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

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Type

AnyBrainteaserTechnicalCaseMarket viewFit

1. 014Here is a game. What is the expected value of winning under three different strategies, and which one would you choose?Expected valueHardsuperdayJane StreetTrading · London · 2025OptiverGeneralist · Chicago · 2025

   Say this

   Set up the state and the decision rule before you compute anything, price each strategy with a clean conditional expectation, then choose on expected value first and on variance and ruin risk second. Say the comparison out loud as you go so the interviewer can follow your bookkeeping.

   Then walk it

   1. Step one, define the state precisely: what you know when you decide, and what the payoff function is. Most errors in these problems are specification errors, not arithmetic.
   2. Step two, price each strategy by conditioning on the first move. E of payoff equals the sum over first outcomes of probability times conditional value. If the game is repeated or recursive, write V in terms of V and solve the fixed point.
   3. Step three, do the arithmetic in fractions, not decimals. Fractions let the interviewer audit you and they do not accumulate error.
   4. Step four, choose. If one strategy dominates on expected value, say so and stop. If they are close, break the tie on the second moment: I would take the lower-variance strategy at the same expected value, and I would pay a small amount of expected value to avoid a path that can lose more than my stake.
   5. Then state the assumption you are relying on, unprompted: whether you may stop adaptively, whether the game is repeated, and whether the payoff is linear in money. Those three change the answer more than the arithmetic does.

   Where candidates lose it

   Diving into arithmetic before defining the state, and then losing track of which branch you are on. The other failure is picking the highest expected value without a word about variance. A trading floor cares about the distribution of outcomes, so say which strategy you would actually run with real money and why.

   Expect next

   • Now suppose you can play the game a hundred times. Does your choice change?
   • What if the payoff were doubled but the probability halved?
   • What is the variance of your preferred strategy?

   Reported by candidates at Jane Street (Trading, London, 2025); Optiver (Generalist, Chicago, 2025). Source: Wall Street Oasis.

2. 037You stand on a road and watch cars drive past. How would you estimate the parameter of the underlying distribution?StatisticsHardtechnicalJump TradingQuantitative Research · Chicago · 2018

   Say this

   First I would state the model: arrivals as a Poisson process with rate lambda, so inter-arrival times are exponential with mean 1 over lambda. Then the maximum likelihood estimate of lambda is just the count divided by the observation time, and its standard error is lambda over the square root of the count.

   Then walk it

   1. Model choice first, and justify it: independent arrivals at a constant rate with no memory gives a Poisson process. That is reasonable on a quiet road, and clearly wrong near a traffic light where cars arrive in platoons.
   2. MLE: for n arrivals in time T, lambda hat is n over T. It is unbiased, and the variance is lambda over T, so the relative standard error is 1 over the square root of n. Twenty-five cars gives you a 20 percent standard error, a hundred cars gives 10 percent.
   3. That tells you the sample size you need before you open your mouth about precision. If someone wants the rate to five percent, you need 400 cars.
   4. Now the diagnostics, which are what a research interview is actually about. Plot the inter-arrival times and check whether they look exponential. Over-dispersion, meaning variance above the mean of the counts, tells you arrivals are clustered and Poisson is wrong. Then I would go to a Cox process or a Hawkes process with self-excitation.
   5. And I would flag the estimation trap: if instead I sampled by picking a random moment and measuring the gap I happened to land in, I would oversample long gaps. That is the inspection paradox, and it biases the mean gap upward by a factor of one plus the squared coefficient of variation. It is the same bias that makes waiting times feel longer than the timetable says.

   Where candidates lose it

   Jumping to a formula without stating the model or checking it. The interviewer wants model, estimator, standard error, then diagnostics. The specific failure mode they are hunting is the inspection paradox, so mention length-biased sampling unprompted. Hawkes processes are the right answer for clustered arrivals and they are also how trade arrivals actually behave in markets.

   Expect next

   • How would you test whether the Poisson assumption holds?
   • What if the cars arrive in clusters?
   • How long do you need to watch to get the rate within five percent?

   Reported by candidates at Jump Trading (Quantitative Research, Chicago, 2018). Source: Wall Street Oasis.

3. 040Here is a dataset. Analyse it using probability metrics and tell me what you find.StatisticsHardcase studyJane StreetCredit Risk · London · 2025

   Say this

   I would spend the first third of the time on the data itself before any modelling: shape, missingness, duplicates, timestamps, and the univariate distributions. Then state a hypothesis, test it, and report the effect size with an honest uncertainty. Narrate every step, because the interviewer is grading the process, not the punchline.

   Then walk it

   1. Start with the boring checks, out loud. Row count, date range, obvious duplicates, missing values and whether they are missing at random, and whether any column is a leak of the outcome. Most real findings in interviews of this kind are data artefacts.
   2. Then univariates: mean, median, standard deviation, skew, kurtosis, and the tails. Plot histograms and the empirical CDF. If a column is heavy-tailed or bimodal, say so, because it changes every subsequent choice.
   3. Then the relationship you were asked about. Give a point estimate plus a confidence interval, and prefer a plot to a coefficient. If the data are time-ordered, check for autocorrelation and regime change before quoting any p-value, because serial dependence inflates significance badly.
   4. Then the discipline: state your null, say what result would change your mind, and count how many hypotheses you have looked at. If you tested twenty things, say so and adjust.
   5. Close with what the data cannot tell you. A credit dataset with survivors only cannot tell you about defaults. Ending on the limitation is what separates an analyst from someone producing numbers, and in a live exercise it is the cheapest way to sound senior.

   Where candidates lose it

   Going straight to a model. Almost every candidate opens a regression and never looks at a histogram, then reports a spurious result driven by three outliers or a broken timestamp. Talk through the data integrity checks first, and say your uncertainty on every number you quote.

   Expect next

   • What would you check before trusting that correlation?
   • How many hypotheses did you test, and how does that change your p-value?
   • What would you want that is not in this dataset?

   Reported by candidates at Jane Street (Credit Risk, London, 2025). Source: Wall Street Oasis.

4. 045You test two hundred signals and three come back significant at the five percent level. What do you conclude?StatisticsHardtechnicalQuant researchQuant trading

   Say this

   That you have found nothing. Under a pure null you would expect ten false positives from two hundred tests at five percent, so three is fewer than chance. If anything the result is evidence against there being any signal at all.

   Then walk it

   1. Expected false positives are 200 times 0.05 equals 10. Getting three significant results is below what noise alone produces, so the finding is not just unimpressive, it is worse than random.
   2. The right frame is family-wise error or false discovery rate. Bonferroni sets the threshold at 0.05 over 200, which is 0.00025, brutal but valid. Benjamini-Hochberg controls the expected proportion of false discoveries among the rejections and is much less conservative, which is usually the better choice when you are screening.
   3. The subtlety with financial signals: they are heavily correlated with each other, so the effective number of independent tests is far below 200. Bonferroni is then too harsh. I would estimate the effective number of tests, for example from the eigenvalue spectrum of the signal correlation matrix, or use a permutation or block-bootstrap null that preserves the correlation structure.
   4. The right test of whether anything survived is not a p-value at all. It is out-of-sample: hold back a period, or better a different market, and see whether the three signals still work with the sign you predicted.
   5. And the disclosure discipline, which is the answer a research head wants to hear: I would report the number of specifications tried alongside the result. The deflated Sharpe ratio and Harvey and Liu's work on multiple testing in finance both exist because the profession spent decades not doing this.

   Where candidates lose it

   Getting excited about the three and building a strategy on them. The whole question is whether you compute the expected number of false positives before you get attached. Say ten out of two hundred immediately, then talk about correlated tests, because that is where the technical depth is.

   Expect next

   • How would you estimate the effective number of independent tests?
   • What is the deflated Sharpe ratio?
   • How would you set up the experiment properly from the start?
5. 049You need a covariance matrix for five hundred assets and you have two years of daily data. What is the problem and how do you fix it?StatisticsHardsuperdayQuant researchRisk

   Say this

   You have 500 assets and roughly 500 observations, so the sample covariance matrix is nearly singular and its smallest eigenvalues are garbage. Any optimiser will load up on exactly those directions, so you have to shrink or impose factor structure.

   Then walk it

   1. Count the parameters: 500 times 501 over 2 is about 125,000 numbers estimated from 250,000 data points. The ratio of assets to observations, roughly one here, is what governs the damage, and the sample eigenvalue spectrum is badly biased even at a ratio of a quarter.
   2. Marchenko-Pastur describes exactly how the eigenvalues spread out. The largest are overstated and the smallest understated, and the smallest ones are the low-variance directions a mean-variance optimiser will concentrate in. That is why naive optimisers produce absurd leveraged long-short positions.
   3. Fix one, shrinkage. Ledoit-Wolf shrinks the sample matrix towards a structured target like a constant-correlation matrix, with an optimal intensity derived in closed form. Cheap, well-behaved and hard to beat as a default.
   4. Fix two, factor structure. Model returns as exposures to a few factors plus idiosyncratic noise, so the covariance is B times F times B transpose plus a diagonal. You have gone from 125,000 parameters to a few thousand. This is what every commercial risk model does.
   5. Fix three, random matrix filtering: keep the eigenvalues above the Marchenko-Pastur bulk edge as signal and replace the bulk with its average. Then state the practical check, which is out-of-sample portfolio variance rather than any in-sample fit statistic, because in-sample the sample matrix always wins and is always wrong.

   Where candidates lose it

   Saying you would just use the sample covariance matrix because two years is a lot of data. It is not, relative to 500 assets. The interviewer is testing whether you know that estimation error in the covariance matrix, not in the means, is what breaks portfolio optimisation in practice, and whether you can name shrinkage or factor models as the fix.

   Expect next

   • Why does the optimiser concentrate in the smallest eigenvalue directions?
   • How do you choose the shrinkage intensity?
   • How would you test whether your covariance matrix is any good?
6. 059A strategy shows a Sharpe ratio of 2 over one year. How much do you believe it?Time seriesHardsuperdayQuant researchQuant trading

   Say this

   Not much. The standard error of an annualised Sharpe estimated over T years is roughly the square root of (1 plus half the Sharpe squared) divided by T, so with one year and a Sharpe of 2 the standard error is about 1.7. The 95 percent interval runs from roughly minus 1.4 to 5.4, which comfortably includes zero.

   Then walk it

   1. The formula, for iid normal returns: standard error of the Sharpe estimate is root of ((1 plus SR squared over 2) divided by T), with T in years for an annualised Sharpe.
   2. With T equal to 1 and SR equal to 2, that is the square root of (1 plus 2) over 1, which is the square root of 3, about 1.73. Two standard errors either side of the point estimate spans minus 1.4 to 5.4, so one year of data cannot even establish that the strategy makes money.
   3. Turn it around into the useful statement: to establish statistical significance at two standard errors you need roughly T of at least 4 over SR squared years. A Sharpe of 2 needs about a year to be marginally significant, a Sharpe of 1 needs four years, and a Sharpe of 0.5 needs sixteen years. Most equity factors fall in that last bucket, which is why the factor literature is so contested.
   4. The estimation error is only half the problem. The other half is selection. If this strategy is the best of a hundred I tested, the honest benchmark is the expected maximum Sharpe under the null, which for a hundred trials is around 2.5 standard errors above zero. The deflated Sharpe ratio adjusts for exactly this.
   5. And the formula assumes iid normal returns. Autocorrelated returns, which is common in anything holding illiquid or smoothed positions, inflate the Sharpe substantially, and negative skew means the Sharpe misses the risk that actually matters. So I would also want the drawdown profile, the turnover, and the capacity before I believed anything.

   Where candidates lose it

   Treating a one-year Sharpe as a fact. This question separates people who have evaluated real strategies from people who have read about them. Give the standard error formula, invert it into how many years you need, and then raise selection bias yourself.

   Expect next

   • How many years would you need for a Sharpe of 0.5 to be significant?
   • What if the returns are autocorrelated?
   • What else would you want to see besides the Sharpe?
7. 060You backtested a strategy and it performed brilliantly, but in live trading you keep losing money. What would you do?Time seriesHardsuperdayJump TradingQuantitative Research · Chicago · 2018

   Say this

   First I would cut the size, because the priority is to stop bleeding while I diagnose. Then I would work through the causes in order of likelihood: costs and slippage, look-ahead or survivorship bias in the backtest, overfitting from too many trials, and only last the possibility that the edge was real and has decayed.

   Then walk it

   1. Costs first, because it is the most common and the easiest to check. Compare realised fill prices against the prices the backtest assumed. If the backtest filled at mid and you are paying the spread plus impact, a strategy with a one basis point edge and a two basis point cost is a losing strategy that looked like a winner. Reconstruct the P&L attribution trade by trade against the simulated trades.
   2. Then look-ahead bias. Did any feature use data timestamped after the decision, including restated fundamentals, index membership known only later, or a corporate action applied on the announcement date rather than the effective date? Survivorship bias in the universe is the same family of error.
   3. Then overfitting. How many variants did I try before this one? If the answer is hundreds, the in-sample Sharpe is a maximum over many draws, and the deflated Sharpe is the honest number. Test on a market or a period I never touched.
   4. Then regime and decay. Plot the backtest P&L by year and see whether the edge was concentrated in one period. Check whether the alpha has been crowded out, which usually shows up as the signal still predicting but the entry price already moved.
   5. And the meta-answer, which is the one they want: I would write the diagnosis as a hypothesis with a test, not a list of possibilities. For example, if costs are the cause, the loss should scale with turnover, so I would compare the live P&L of the highest and lowest turnover sleeves. Then I would say what would make me shut it off permanently, and I would set that threshold before I looked at any more data.

   Where candidates lose it

   Jumping straight to the market regime changed. That is the excuse every losing strategy gets and it is almost never the first cause. The ordered list of costs, bias, overfitting, then decay is what a research head wants to hear, along with the instinct to reduce size before you finish diagnosing.

   Expect next

   • How exactly would you test whether costs are the cause?
   • How many strategy variants did you try, and how should that change your prior?
   • At what point do you shut it off for good?

   Reported by candidates at Jump Trading (Quantitative Research, Chicago, 2018). Source: Wall Street Oasis.

8. 062You have made me a market. If the true answer falls inside your market, how much would you risk to win a hundred dollars?Market makingHardtechnicalAkuna CapitalTrading · Chicago · 2025

   Say this

   That depends entirely on how wide I quoted and how confident I am, and those two are linked. If I quoted a tight market I should not be very confident the answer is inside it, so I would risk little. If I quoted wide, I should be confident, and I would risk more. The honest answer is to price my own probability and then bet a fraction of Kelly.

   Then walk it

   1. The question is a consistency check. A tight market is a strong claim, and the interviewer is testing whether my stated width matches my stated confidence. If I said 300 at 310 on the number of Starbucks in New York and then say I am 90 percent sure the truth is inside, one of those is a lie.
   2. So I quantify. Suppose I think there is a 60 percent chance the answer is inside my market. Then risking x to win 100 has expected value 0.6 times 100 minus 0.4 times x, which is positive for x below 150. So fair value is 150 and I would bet meaningfully below that.
   3. Kelly gives the size: bet a fraction of capital equal to edge over odds. At 60 percent on an even-money-ish bet the full Kelly fraction is around 20 percent of capital, and I would take a quarter to a half of that, because my 60 percent is itself an estimate and overbetting Kelly is far more punishing than underbetting.
   4. I would also name the asymmetry in the setup. The interviewer chooses whether to take the bet, so they only take it when they think my price is wrong. That is adverse selection, and it means I should shade my number down from the naive fair value.
   5. So a concrete answer: with a 60 percent belief and an adversary who selects, I would risk around 50 to 70 dollars to win 100, and I would say out loud that I am shading below the 150 fair value because you get to choose whether to trade.

   Where candidates lose it

   Giving a bravado number like I'd risk a thousand, or refusing to name a figure. Both fail. Also failing to notice that your quoted width already implied a confidence level, so an answer inconsistent with your own market gets picked apart immediately. Name your probability, compute fair value, then shade for adverse selection.

   Expect next

   • So tighten your market and answer again.
   • What if I let you choose which side of the bet to take?
   • Explain why you shaded below fair value.

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

9. 071Here is a scenario. Walk me through how you would analyse the trade.Market makingHardcase studySchonfeldQuantitative Research · New York · 2021

   Say this

   I would structure it as five questions: what is the thesis and what would make it wrong, what is the expected value, how do I size it, how do I hedge what I am not trying to be exposed to, and what is my exit. Then say the number, because a trade analysis without a number is an opinion.

   Then walk it

   1. Thesis first, stated as a falsifiable claim with a horizon. Not this looks cheap, but I think this spread compresses from 80 to 50 basis points over three months because of a specific mechanism, and if it is still at 80 in three months I am wrong.
   2. Expected value: probability times payoff on each branch. If there is a 60 percent chance of making 3 and a 40 percent chance of losing 2, that is 1.8 minus 0.8, so plus 1 with a 5-point range of outcomes. The range matters as much as the mean.
   3. Sizing: from the loss branch, not the win branch. I size so that the bad case is a loss I can carry, which in practice means a fraction of my risk budget, and I say what that fraction is.
   4. Hedging: separate the exposure I want from the ones that come attached. If the view is idiosyncratic, hedge out the market beta, the sector, and the rate duration, then check what basis risk remains after hedging, because that is the risk I did not choose.
   5. Exit and monitoring: the level or the date at which I am out, plus the two or three observables that would tell me the thesis is breaking before the P&L does. And I would name the thing I cannot hedge, because every trade has one and being explicit about it is what makes the analysis credible rather than promotional.

   Where candidates lose it

   Describing the thesis at length and never getting to sizing, hedging or the exit. Anyone can have a view. What a multi-manager platform is hiring for is the risk framework around it, so spend at least half your answer on size, hedge and exit, and name the unhedgeable residual yourself.

   Expect next

   • What is your stop, and why there?
   • What would make you double the position?
   • What risk are you left with after hedging?

   Reported by candidates at Schonfeld (Quantitative Research, New York, 2021). Source: Wall Street Oasis.

10. 073Why do alphas decay, and how would you detect that yours is dying?Time seriesHardsuperdayQuant researchQuant trading

    Say this

    Because a profitable pattern attracts capital until the price moves to where the profit was. Detect it by tracking realised versus expected performance, the signal's own predictive power separately from the P&L, and crowding measures, and set the decision rule before performance deteriorates.

    Then walk it

    1. Mechanisms in order of frequency. Crowding, where other people trade the same signal and the entry price moves. Structural change, where the market feature the signal exploited is regulated or engineered away. Arbitrage by faster participants. And plain overfitting, where the alpha was never there.
    2. Separate the two things that can break. Is the signal still predicting, measured by information coefficient, the correlation between forecast and subsequent return? Or is it predicting but no longer profitable after costs? The first is decay, the second is crowding or impact, and the fixes differ.
    3. Concrete measures: rolling information coefficient, rolling Sharpe, realised transaction cost versus modelled, and the fraction of your expected edge captured on a typical fill. If the signal is intact and the capture rate is falling, other people are in front of you.
    4. Crowding proxies: short interest and borrow costs for the short leg, correlation of your P&L with published factor returns, and how your strategy behaves on days when leveraged players deleverage. A crowded trade has fat negative tails on those days.
    5. The discipline is the answer though. Set the decay threshold in advance, for example halve the allocation if the rolling one-year information coefficient falls below half its backtest level for two consecutive quarters. Deciding in the middle of a drawdown is how people turn a decayed alpha into a large loss, and having the rule written down before you need it is the part an interviewer is actually testing.

    Where candidates lose it

    Answering only markets get more efficient. Be specific about mechanisms and about measurement, and above all separate whether the signal stopped predicting from whether the trade stopped being profitable. A pre-committed decision rule is the piece most candidates never mention.

    Expect next

    • What is an information coefficient and what is a good value?
    • How would you measure crowding in a trade?
    • Would you turn it off, or reduce it, and who decides?

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.