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. 065What is adverse selection and why is it a market maker's real cost?Market makingIntermediatetechnicalProp trading firmsQuant trading

   Say this

   Adverse selection is the fact that whoever trades with you chose to, and sometimes they chose because they know something you do not. Your quote gets hit disproportionately when it is wrong, so on average the trades you get are worse than the trades you wanted.

   Then walk it

   1. The mechanism: you post a two-sided quote at your fair value. Uninformed flow hits both sides roughly equally and you earn the spread. Informed flow only takes the side that is mispriced, so those trades lose you money immediately.
   2. The measurement is simple and it is what every market making desk tracks: mark your fills against the mid price a few seconds or minutes later. If your buys are systematically below where the market goes, you are being adversely selected. The industry term is markout.
   3. This is why the spread must be wide enough that the profit from uninformed flow covers the loss to informed flow. Glosten and Milgrom's model makes the spread purely a function of the probability of informed trading, with zero inventory risk at all.
   4. It explains observable behaviour. Spreads widen before earnings and economic releases, when the probability of informed flow spikes. Market makers pay for retail order flow precisely because retail flow is less informed, so it is worth more.
   5. And the extreme version is why quotes get pulled. If adverse selection becomes severe enough that no spread compensates, the correct response is not to widen but to stop quoting. That is what a flash crash looks like from the inside, and saying that shows you understand the business rather than just the term.

   Where candidates lose it

   Confusing adverse selection with inventory risk. Inventory risk is the price moving while you hold a position you did not want. Adverse selection is getting the position in the first place precisely when it is wrong. Interviewers ask candidates to distinguish them, so have both definitions crisp and know that markout is how you measure it.

   Expect next

   • How is that different from inventory risk?
   • How would you measure it on your own fills?
   • Why is retail order flow worth paying for?
2. 066Explain the Kelly criterion, and why do real traders bet less than it says?Market makingHardtechnicalQuant tradingProp trading firms

   Say this

   Kelly maximises the expected growth rate of your capital by betting a fraction equal to your edge divided by the odds. For an even-money bet at probability p, that fraction is 2p minus 1. Real traders bet a fraction of it because Kelly assumes you know your edge exactly, and overbetting is far more damaging than underbetting.

   Then walk it

   1. The derivation in one line: maximise the expected log of wealth, because log wealth is additive across repeated bets and its expectation governs the long-run growth rate. For a bet paying b to 1 with win probability p, the optimal fraction is (pb minus (1-p)) over b.
   2. Numbers: a 55 percent even-money bet gives f equal to 0.1, so ten percent of capital. A 60 percent bet gives 20 percent. That is a lot more than most people's intuition, which is the first surprise of Kelly.
   3. For continuous returns the analogue is mean over variance, which is why a Sharpe ratio maps directly to a leverage level. Full Kelly leverage equals the Sharpe divided by the volatility.
   4. The asymmetry is the key insight. Growth rate as a function of bet size is a concave parabola, so betting half Kelly gives you three quarters of the growth with half the volatility. Betting double Kelly gives you zero growth. Overestimating your edge by a factor of two therefore destroys the entire benefit.
   5. And full Kelly's drawdowns are intolerable in practice: the probability of at some point halving your capital under full Kelly is fifty percent. Nobody running other people's money survives that, and no risk manager permits it. So a quarter to a half Kelly is standard, and the honest reason is parameter uncertainty plus career risk, not mathematics.

   Where candidates lose it

   Reciting the formula without the asymmetry. The gradeable insight is that the growth curve is flat near the optimum and falls off a cliff past it, which is why uncertainty in your edge estimate pushes you to bet less. Also mention the fifty percent chance of a fifty percent drawdown, because it makes the practical argument concrete.

   Expect next

   • What is the probability of a fifty percent drawdown under full Kelly?
   • How does Kelly relate to mean-variance optimisation?
   • How would you size when your edge estimate itself has a standard error?
3. 067What is the difference between a market order and a limit order, and who pays the spread?Market makingCorephone / first roundProp trading firmsQuant trading

   Say this

   A market order takes whatever price is available and pays the spread for certainty of execution. A limit order posts a price and waits, earning the spread if it fills, but with no guarantee it fills at all. You are choosing between price risk and execution risk.

   Then walk it

   1. The taker of liquidity pays. Buy with a market order and you pay the offer, which is above mid, so you start down by half the spread. The passive side on the other end of that trade collects it.
   2. On most exchanges the fee structure reinforces this: makers get a rebate, takers pay a fee. So the maker's economics are spread capture plus rebate minus adverse selection.
   3. The cost of a limit order is not zero, it is optionality you are giving away. A resting bid is a free put you have written to the market: it fills when the price is falling and does not fill when the price rises. That is adverse selection expressed as execution risk.
   4. So the choice is horizon-dependent. If I need to be done now because I have information or a hedge to put on, I pay the spread. If I am providing liquidity or my signal has a multi-day horizon, I post and wait.
   5. Worth adding the practical middle ground, since this is what execution desks actually do: split the order, post passively and cross only when the queue is not filling or when the signal decays. Implementation shortfall against the arrival price is how you measure whether you got that balance right.

   Where candidates lose it

   Getting the definitions right but not answering who pays the spread. The taker pays. The second miss is treating a limit order as free, when the real cost is the option you have written to anyone with better information. Say that and you are ahead of most candidates.

   Expect next

   • What is the hidden cost of a resting limit order?
   • How would you decide between posting and crossing?
   • What is implementation shortfall?
4. 074How would you model market impact and slippage for a strategy you are sizing?Market makingHardtechnicalQuant researchQuant trading

   Say this

   Split the cost into spread, temporary impact and permanent impact. The empirical regularity worth knowing is the square-root law: impact scales roughly with the square root of the order size as a fraction of daily volume, times the volatility.

   Then walk it

   1. The square-root law: impact in volatility units is approximately a constant times the square root of order size over average daily volume, with the constant usually estimated around 0.5 to 1. So trading 1 percent of ADV in a 2 percent daily vol name costs roughly 0.1 times 2 percent, about 20 basis points.
   2. That non-linearity is what caps capacity. Doubling your size only increases impact by 41 percent per share, but total cost grows as size to the power 1.5, so cost eats your edge faster than your edge grows.
   3. Separate temporary from permanent. Temporary impact reverts after you stop trading and is a function of how fast you trade. Permanent impact is the information your trading revealed, and it does not come back. Almgren-Chriss style frameworks trade off the two against the risk of trading slowly.
   4. Estimating it honestly: use your own fills against arrival price, not a vendor model, and regress realised shortfall on participation rate, volatility and spread. You need a lot of trades, and you must control for the fact that you traded more aggressively when you had more signal, which biases the estimate.
   5. And the modelling discipline: be conservative, because impact is the parameter most likely to turn a profitable backtest into a losing strategy. I would rather assume twice the cost and discover I was pessimistic than the reverse. That preference is the answer they want to hear.

   Where candidates lose it

   Assuming linear impact or using the quoted spread as the whole cost. For any size that matters the spread is the small part. Know the square-root law and know that cost scaling as size to the power 1.5 is what determines capacity, because that is the link between a research result and a business decision.

   Expect next

   • Why does cost scale as size to the power one and a half?
   • How do you separate permanent from temporary impact empirically?
   • How does impact determine the capacity of a strategy?

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.