Quant interview preparation

Questions

100

Traced to a firm

53

Firms

15

Updated

September 2026

Asked at

All firmsOld Mission Capital12Tower Research Capital10Jump Trading7Akuna Capital5Citadel4DED.E. Shaw3Jane Street3ACAQR Capital Management2DRW2Millennium Management2Schonfeld2SCSquarepoint Capital2Susquehanna International Group2Belvedere Trading1Optiver1

Topic

All topicsProbability10Coins, cards and games6Expected value8Statistics11Market making15Estimation and mental maths4Stochastic processes4Regression5Machine learning6Time series6Programming10Options and derivatives8Fit and motivation7

Level

AnyCoreIntermediateHard

Type

AnyBrainteaserTechnicalCaseMarket viewFit

1. 015Two games have exactly the same expected value. Which one would you choose to play?Expected valueIntermediatetechnicalAkuna CapitalSales and Trading · Chicago · 2025Belvedere TradingProp Trading · Chicago · 2022

   Say this

   If the expected values tie, I choose on variance, on how many times I get to play, and on whether any outcome can wipe me out. As a one-off with a fixed stake I take the lower-variance game. Repeated many times with the ability to size, I might prefer the higher-variance one.

   Then walk it

   1. First, ask the question the interviewer wants you to ask: how many times do I get to play, and can I choose my size? Those two facts change the answer completely.
   2. One shot, fixed size: take low variance. Same mean, less dispersion, strictly better under any concave utility, and a trader's utility is concave because a bad first day costs them their limits.
   3. Repeated, and I can size: variance becomes something I can dial. Kelly says bet a fraction proportional to edge over variance, so the high-variance game just gets a smaller position. Per unit of risk they may be identical.
   4. Then the killer criterion, which is ruin. If one game has any probability of a loss larger than my capital, its long-run growth rate is minus infinity regardless of its expected value. Expected value is a bad objective when the bet is not repeatable.
   5. One more real consideration: correlation with everything else I have on. A game with the same mean and variance but zero correlation to my book is worth more than one that doubles my existing exposure. On a desk that is usually the deciding factor.

   Where candidates lose it

   Saying I am indifferent because the expected values are equal. That answers the arithmetic and fails the question, which is about risk preference. Also do not just say I prefer lower variance and stop, because the interesting answer depends on repetition, sizing and ruin. Ask the clarifying question first.

   Expect next

   • What if you could play one of them a thousand times?
   • How would you size each one?
   • Explain the Kelly criterion and why traders bet less than Kelly.

   Reported by candidates at Akuna Capital (Sales and Trading, Chicago, 2025); Belvedere Trading (Prop Trading, Chicago, 2022). Source: Wall Street Oasis.

2. 016You win a hundred dollars if you roll a ten with two dice. How much would you risk to play?Market makingIntermediatetechnicalAkuna CapitalTrading · Chicago · 2025

   Say this

   Fair value is eight dollars and a third. Three of the 36 outcomes make ten, so probability is 1/12 and the expected payoff is 100 over 12. I would pay up to about seven to leave edge, and if I am being asked to make a two-way price I would quote around 7 at 9.

   Then walk it

   1. Count the outcomes: 6-4, 4-6, 5-5. Three ways out of 36, so 1/12, about 8.33 percent.
   2. Expected payoff 100 times 1/12 equals 8.33. That is fair value, and fair value is where you break even, not where you trade.
   3. So I need edge. I would bid 7 and offer 9 if I have to two-way it, which is about a dollar and a half of edge either side, roughly fifteen percent of fair value. That width reflects the fact that I cannot hedge a one-off die roll.
   4. Size matters as much as price. This bet has a standard deviation of about 28 dollars against a mean of 8.33, which is a terrible ratio. I would do it small even at a good price, and I would want to repeat it many times rather than do it once large.
   5. If the game is repeatable and I can do it a thousand times, I pay closer to 8. The edge I demand is compensation for variance I cannot diversify, and repetition diversifies it.

   Where candidates lose it

   Answering with the fair value of 8.33 as if that were your bid. A trader never pays fair value, and saying eight and a third is what I would risk tells the interviewer you do not understand where the money comes from. Quote a price below fair value, name your width, and say your size.

   Expect next

   • Now make me a two-way market on it and I will trade you.
   • What if I could roll a hundred times?
   • What is the standard deviation of your P&L on one play?

   Reported by candidates at Akuna Capital (Trading, Chicago, 2025). Source: Wall Street Oasis.

3. 050A colleague is excited about an R squared of 0.9 on a returns regression. What is your reaction?RegressionIntermediatetechnicalQuant researchQuant trading

   Say this

   Suspicion, not excitement. An R squared of 0.9 on returns almost always means a bug: a look-ahead leak, a regression of a price level on another price level, or the dependent variable included on the right-hand side. Real return predictability lives at an R squared of a fraction of a percent.

   Then walk it

   1. Benchmark it. A genuinely good daily return predictor has an R squared around 0.001 to 0.01. A monthly cross-sectional factor model might reach a few percent. Anything above 0.1 on returns is a red flag rather than a result.
   2. Most likely causes in order: the target is in the features, the features are computed with future information, you regressed levels on levels where both are trending, or you regressed a variable on itself lagged by zero periods.
   3. The levels problem deserves a name. Two independent random walks regressed on each other will produce a high R squared and a significant t statistic almost every time, because the standard errors are wrong under non-stationarity. That is spurious regression, and it is Granger and Newbold's result.
   4. Also note what R squared does not tell you even when it is right: nothing about out-of-sample performance, nothing about economic significance, and it always rises when you add regressors, which is why adjusted R squared exists, penalising by (n-1)/(n-k-1).
   5. So what I would do: check for leakage first, difference the series and re-run, then look at out-of-sample R squared. And the thing worth knowing is that an out-of-sample R squared of 0.005 on daily returns, if it is real and tradeable, is a very good strategy. Small numbers are the norm and big numbers are bugs.

   Where candidates lose it

   Congratulating them. Knowing the realistic magnitude of return predictability is a strong signal that you have done real work, and not knowing it is a strong signal that you have not. Name look-ahead bias and spurious regression on levels as the two prime suspects.

   Expect next

   • What is a realistic R squared for a daily return forecast?
   • Explain spurious regression between two random walks.
   • What is out-of-sample R squared and how do you compute it honestly?
4. 055When would you use gradient boosting on market data, and when would you stick with a linear model?Machine learningIntermediatetechnicalQuant researchQuant trading

   Say this

   Boosting earns its keep when you have a lot of data, genuine non-linearity and interactions, and a target with enough signal to support the extra capacity. For low-frequency return prediction with a few hundred monthly observations I would use a regularised linear model almost every time.

   Then walk it

   1. The case for trees: they capture interactions and thresholds automatically, handle mixed feature types, are insensitive to monotone transforms, and do not care about outliers in the features. On microstructure problems with millions of observations they genuinely win.
   2. The case against on returns: the signal-to-noise is so low that a flexible learner mostly memorises noise, and the model cannot extrapolate beyond the range it saw, which is exactly where the interesting market states live. A boosted tree trained through 2019 has no representation of March 2020.
   3. Data volume is the deciding variable. Daily cross-sectional data with 3,000 names times 20 years is 15 million rows and trees are viable. Monthly aggregate time series with 300 observations is not, no matter how you tune it.
   4. If I use boosting, I use it with heavy constraints: shallow trees of depth three to five, low learning rate, strong subsampling, early stopping on a purged time-series split, and monotonic constraints where I have a prior on the sign.
   5. And I would always run the regularised linear baseline first and report both. In practice the boosted model often adds a modest amount of out-of-sample R squared over a good linear model on financial data, which is a real gain but far from the step change people expect. Knowing that the gain is modest rather than transformative is the useful piece of experience here.

   Where candidates lose it

   Defaulting to whatever is fashionable with no reference to data volume or signal-to-noise. The interviewer wants a judgement, not a preference. Also name the extrapolation limitation of trees, because that is the specific reason they fail in a regime the training set never saw, which is when you most need the model.

   Expect next

   • How would you stop a boosted model overfitting on financial data?
   • Why can trees not extrapolate, and when does that hurt you?
   • How much out-of-sample improvement would make you switch from the linear model?
5. 064You are long five hundred lots and the market keeps offering below you. What do you do with your quotes?Market makingIntermediatetechnicalProp trading firmsQuant trading

   Say this

   Skew. Lower both my bid and my offer so I am more likely to sell than to buy, because I want to reduce inventory, and widen if the flow suggests the market is informed. Skewing quotes is how a market maker manages inventory without crossing the spread.

   Then walk it

   1. The mechanism: a market maker's reservation price moves against their inventory. Long inventory means I value the next unit less, so my fair value shifts down and my quotes should shift with it. That is the core result of the Avellaneda-Stoikov style inventory models.
   2. Skewing is cheaper than hedging aggressively. If I dump 500 lots at market I pay the spread plus impact immediately. If I skew, I get paid the spread to unwind, just more slowly.
   3. But I need to distinguish two situations. If the offers are noise traders, I keep skewing and unwind profitably. If the offers are informed flow ahead of news, skewing just means I keep buying into a falling market, which is how market makers blow up.
   4. The tell is whether the market comes back. If I sell some and the price recovers, I was providing liquidity. If every trade is followed by the market moving further against me, I am being run over and I should widen, reduce size, or cross the spread and get flat.
   5. So the decision rule I would say out loud: skew first, size down second, and cross the spread third if my position is still growing against me. And I would have a hard limit set in advance, because the one thing you cannot do is decide your maximum loss while you are losing.

   Where candidates lose it

   Answering hold and wait for it to come back, which is the losing trader's answer. Also answering just hedge without noting that hedging costs the spread. The interviewer wants to see the skew mechanism named, and wants to hear you distinguish noise flow from informed flow.

   Expect next

   • How do you tell whether the flow is informed?
   • At what point do you cross the spread and get flat?
   • How would you set your position limit in advance?
6. 069You quote a tight market and get lifted on your offer immediately. Are you happy?Market makingIntermediatetechnicalProp trading firmsQuant trading

   Say this

   No, not immediately. An instant fill is usually bad news: it means my offer was the cheapest thing available, which suggests my fair value was too low. I would shift my market up, not celebrate the spread I just earned.

   Then walk it

   1. The right frame is that a fill is information. If the market wanted my offer that fast, my offer was probably below consensus fair value.
   2. The fill I actually want is slow and two-sided: I buy on the bid, sell on the offer, and end the day roughly flat having collected the spread many times. Getting filled on one side only is a warning.
   3. So the immediate action is to move both quotes in the direction of the flow and reconsider the width. The mid moves up, and I may widen because I am now less sure where fair value is.
   4. How to measure whether it was actually bad: markout. Look at the mid a minute later. If the market is above where I sold, I was adversely selected regardless of the spread I booked. Booking the spread and losing on the markout is the classic way a market maker loses money while showing positive spread capture.
   5. The one case where I am genuinely happy is if I know the flow is uninformed, for instance a retail-sized order or a predictable end-of-day hedger. Then an instant fill is exactly the business. So the honest answer is: it depends who traded with me, and I would want to know that before I formed a view.

   Where candidates lose it

   Saying yes, I made the spread. That is the answer of somebody who thinks the spread is profit rather than gross revenue. Instant one-sided fills are the signature of adverse selection, and the interviewer is checking whether your instinct is to update or to congratulate yourself.

   Expect next

   • How would you check whether you were picked off?
   • What do you do with your quotes now?
   • When would an instant fill be good news?
7. 070Something goes badly wrong on your book during the session. How do you react?Market makingIntermediatetechnicalOld Mission CapitalProp Trading · Chicago · 2025

   Say this

   Reduce risk first, diagnose second, and tell someone immediately. In that order. The instinct to understand the problem before acting on it is the wrong instinct when the position is still live and the loss is still growing.

   Then walk it

   1. Step one, stop the bleeding. Pull quotes, flatten or hedge the exposure I did not intend to have, and cap any automated system that might still be adding to it. Getting smaller is almost never the wrong move under uncertainty.
   2. Step two, escalate. Tell the senior trader on the desk and the risk desk straight away, before I know the cause. Every trading floor's disaster stories are about someone who tried to fix it quietly first.
   3. Step three, establish the facts. What is my actual position, what is the realised and unrealised loss, is the pricing wrong or is the position wrong, and is anything still running that I have not stopped.
   4. Step four, only then diagnose and fix. A bad parameter, a stale feed, a hedge that did not go through, a fat finger, a genuine adverse move.
   5. And afterwards, write it up. A one-page post-mortem with a concrete control change is what stops the same failure twice. What a desk actually wants to hear from a junior candidate is that you act to reduce risk without needing permission, and escalate without needing to look competent first. Composure plus disclosure, in that order.

   Where candidates lose it

   Answering that you would investigate the cause first. On a live book that is exactly backwards, and a prop trading interviewer is listening for the reduce-then-escalate-then-diagnose sequence. Also do not claim you would stay completely calm. Say you would act on a checklist precisely because you would not be calm.

   Expect next

   • Who do you tell, and how quickly?
   • Tell me about a time you made a real mistake and what you did.
   • What would you put in the post-mortem?

   Reported by candidates at Old Mission Capital (Prop Trading, Chicago, 2025). Source: Wall Street Oasis.

8. 087You think the market is overestimating volatility. What options strategy would you use?Options and derivativesIntermediatetechnicalOld Mission CapitalProp Trading · Chicago · 2025

   Say this

   Sell volatility and hedge the direction out. The cleanest expression is a short straddle or strangle, delta-hedged so the position is a bet on volatility rather than on the underlying. If implied vol is above what I think realised vol will be, I collect the difference through the gamma-hedging P&L.

   Then walk it

   1. The mechanism: a delta-hedged short option position makes money when realised volatility comes in below the implied vol you sold. Your P&L is approximately half of gamma times the difference between implied variance and realised variance, integrated over the life of the trade.
   2. The instrument choice. A short straddle at the money has the most vega and gamma per unit of premium, so it is the purest vol expression. A short strangle has less gamma but a wider profitable range and less immediate pin risk. If I wanted a cleaner exposure with no path dependence I would sell a variance swap, where the payoff is literally implied minus realised variance.
   3. Risk management is the whole trade. Short gamma means every hedge is at a worse price than the last, so a gap move is where the loss lives. I would cap it with a long wing, turning the strangle into an iron condor, which sacrifices some premium to remove the unbounded tail.
   4. Sizing from the tail: I would set the position so the worst plausible gap, say a five percent overnight move, is a loss I can carry, not from the expected daily P&L. Short vol positions have positive expected value most days and lose several months of it in one session.
   5. And the honest caveat: implied vol trading above realised vol is the normal state of the world, not a mispricing. The variance risk premium exists because sellers are being paid to warehouse gap risk. So I need to believe implied is rich relative to that premium, not merely rich relative to realised, otherwise I am just collecting a risk premium and calling it alpha.

   Where candidates lose it

   Answering short straddle and stopping. Two things must follow: that you delta hedge to isolate the vol view, and that short gamma means a fat left tail so you cap or size for it. Also the variance risk premium point, because saying implied is above realised therefore sell it is the reasoning that ends careers.

   Expect next

   • How do you make it a pure volatility trade?
   • What happens if the stock gaps ten percent overnight?
   • Why is implied usually above realised in the first place?

   Reported by candidates at Old Mission Capital (Prop Trading, Chicago, 2025). Source: Wall Street Oasis.

9. 091You want to express a view that the underlying will move a lot but you have no view on direction. Straddle or strangle?Options and derivativesIntermediatetechnicalProp trading firmsDerivatives

   Say this

   Straddle if I think the move is likely but might be moderate, strangle if I think the move will be large but is less likely. The straddle costs more and starts paying sooner; the strangle is cheaper with a further breakeven and more leverage to a big move.

   Then walk it

   1. Definitions: a straddle is a call and a put at the same strike, usually at the money. A strangle is a call and a put at different out-of-the-money strikes.
   2. Put numbers on it. Stock at 100, one-month at-the-money vol 20 percent, so a monthly standard deviation of about 5.8 percent. The at-the-money straddle costs roughly 0.8 times spot times vol times root T, about 4.6, so breakevens near 95.4 and 104.6. A 95 to 105 strangle might cost 1.8, with breakevens near 93 and 107.
   3. So the straddle needs about a 4.6 percent move to break even and the strangle about 7 percent, but the strangle risks 1.8 rather than 4.6 and pays more per unit risked on a ten percent move.
   4. Greeks tell the same story. The straddle has more gamma and vega per contract and the most theta decay, concentrated near the strike. The strangle has less of everything but a flat maximum loss region, and it gains relatively more from an increase in the wings of the vol surface.
   5. What I would actually decide on, and this is the part interviewers want: whether the implied vol I am paying is cheap relative to my forecast, and where on the smile I am buying it. Out-of-the-money strikes usually carry higher implied vol because of the skew, so the strangle can be the more expensive trade in vol terms even though it is cheaper in premium. If the whole surface is cheap I buy the straddle; if only the wings are cheap I buy the strangle.

   Where candidates lose it

   Answering purely on cost, as if cheaper were better. Compare them on breakeven distance, on cost, and on where you are buying the vol surface. The skew point, that out-of-the-money options often carry higher implied vol, is the answer that shows you think in vol terms rather than premium terms.

   Expect next

   • What if the event has a known date, like earnings?
   • How would the skew change your strike choice?
   • When would you prefer a calendar spread instead?

Firm tags come from public, anonymous candidate reports on Wall Street Oasis: strong signal, not sworn testimony. Firms are named as the places a question was reported, not as partners of Fin Maverick. Answers are written for this page to show how to think out loud; they are not scripts to recite.