously compounded. Parity says call minus put equals stock minus the present value of the strike. Here 12 minus 7 is 5, so the present value of 100 must be 95. A one-year discount factor of 0.95 means 100 over 95 minus 1, about 5.26%.
Why must call minus put equal the stock minus the discounted strike?
Agreeing today to buy a house next year at a fixed price is the same as buying it now with money borrowed until then: either way you own the house next year and pay the fixed price. A long call plus a short put at the same strike is that agreement. At expiry the pair pays the stock minus the strike in every state, so today it must cost the same as owning the stock and owing the strike in a year, which is S minus the present value of K.
A long call and a short put struck at 100 together pay the stock price minus 100 in every outcome. Call 12 minus put 7 is 5, which must equal the stock at 100 minus the present value of the strike, so that present value is 95 and the implied rate is 5.26% a year. Why would a risk manager care about the rate hidden in option prices?
Because it is a check that comes free. If the rate implied by parity sits far from the funding rate the desk actually pays, either the marks are stale, a dividend has been missed, or the options are American and parity no longer holds exactly. Model validation teams run exactly this test on option books to catch mispriced marks before they show up as a loss.
The relationshipC, P the call and put prices, 12 and 7 S the stock price, 100 K the common strike, 100 r the one-year interest rate implied by the prices What it says in wordsThe gap between an at-the-money call and put is the interest on the strike, so the prices reveal the rate.The limitation: parity holds exactly only for European options on a stock paying no dividend before expiry. A dividend would lower the stock's forward and push the implied rate the other way, so state the assumption before you give the number.
Where candidates lose it
The common error is to write 5 over 100 and answer 5%. That treats 5 as the interest on 100, but 5 is what you save today, and the rate is measured on the 95 you actually pay. 100 over 95 minus 1 is 5.26%.
The other trap is forgetting the conditions. Say European, no dividends, and one year, then give the number; an interviewer will often follow up with a dividend to see if you adjust.
What the interviewer asks next
- The stock pays a dividend of 2 in six months. What rate is implied now?
- The call trades at 13 with the put unchanged. What trade locks in a profit?
- Why does parity not hold exactly for American options?