Systematic & Data-Driven Trading Interview Questions for Quant Researchers
The same round is marked differently depending on the seat you are interviewing for. This is the systematic & data-driven trading set as it applies to quant researchers.
300 questions, all free to practise. The split is 46 easy, 158 medium, 96 hard. The topics that come up most are probability (67), statistics (65), random variables (61), combinatorics (54).
- A coin that branches into a dieEasyCombinatoricsExpected ValueView →
- A race between two small-angle ratesEasyCalculusView →
- All the squares on a chessboardEasyCombinatoricsBrainteasersView →
- Angle under an orthogonal mapEasyLinear AlgebraView →
- Correlation under rescalingEasyRandom VariablesStatisticsView →
- Counting complement pairsEasyProgramming & DSAView →
- Covariance of a chi-square and a ratioEasyRandom VariablesStatisticsView →
- Covariance of summed Brownian motionsEasyStochastic ProcessesView →
- Determinant after antisymmetrizingEasyProbabilityLinear AlgebraView →
- Determinant from trace and one eigenvalueEasyLinear AlgebraView →
- Determinant of a scaled productEasyLinear AlgebraView →
- Diagonal parameter from a triangular determinantEasyLinear AlgebraView →
- Eigenvalues of a 2×2 matrixEasyLinear AlgebraView →
- Even numbers, distinct digitsEasyCombinatoricsView →
- Even-size, non-empty subsetEasyProbabilityCombinatoricsView →
- Exactly one clears two-thirdsEasyProbabilityRandom VariablesView →
- Interquartile range of an exponentialEasyRandom VariablesStatisticsView →
- Largest eigenvalue after squaringEasyLinear AlgebraView →
- Largest possible covarianceEasyRandom VariablesStatisticsView →
- MISSISSIPPI with the P's togetherEasyCombinatoricsView →
- Maximum of four uniforms in a bandEasyProbabilityRandom VariablesView →
- Multiplications saved by Horner's methodEasyProgramming & DSAView →
- No heads in a random number of flipsEasyProbabilityRandom VariablesView →
- Norm after imposing orthogonalityEasyLinear AlgebraView →
- Parameter values for a singular matrixEasyLinear AlgebraView →
- Pooling two independent estimatesEasyRandom VariablesStatisticsView →
- Posterior from a likelihood ratioEasyConditional Probability & ExpectationStatisticsView →
- R-squared from the sums of squaresEasyStatisticsView →
- R-squared when you duplicate every pointEasyStatisticsView →
- Regressing with zero covarianceEasyRandom VariablesStatisticsView →
- Sample SD with Bessel's correctionEasyStatisticsView →
- Second moment from varianceEasyRandom VariablesStatisticsView →
- Sharing your weekday of birthEasyProbabilityView →
- Sharpe of two combined uncorrelated strategiesEasyStatisticsFinance & DerivativesView →
- Skewness of a Laplace variableEasyRandom VariablesStatisticsView →
- Standard deviation of a correlated sumEasyRandom VariablesStatisticsView →
- Sum of cubed eigenvaluesEasyLinear AlgebraView →
- Sum of the OLS coefficientsEasyStatisticsView →
- Three-one strings with matching endpointsEasyCombinatoricsView →
- Two ordering constraints at onceEasyProbabilityCombinatoricsView →
- Two searches, neither hitsEasyRandom VariablesView →
- Upper bound on a dry weekendEasyProbabilityView →
- Variance of a sum of Brownian motionEasyStochastic ProcessesView →
- Weighting a fixed sumEasyConditional Probability & ExpectationExpected ValueView →
- Where the arrivals landEasyProbabilityStochastic ProcessesView →
- Where x squared log x bottoms outEasyCalculusView →
- 25 horses, 5 tracksMediumBrainteasersView →
- A CLT tail probabilityMediumStatisticsView →
- A Cholesky diagonal entryMediumLinear AlgebraView →
- A Gram–Schmidt R entryMediumLinear AlgebraView →
- A cube ending in elevenMediumProbabilityBrainteasersView →
- A cube root by tangent lineMediumCalculusView →
- A difference of three normalsMediumRandom VariablesStatisticsView →
- A divergent reciprocal expectationMediumRandom VariablesCalculusView →
- A mean-reverting processMediumStochastic ProcessesFinance & DerivativesView →
- A ratio of gamma valuesMediumRandom VariablesView →
- A stationary probabilityMediumStochastic ProcessesView →
- A tenth power of a matrixMediumLinear AlgebraView →
- A two-step transitionMediumStochastic ProcessesView →
- All six faces (coupon collector)MediumRandom VariablesExpected ValueView →
- An ant returning to its cornerMediumExpected ValueStochastic ProcessesView →
- Arbitraging a mispriced forward loanMediumFinance & DerivativesView →
- Arc length of a curveMediumCalculusView →
- Arrivals before the rival streamMediumProbabilityStochastic ProcessesView →
- Average salary, kept privateMediumBrainteasersStatisticsView →
- Back out the market premium, then price a stockMediumStatisticsFinance & DerivativesView →
- Balanced parenthesesMediumCombinatoricsProgramming & DSAView →
- Bayes: did it rain?MediumConditional Probability & ExpectationStatisticsView →
- Best linear blend of two estimatesMediumRandom VariablesStatisticsView →
- Boy–girl neighbors in a lineMediumCombinatoricsExpected ValueView →
- Classify critical points of x^3 - 3xMediumCalculusView →
- Condition numberMediumLinear AlgebraView →
- Conditional mean on a circleMediumConditional Probability & ExpectationRandom VariablesView →
- Conditioning Brownian motion on its futureMediumStochastic ProcessesView →
- Confidence interval with the right pivotMediumStatisticsView →
- Convexity correction signMediumFinance & DerivativesView →
- Correlation of two face-countsMediumProbabilityStatisticsView →
- Cosine of a conditional meanMediumProbabilityConditional Probability & ExpectationView →
- Covariance from a triangular densityMediumRandom VariablesStatisticsView →
- Covariance of a Poisson processMediumStochastic ProcessesView →
- Covariance of sum and differenceMediumRandom VariablesStatisticsView →
- Deleting every other number on a circleMediumCombinatoricsBrainteasersView →
- Density of a sum of two uniformsMediumProbabilityRandom VariablesView →
- Derangements of four itemsMediumCombinatoricsView →
- Derivative of xˣMediumCalculusView →
- Determinant of a 3×3MediumLinear AlgebraView →
- Determinant of a compound expressionMediumLinear AlgebraView →
- Determinant of an orthogonal matrixMediumLinear AlgebraView →
- Digits of concatenated powersMediumBrainteasersView →
- Disease test (Bayes)MediumConditional Probability & ExpectationStatisticsView →
- Distinct faces in five rollsMediumCombinatoricsExpected ValueView →
- Distinct faces in three rollsMediumExpected ValueView →
- E[X | X > 0] for a standard normalMediumStatisticsCalculusView →
- Eigenvalues of a projectionMediumLinear AlgebraView →
- Eigenvalues of a rotationMediumLinear AlgebraView →
- Enlarging a square orchardMediumBrainteasersView →
- Equivalent continuously-compounded rateMediumFinance & DerivativesView →
- Euclid's worst-case step countMediumProgramming & DSAView →
- Expected ascents in a shuffleMediumCombinatoricsExpected ValueView →
- Expected flips for HHMediumRandom VariablesExpected ValueView →
- Expected gap between two normalsMediumRandom VariablesView →
- Expected gap on 30-sided diceMediumProbabilityExpected ValueView →
- Expected square of a random unit complex numberMediumProbabilityRandom VariablesView →
- Expected sum of a random subsetMediumExpected ValueView →
- Expected value of a mean-reverting processMediumStochastic ProcessesView →
- Finite-difference stabilityMediumFinance & DerivativesProgramming & DSAView →
- First passage to ±1MediumStochastic ProcessesView →
- Forward vs. futures priceMediumFinance & DerivativesView →
- Fourth moment of a shifted normalMediumProbabilityRandom VariablesView →
- Gambler's ruinMediumProbabilityStochastic ProcessesView →
- Gap between two uniformsMediumExpected ValueStatisticsView →
- Growth rate of a rank-one eigenvalueMediumLinear AlgebraView →
- Guess 2/3 of the averageMediumMarket Making & Betting GamesView →
- How explosive is naive Fibonacci?MediumProgramming & DSAView →
- How fast is the balloon growing?MediumCalculusView →
- How large can the off-diagonal be?MediumLinear AlgebraView →
- How many trials to poll a proportionMediumRandom VariablesStatisticsView →
- How much a control variate helpsMediumFinance & DerivativesProgramming & DSAView →
- Kelly sizing on an asymmetric betMediumMarket Making & Betting GamesView →
- Largest eigenvalue of a rank-one updateMediumLinear AlgebraView →
- Largest pen against a riverMediumCalculusView →
- Letters into envelopesMediumProbabilityExpected ValueView →
- Log-dynamics of a geometric Brownian motionMediumStochastic ProcessesView →
- Macaulay duration of a coupon bondMediumFinance & DerivativesView →
- Marking a seasoned forwardMediumFinance & DerivativesView →
- Maximum rate of increaseMediumLinear AlgebraCalculusView →
- Maximum variance on an intervalMediumRandom VariablesStatisticsView →
- Mean value theorem for x^2MediumCalculusView →
- Median of a linear densityMediumRandom VariablesCalculusView →
- Median of a list and its squaresMediumCombinatoricsStatisticsView →
- Memoryless waitingMediumConditional Probability & ExpectationRandom VariablesView →
- Minimum-variance portfolio weightMediumStatisticsFinance & DerivativesView →
- Minimum-variance weightsMediumStatisticsFinance & DerivativesView →
- Multiplications in fast exponentiationMediumProgramming & DSAView →
- Newton's division-free reciprocalMediumCalculusView →
- No two neighboring bulbs litMediumProbabilityCombinatoricsView →
- Non-attacking rooksMediumCombinatoricsView →
- Norm of a doubly-stochastic stationary vectorMediumLinear AlgebraStochastic ProcessesView →
- Nullity of a concrete matrixMediumLinear AlgebraView →
- One hundred light bulbsMediumBrainteasersView →
- Onto functionsMediumCombinatoricsView →
- Positive semidefinitenessMediumStatisticsLinear AlgebraView →
- Power iterationMediumLinear AlgebraProgramming & DSAView →
- Power of three in a factorialMediumCombinatoricsView →
- Projecting onto a lineMediumLinear AlgebraView →
- Quickselect average complexityMediumProgramming & DSAView →
- Rank and nullity of a rotationMediumLinear AlgebraView →
- Ratio of partial sumsMediumRandom VariablesExpected ValueView →
- Reading an R²MediumStatisticsView →
- Rebuilding a tower of ten ringsMediumBrainteasersProgramming & DSAView →
- Recovering an eigenvector from its eigenvalueMediumLinear AlgebraView →
- Regression to the meanMediumBrainteasersStatisticsView →
- Renewal-reward fraction of time runningMediumExpected ValueStochastic ProcessesView →
- Resonance in undetermined coefficientsMediumCalculusView →
- Return time from a three-state chainMediumStochastic ProcessesView →
- Right angles in 12 hoursMediumBrainteasersView →
- Risk-neutral up probabilityMediumStochastic ProcessesFinance & DerivativesView →
- Sampling an exponential from a uniformMediumRandom VariablesProgramming & DSAView →
- Screening a rare diseaseMediumConditional Probability & ExpectationStatisticsView →
- Second moment via the MGFMediumRandom VariablesCalculusView →
- Short-rate modelsMediumStochastic ProcessesFinance & DerivativesView →
- Singular values via AᵀAMediumLinear AlgebraView →
- Sizing an index-futures hedge in contractsMediumStatisticsFinance & DerivativesView →
- Spam filterMediumProbabilityConditional Probability & ExpectationView →
- Spectrum of a constant-diagonal matrixMediumLinear AlgebraView →
- Spectrum of a symmetric matrixMediumStatisticsLinear AlgebraView →
- Squares on a chessboard, tilted ones includedMediumCombinatoricsBrainteasersView →
- Stationary distribution of a two-state chainMediumProbabilityStochastic ProcessesView →
- Subsets with no neighborsMediumCombinatoricsView →
- Sum and difference of perfectly correlated variablesMediumRandom VariablesStatisticsView →
- Sum of squared standard normalsMediumRandom VariablesStatisticsView →
- Sum of the pandigital numbersMediumCombinatoricsBrainteasersView →
- Swapping the regression variablesMediumStatisticsView →
- The Gaussian integralMediumCalculusView →
- The German tank problemMediumExpected ValueStatisticsView →
- The cab problemMediumProbabilityConditional Probability & ExpectationView →
- The first component to failMediumRandom VariablesView →
- The last lightbulb to burn outMediumRandom VariablesExpected ValueView →
- The painted cubeMediumBrainteasersView →
- The same number of tailsMediumProbabilityCombinatoricsView →
- Trace of A-transpose-AMediumLinear AlgebraView →
- Trace of a productMediumLinear AlgebraView →
- Trailing zeros of 100!MediumCombinatoricsView →
- Two positive testsMediumProbabilityConditional Probability & ExpectationView →
- Uncorrelated but dependentMediumRandom VariablesStatisticsView →
- Variance explained by a regressionMediumStatisticsLinear AlgebraView →
- Variance of a Brownian combinationMediumStochastic ProcessesView →
- Variance of a lognormalMediumRandom VariablesFinance & DerivativesView →
- Variance of a squared normalMediumRandom VariablesStatisticsView →
- Variance of a time-weighted Itô integralMediumCalculusStochastic ProcessesView →
- Variance of a two-regime returnMediumRandom VariablesStatisticsView →
- Variance of hearts in eight cardsMediumCombinatoricsStatisticsView →
- Variance of integrated Brownian motionMediumStochastic ProcessesView →
- Variance of the larger of two diceMediumRandom VariablesStatisticsView →
- Variance-minimizing hedgeMediumProbabilityStatisticsView →
- What 'unbiased' meansMediumStatisticsView →
- When the naive shuffle is biasedMediumProgramming & DSAView →
- Which machine made the defect?MediumConditional Probability & ExpectationStatisticsView →
- Why covariance matrices are PSDMediumStatisticsLinear AlgebraView →
- Will they meet?MediumProbabilityView →
- Winning from deuceMediumProbabilityConditional Probability & ExpectationView →
- X positive given the sum is positiveMediumProbabilityRandom VariablesView →
- k-th order statisticMediumExpected ValueStatisticsView →
- x^4 coefficient of a composed seriesMediumCalculusView →
- A 12 before two 7sHardProbabilityStochastic ProcessesView →
- A function minus its derivativeHardCalculusView →
- A geometric series that sums to a squareHardBrainteasersView →
- A half-plane, given positiveHardProbabilityRandom VariablesView →
- A rectangle over the shaded rowHardProbabilityCombinatoricsView →
- A telescoping partial-fraction sumHardCalculusView →
- A weighted sum of binomialsHardCombinatoricsBrainteasersView →
- Absorption in naive floating-point summationHardCalculusProgramming & DSAView →
- Ages from product and sumHardCombinatoricsBrainteasersView →
- Amoeba extinctionHardProbabilityStochastic ProcessesView →
- Average of near-diagonal numbersHardCombinatoricsBrainteasersView →
- Bertrand's chordHardProbabilityBrainteasersView →
- Blue-eyed islandersHardBrainteasersView →
- Branching process extinction (supercritical)HardProbabilityStochastic ProcessesView →
- Broken-stick triangleHardProbabilityView →
- Buffon's needleHardProbabilityCalculusView →
- Cars advancing to the endHardProbabilityExpected ValueView →
- Conditioning a Brownian bridgeHardStochastic ProcessesView →
- Correlation of min and maxHardProbabilityRandom VariablesView →
- Covariance of X with Y squaredHardRandom VariablesStatisticsView →
- Cuts until one orb remainsHardProbabilityExpected ValueView →
- Cycles in a shuffleHardCombinatoricsExpected ValueView →
- Digits with distinct pairwise sumsHardCombinatoricsBrainteasersView →
- Distinct toys from seven boxesHardProbabilityExpected ValueView →
- Doors toggled by primesHardCombinatoricsBrainteasersView →
- Draws to beat a hidden uniformHardRandom VariablesExpected ValueView →
- Draws to pass a log thresholdHardProbabilityRandom VariablesView →
- Draws to pass twoHardProbabilityRandom VariablesView →
- Draws until a smaller valueHardExpected ValueView →
- Ehrenfest urn stationary distributionHardProbabilityStochastic ProcessesView →
- Expected arc covering a fixed pointHardProbabilityExpected ValueView →
- Expected duration of a fair walkHardExpected ValueStochastic ProcessesView →
- Expected largest of ten ballsHardCombinatoricsExpected ValueView →
- Expected revisits of the start stateHardExpected ValueStochastic ProcessesView →
- Exponential martingale compensatorHardCalculusStochastic ProcessesView →
- Handshakes at a dinner partyHardCombinatoricsBrainteasersView →
- Hats with 100 colorsHardBrainteasersView →
- Head density with no two in a rowHardProbabilityCombinatoricsView →
- Hitting zero on a ringHardProbabilityStochastic ProcessesView →
- Inverse via Cayley–HamiltonHardLinear AlgebraView →
- Laplace's rule of successionHardProbabilityConditional Probability & ExpectationView →
- Last one standingHardCombinatoricsBrainteasersView →
- Locks for a four-of-seven safeHardCombinatoricsBrainteasersView →
- Long cycles in a random permutationHardCombinatoricsExpected ValueView →
- Loops from tying noodlesHardProbabilityExpected ValueView →
- Making change in lineHardCombinatoricsStochastic ProcessesView →
- Mean of a mean-reverting processHardStochastic ProcessesFinance & DerivativesView →
- Median of a streamHardStatisticsProgramming & DSAView →
- Minimum coins where greedy failsHardProgramming & DSAView →
- No two samples too closeHardProbabilityCombinatoricsView →
- Odd sums on a 3×3 gridHardProbabilityCombinatoricsView →
- Only seven left unchosenHardProbabilityCombinatoricsView →
- Optional stopping between +3 and −5HardExpected ValueStochastic ProcessesView →
- Order statistics are BetaHardRandom VariablesStatisticsView →
- Overshoot past oneHardProbabilityRandom VariablesView →
- Pairing gloves within oneHardProbabilityCombinatoricsView →
- Pairing with a difference of 1 or 11HardCombinatoricsBrainteasersView →
- Penalty kicks with a shifting rateHardProbabilityRandom VariablesView →
- Pricing an inverse floaterHardFinance & DerivativesView →
- Prisoners and the boxesHardProbabilityBrainteasersView →
- Quadratic variation in mean-squareHardStochastic ProcessesView →
- Quadratic variation of a scaled Itô integralHardCalculusStochastic ProcessesView →
- Range beats the midpointHardProbabilityRandom VariablesView →
- Reading N(d₂) in Black–ScholesHardFinance & DerivativesView →
- Reflected paths ending below the levelHardProbabilityStochastic ProcessesView →
- Repainting balls to one colorHardExpected ValueStochastic ProcessesView →
- Reservoir samplingHardStatisticsProgramming & DSAView →
- Rolls to a six, given all evenHardConditional Probability & ExpectationExpected ValueView →
- Rounds to see all faces with two diceHardProbabilityExpected ValueView →
- Runs of red and blue marblesHardCombinatoricsExpected ValueView →
- Shuffles to restore the deckHardCombinatoricsBrainteasersView →
- Smallest possible MGF valueHardRandom VariablesStatisticsView →
- Spread of a lognormal raised to the fourthHardRandom VariablesStatisticsView →
- Spread of a multinomial count gapHardRandom VariablesStatisticsView →
- Subsets with one consecutive pairHardCombinatoricsView →
- Sum of repeating decimalsHardCombinatoricsBrainteasersView →
- Ten prime digits with a set productHardCombinatoricsView →
- The decreasing run of uniformsHardRandom VariablesExpected ValueView →
- The drunk passengerHardProbabilityConditional Probability & ExpectationView →
- The racing camelsHardBrainteasersView →
- The two-envelopes paradoxHardProbabilityConditional Probability & ExpectationView →
- Three eggs, nine dropsHardCombinatoricsBrainteasersView →
- Triangle from three independent sticksHardProbabilityCalculusView →
- Two Brownian values, both positiveHardProbabilityStochastic ProcessesView →
- Two Newton iterations for a square rootHardCalculusProgramming & DSAView →
- Two coprime integersHardProbabilityCombinatoricsView →
- Two eggs, 100 floorsHardBrainteasersView →
- Two elements in the long cycleHardProbabilityCombinatoricsView →
- Two walks returning togetherHardProbabilityCombinatoricsView →
- Two-color necklacesHardCombinatoricsView →
- Uniforms summing past 1HardRandom VariablesExpected ValueView →
- Variance of an Itô integralHardStochastic ProcessesView →
- Variance of the exponential of a gammaHardRandom VariablesStatisticsView →
- Variance under random parametersHardRandom VariablesStatisticsView →
- When k-to-the-k is a squareHardCombinatoricsBrainteasersView →
- When the extremes sum above oneHardProbabilityRandom VariablesView →
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