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. 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?
2. 052Explain the bias-variance tradeoff, and where a quant strategy usually sits on it.Machine learningCoretechnicalQuant researchQuant development

   Say this

   Expected prediction error decomposes into squared bias, variance and irreducible noise. Bias is how wrong your model class is on average, variance is how much your fit moves with a different sample. In financial data the noise term dominates everything, so you sit far towards the high-bias, low-variance end.

   Then walk it

   1. The decomposition: E of (y minus f hat) squared equals bias squared plus variance plus sigma squared. Only the first two are under your control.
   2. Flexible models cut bias and raise variance. A deep tree fits any shape and moves wildly with resampling. A linear model with three factors barely moves but cannot represent an interaction.
   3. The financial context is what makes the answer different from a generic machine learning answer. Signal-to-noise on returns is tiny, sigma squared swamps the other terms, and a flexible model spends all its capacity fitting noise. So simple, heavily regularised, few-parameter models win out of sample far more often than they should on pure machine learning intuition.
   4. How you find your place on the curve: cross-validation that respects the time ordering, learning curves, and watching the gap between in-sample and out-of-sample performance. If the gap is large you are on the variance side.
   5. One honest complication: the classic U-shaped curve is not the whole story. Very overparameterised models can show double descent, where test error falls again past the interpolation threshold. That is real in vision and language. I have not seen it be useful on noisy financial data, where the tiny signal means regularisation still dominates.

   Where candidates lose it

   Giving the textbook decomposition with no view on where financial data sits. Every candidate can recite bias plus variance. The differentiator is saying that low signal-to-noise pushes you towards simple models, and being able to say how you would diagnose which side you are on.

   Expect next

   • How would you diagnose which side of the tradeoff you are on?
   • Why do simple models often win on financial data?
   • What is double descent?
3. 053How would you cross-validate a model on time series data, and why is standard k-fold wrong?Time seriesHardtechnicalQuant researchQuant trading

   Say this

   Standard k-fold trains on data that comes after your test set, which leaks the future. You need a forward-walking scheme: train on a window, test on the next block, roll forward, and put a gap between train and test so overlapping labels do not bleed across the boundary.

   Then walk it

   1. Two distinct leaks. First, random folds put future observations in the training set, so the model learns things it could not have known. Second, features and labels are usually built from overlapping windows, so even adjacent-in-time observations share information across a fold boundary.
   2. The fix for the first is walk-forward or expanding-window validation: fit on 1 to t, test on t plus 1 to t plus h, roll. Expanding window mimics how you would actually retrain in production. A fixed rolling window is better if the process is non-stationary.
   3. The fix for the second is purging and embargoing, from Lopez de Prado. Remove training observations whose label window overlaps the test period, and embargo a short period immediately after the test block. On a 20-day forward return label you need at least a 20-day purge.
   4. Also beware the hidden leaks that sit outside the folds entirely: fitting a scaler, doing feature selection, or choosing hyperparameters on the full dataset before splitting. Every preprocessing step has to sit inside the fold.
   5. What I would actually report, and this is the part that matters: one final untouched hold-out period tested once, plus how many configurations I tried before I got there. Walk-forward validation run a hundred times is itself an overfitting device, and the number of trials is the honest measure of how much to discount the result.

   Where candidates lose it

   Saying you would use k-fold with shuffle turned off and stopping there. That fixes the ordering but not the overlapping-label leak, and interviewers at systematic shops probe exactly that. Mention purging and embargo, and mention that scalers and feature selection must live inside the fold.

   Expect next

   • How long should the embargo be?
   • Expanding window or fixed rolling window, and why?
   • How do you account for the number of configurations you tried?
4. 054What does PCA do, how do you choose the number of components, and what are its limitations on financial data?Machine learningCoretechnicalQuant researchRisk

   Say this

   It finds the orthogonal directions of maximum variance, which are the eigenvectors of the covariance matrix, and lets you describe the data with fewer numbers. Choose the number of components by explained variance, a scree elbow, or the Marchenko-Pastur bulk edge if you want a principled cutoff.

   Then walk it

   1. Mechanically: eigendecompose the covariance or correlation matrix, or take the SVD of the centred data. Eigenvalues are the variance along each component, eigenvectors are the directions.
   2. Correlation versus covariance matters. On assets with wildly different volatilities, PCA on the covariance matrix is dominated by the most volatile names, so standardise first unless the scale is meaningful.
   3. Concrete example everyone in rates knows: PCA on the yield curve gives level, slope and curvature, explaining roughly 90, 8 and 2 percent of variance. On equities the first component is the market, explaining 25 to 40 percent depending on the regime, and it rises sharply in a crisis.
   4. Choosing k: cumulative explained variance at 90 or 95 percent, the scree elbow, or eigenvalues above the random matrix bulk edge, which is the statistically defensible version because it separates signal from estimation noise.
   5. Limitations, and these are the answer to the real question. PCA maximises variance, not predictive power, so the components need not have anything to do with your target. It is unstable: eigenvectors rotate sample to sample when eigenvalues are close, so your factor two and factor three swap places. It assumes linearity. And the components are usually uninterpretable outside a structured setting like the yield curve, which makes them awkward to risk-manage.

   Where candidates lose it

   Describing PCA as dimensionality reduction and stopping. Two things get graded: that it is unsupervised so high-variance directions are not necessarily predictive, and that you must standardise when scales differ. Also have a real example ready, because level-slope-curvature or the equity market factor proves you have used it rather than read about it.

   Expect next

   • Why is PCA not necessarily good for prediction?
   • What does the first principal component of an equity universe represent, and what happens to it in a crisis?
   • How is PCA related to a factor risk model?
5. 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?
6. 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?
7. 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?
8. 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?
9. 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?
10. 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.

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.