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. 048Asset volatility comes in clusters. What does that break, and how do you model it?Time seriesIntermediatetechnicalQuant researchRisk

   Say this

   It breaks the constant-variance assumption behind almost everything: OLS standard errors, iid return models and Black-Scholes. The standard answer is a GARCH model, where today's variance depends on yesterday's variance and yesterday's squared shock.

   Then walk it

   1. The empirical fact first: returns are close to unpredictable in the mean but their squares and absolute values are strongly autocorrelated, with the autocorrelation of squared returns decaying over weeks. Big moves cluster.
   2. GARCH(1,1) is sigma squared at t equals omega plus alpha times the last squared return plus beta times the last variance. On daily equities alpha is typically around 0.05 to 0.1 and beta around 0.85 to 0.92, with alpha plus beta just under one, meaning very persistent but eventually mean reverting.
   3. Long-run variance is omega over (1 minus alpha minus beta). If alpha plus beta hits one you get integrated GARCH, which is essentially an exponentially weighted moving average with no mean reversion, and that is what RiskMetrics used.
   4. It matters for options because it generates both fat unconditional tails and a term structure of volatility, which is why implied vol curves upward or downward towards the long-run level depending on where spot vol sits.
   5. Variants worth naming and the honest limitation: GJR-GARCH or EGARCH add the leverage effect, since negative returns raise vol more than positive ones, which plain GARCH cannot capture. And for anything intraday I would prefer realised volatility from high-frequency data, because a HAR model on realised vol usually forecasts better than GARCH on daily closes.

   Where candidates lose it

   Describing GARCH mechanically without saying what it is for. The point is that conditional variance is forecastable even when the mean is not, which is why volatility trading exists and directional trading is hard. Also do not forget the leverage effect, since plain GARCH is symmetric in the sign of returns and equity vol is not.

   Expect next

   • Why does alpha plus beta sit so close to one?
   • What is the leverage effect and which model captures it?
   • Would you use GARCH or realised volatility to forecast tomorrow's vol?
2. 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?
3. 051What is omitted variable bias, and how would it show up in a factor regression?RegressionIntermediatetechnicalQuant researchPortfolio management

   Say this

   If you leave out a variable that belongs in the model and it is correlated with a regressor you kept, the kept coefficient absorbs part of its effect. The bias equals the true coefficient on the omitted variable times the regression coefficient of the omitted variable on the included one.

   Then walk it

   1. Formula worth knowing: if the truth is y equals b1 x1 plus b2 x2 plus e and you regress y on x1 alone, you estimate b1 plus b2 times delta, where delta is from regressing x2 on x1.
   2. So the bias has a sign you can reason about. If the omitted factor has a positive premium and your included factor loads positively on it, you overstate your factor's premium.
   3. In factor work this is everywhere. Run a single-factor CAPM regression on a value portfolio and the alpha looks large, because you omitted the value factor. Add HML and the alpha collapses. That is not a bug, it is omitted variable bias doing exactly what the formula says.
   4. Momentum is the classic trap in the other direction. Omit momentum from a regression on a quality portfolio and quality's alpha inherits whatever momentum exposure quality happens to carry in your sample.
   5. How to handle it honestly: report alpha against a nested sequence of models, one factor then three then five plus momentum, and show what survives. And say the limitation out loud, because you can never rule out the factor nobody has published yet. The defence is out-of-sample and out-of-market evidence, not a longer regression.

   Where candidates lose it

   Defining it abstractly without giving the sign and magnitude formula, or without a concrete factor example. The interviewer wants to see you reason about the direction of the bias. Also do not confuse it with multicollinearity, which inflates variance without biasing anything.

   Expect next

   • Which direction does the bias go if the omitted factor is positively correlated with yours?
   • How do you test whether your alpha survives the addition of a new factor?
   • How is this different from multicollinearity?
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. 056What is maximum likelihood estimation, and when would you prefer method of moments?StatisticsIntermediatetechnicalQuant researchRisk

   Say this

   MLE picks the parameters that make the observed data most probable under your assumed distribution. It is asymptotically efficient if the model is right, which is exactly the condition that makes method of moments attractive when it is not.

   Then walk it

   1. MLE: maximise the log likelihood, which is the sum of log densities. Under regularity conditions it is consistent, asymptotically normal, and attains the Cramer-Rao bound, with variance given by the inverse Fisher information.
   2. Method of moments: match sample moments to their theoretical expressions and solve. Generalised method of moments extends this to more moment conditions than parameters, weighting them optimally, and it needs no full distributional assumption.
   3. So the tradeoff is efficiency versus robustness. MLE uses the whole density, so it extracts every bit of information and pays for it with sensitivity to misspecification. GMM uses only the moments you trust.
   4. Concrete case: fitting a distribution to daily returns. MLE under a normal assumption gives you the sample mean and variance and will be badly misled by the tails. MLE under a Student t estimates the degrees of freedom and is much better behaved. GMM on a few robust moments avoids committing to either.
   5. Practical points worth raising: MLE can be biased in small samples even when consistent, the classic example being the variance estimator with n rather than n minus 1 in the denominator. And numerically you should always check the Hessian at the optimum, because a flat likelihood means your parameter is not identified, which is common in GARCH and regime models.

   Where candidates lose it

   Describing MLE as the best estimator without the qualifier if the model is correctly specified. That caveat is the entire content of the comparison. Also be ready for the small-sample bias point, since MLE being biased while still consistent catches people who have only memorised the asymptotic properties.

   Expect next

   • Give me an example where MLE is biased.
   • What is the Cramer-Rao bound?
   • How would you fit a Student t to returns, and what does the estimated degrees of freedom tell you?
6. 057What does stationarity mean, how do you test for it, and why do you care?Time seriesIntermediatetechnicalQuant researchRisk

   Say this

   Weak stationarity means constant mean, constant variance and an autocovariance that depends only on the lag. You care because the standard inference machinery assumes it, and regressing non-stationary series on each other produces spurious relationships with impressive t statistics.

   Then walk it

   1. Prices are not stationary, they are close to a random walk with a unit root. Returns are much closer to stationary, which is why every model works on returns and not on levels.
   2. Tests: augmented Dickey-Fuller and Phillips-Perron test the null of a unit root, KPSS tests the null of stationarity. Run both, because they have opposite nulls and agreeing tests are more convincing than either alone. And these tests have low power, so failing to reject is weak evidence.
   3. Spurious regression is the cost of getting it wrong. Regress one independent random walk on another and you reject the null of no relationship far more often than five percent of the time, with an R squared that looks respectable. Granger and Newbold showed this in 1974 and people still do it.
   4. The exception that matters for trading: cointegration. Two non-stationary series can have a stationary linear combination, which is precisely the statistical statement of a pair trade. Test it with Engle-Granger or Johansen, and then the correct specification is an error-correction model rather than a regression in levels.
   5. The practical honesty: financial series are not stationary even in returns, because volatility and correlation regimes shift. So I treat stationarity as a working approximation over a limited window, and I check parameter stability across subsamples rather than trusting one test on the full history.

   Where candidates lose it

   Answering just difference it until the test passes. Over-differencing destroys the signal, and a cointegrated pair loses its whole tradeable relationship if you difference both series. Say what stationarity buys you, name the spurious regression result, and bring up cointegration unprompted since it is where the money is.

   Expect next

   • What is cointegration and how does it differ from correlation?
   • How do you test it, and what is an error-correction model?
   • What if a series is stationary in one decade and not the next?
7. 058Daily equity returns are not normal. How are they different, and what do you do about it?StatisticsIntermediatetechnicalQuant researchRisk

   Say this

   They have fat tails, negative skew and volatility clustering. Daily equity index kurtosis is typically 5 to 10 against 3 for a normal, so moves the normal says should happen once a century happen every few years.

   Then walk it

   1. Put a number on it. A normal assigns a five standard deviation daily move a probability of about one in 3.5 million, roughly once in 14,000 years of trading. The S&P has had several since 1950. The tails are not slightly wrong, they are wrong by orders of magnitude.
   2. Negative skew: large down moves are bigger and faster than large up moves. That is why index option skew exists and why puts are persistently richer than calls in implied vol terms.
   3. Volatility clustering means part of the unconditional fat tail is a mixture effect. Returns standardised by a GARCH-type conditional volatility are much closer to normal, though still fat-tailed, which tells you some but not all of the kurtosis is time-varying vol rather than genuinely fat conditional tails.
   4. What I would do depends on the use. For risk: empirical quantiles, a Student t or a generalised Pareto fit to the tail via extreme value theory, and expected shortfall rather than value at risk, because expected shortfall is sensitive to how bad the tail is. For pricing: a model with jumps or stochastic volatility rather than plain Black-Scholes.
   5. And the aggregation point: monthly returns are considerably closer to normal than daily returns because of the CLT, so the right distributional assumption depends on your horizon. That is worth saying because it stops the conversation becoming a generic tails are fat sermon.

   Where candidates lose it

   Saying fat tails and stopping. Quantify it, because the five sigma comparison is what makes the point land. Also do not forget the skew, since symmetric fat tails would not explain the option skew, and be ready to distinguish unconditional fat tails from conditional heteroskedasticity.

   Expect next

   • How much of the kurtosis is explained by volatility clustering?
   • What is expected shortfall and why prefer it to value at risk?
   • How does this show up in the option surface?
8. 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?
9. 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?
10. 068Why do market makers widen their quotes before a scheduled event like an earnings release or a central bank decision?Market makingIntermediatetechnicalProp trading firmsQuant trading

    Say this

    Because both of their costs spike at once. Expected volatility over the holding period jumps, and the probability that whoever trades with them is better informed jumps too. Wider spreads are the price of continuing to quote into that.

    Then walk it

    1. Inventory risk: any position you hold through the release is exposed to a gap, not a diffusion. You cannot hedge or unwind through the print, so the relevant horizon volatility is much larger.
    2. Adverse selection: more participants have a view, some have better information or faster access to the number, and the flow immediately before a release is disproportionately informed.
    3. You can see it in the options market directly. Implied volatility on the expiry that spans the event is elevated, and it collapses the moment the number is out. That is the volatility crush, and it is a pure statement about event risk being priced.
    4. The usual sequence is widen, then reduce size, then in the final seconds many makers pull quotes entirely, which is why the book gets thin right before a Fed statement and depth collapses.
    5. The interesting trade is on the other side of it. If you think the market is overpaying for the event, you sell that volatility, but the position has a short gamma profile through a gap, so you size it for the tail and not for the expected move. Saying that shows you understand why a wide quote is a risk decision and not just a fee increase.

    Where candidates lose it

    Answering only because volatility is higher. Half the answer is adverse selection, and the interviewer is listening for both. Also be ready to connect it to the options market, since the implied vol term structure around an event is the same phenomenon priced explicitly.

    Expect next

    • What happens to implied volatility right after the print?
    • Would you rather be long or short gamma into the event?
    • Why does the order book get thin rather than just wide?

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.