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. 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?
3. 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?
4. 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?
5. 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.

6. 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.