Hedge Fund Quant Interview Questions for Quant Researchers
The same round is marked differently depending on the seat you are interviewing for. This is the hedge fund quant set as it applies to quant researchers.
288 questions, all free to practise. The split is 36 easy, 178 medium, 74 hard. The topics that come up most are probability (79), combinatorics (59), statistics (57), random variables (46).
- A divisor of a power of tenEasyProbabilityCombinatoricsView →
- A multiple of 15 in ones and zerosEasyBrainteasersView →
- A ratio of Fibonacci sumsEasyBrainteasersView →
- A two-sigma tail probabilityEasyRandom VariablesStatisticsView →
- Age in a square yearEasyBrainteasersView →
- American early exerciseEasyFinance & DerivativesView →
- An odd subset with two small elementsEasyCombinatoricsView →
- Angle under an orthogonal mapEasyLinear AlgebraView →
- Break-even move after a round tripEasyFinance & DerivativesView →
- Chi-square test for a varianceEasyStatisticsView →
- Color switches in a drawEasyRandom VariablesExpected ValueView →
- Counting 8-bit stringsEasyCombinatoricsView →
- Counting nines to 1000EasyCombinatoricsBrainteasersView →
- Covariance of a chi-square and a ratioEasyRandom VariablesStatisticsView →
- Covariance of summed Brownian motionsEasyStochastic ProcessesView →
- Determinant after antisymmetrizingEasyProbabilityLinear AlgebraView →
- Even numbers, distinct digitsEasyCombinatoricsView →
- Integers that contain a zeroEasyCombinatoricsBrainteasersView →
- Interquartile range of an exponentialEasyRandom VariablesStatisticsView →
- MISSISSIPPI with the P's togetherEasyCombinatoricsView →
- Matching a uniform and an exponentialEasyRandom VariablesStatisticsView →
- Norm after imposing orthogonalityEasyLinear AlgebraView →
- Paid a dollar or the drawEasyExpected ValueStatisticsView →
- 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 →
- Skewness of a Laplace variableEasyRandom VariablesStatisticsView →
- Solving a linear Diophantine equationEasyBrainteasersView →
- Standard deviation of a correlated sumEasyRandom VariablesStatisticsView →
- Sum of cubed eigenvaluesEasyLinear AlgebraView →
- Sum of the OLS coefficientsEasyStatisticsView →
- The added babyEasyProbabilityConditional Probability & ExpectationView →
- Upper bound on a dry weekendEasyProbabilityView →
- Variance of a sum of Brownian motionEasyStochastic ProcessesView →
- Where x squared log x bottoms outEasyCalculusView →
- 25 horses, 5 tracksMediumBrainteasersView →
- A Gram–Schmidt R entryMediumLinear AlgebraView →
- A difference of three normalsMediumRandom VariablesStatisticsView →
- A limit via the cosine seriesMediumCalculusView →
- A mean-reverting processMediumStochastic ProcessesFinance & DerivativesView →
- A tenth power of a matrixMediumLinear AlgebraView →
- A two-step transitionMediumStochastic ProcessesView →
- Absorption probability on a lineMediumProbabilityStochastic ProcessesView →
- Aces in a seven-card handMediumCombinatoricsExpected ValueView →
- Adults before the busMediumBrainteasersView →
- Age a fraction of the birth yearMediumBrainteasersView →
- All six faces (coupon collector)MediumRandom VariablesExpected ValueView →
- An ace in the handMediumProbabilityCombinatoricsView →
- Anagrams of LOLLIPOPMediumCombinatoricsView →
- At least two sixes in five rollsMediumProbabilityRandom VariablesView →
- Average salary, kept privateMediumBrainteasersStatisticsView →
- Back out the market premium, then price a stockMediumStatisticsFinance & DerivativesView →
- Backing out a correlationMediumRandom VariablesStatisticsView →
- Bayes: did it rain?MediumConditional Probability & ExpectationStatisticsView →
- Bertrand's boxMediumProbabilityConditional Probability & ExpectationView →
- By parts over an infinite tailMediumCalculusView →
- Cheapest open-top boxMediumCalculusView →
- Classify critical points of x^3 - 3xMediumCalculusView →
- CompositionsMediumCombinatoricsView →
- Condition numberMediumLinear AlgebraView →
- Conditional mean on a circleMediumConditional Probability & ExpectationRandom VariablesView →
- Conditioning Brownian motion on its futureMediumStochastic ProcessesView →
- Confidence interval with the right pivotMediumStatisticsView →
- Conversion arbitrage from a parity violationMediumFinance & DerivativesView →
- Convexity correction signMediumFinance & DerivativesView →
- Correlation of two face-countsMediumProbabilityStatisticsView →
- Counting straightsMediumProbabilityCombinatoricsView →
- Covariance from a triangular densityMediumRandom VariablesStatisticsView →
- Covariance of a Poisson processMediumStochastic ProcessesView →
- Density of a uniform squaredMediumRandom VariablesCalculusView →
- Determinant of a 3×3MediumLinear AlgebraView →
- Determinant of a compound expressionMediumLinear AlgebraView →
- Determinant of an orthogonal matrixMediumLinear AlgebraView →
- Dice game, up to three rollsMediumExpected ValueStochastic ProcessesView →
- Disease test (Bayes)MediumConditional Probability & ExpectationStatisticsView →
- Distinct birthdays representedMediumProbabilityExpected ValueView →
- Distinct die labelingsMediumCombinatoricsBrainteasersView →
- Diversified VaR of two positionsMediumStatisticsFinance & DerivativesView →
- Duration-plus-convexity price moveMediumFinance & DerivativesView →
- E[X | X > 0] for a standard normalMediumStatisticsCalculusView →
- Eigenvalues of a rotationMediumLinear AlgebraView →
- Expectation as a sum of tailsMediumRandom VariablesExpected ValueView →
- Expected absolute difference of two diceMediumExpected ValueView →
- Expected duration of a fair gameMediumExpected ValueStochastic ProcessesView →
- Expected flips for HHMediumRandom VariablesExpected ValueView →
- Expected rolls for two sixes in a rowMediumExpected ValueStochastic ProcessesView →
- Expected square of a random unit complex numberMediumProbabilityRandom VariablesView →
- Expected sum given both evenMediumConditional Probability & ExpectationExpected ValueView →
- Finite-difference stabilityMediumFinance & DerivativesProgramming & DSAView →
- First to roll a sixMediumProbabilityView →
- Five distinct ranksMediumProbabilityCombinatoricsView →
- Four points on a semicircleMediumProbabilityView →
- Four times as long to the first headMediumProbabilityRandom VariablesView →
- Fourth moment of a shifted normalMediumProbabilityRandom VariablesView →
- Gambler's ruin (unfair)MediumProbabilityStochastic ProcessesView →
- Gamma and rehedging P&LMediumFinance & DerivativesView →
- 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 much a control variate helpsMediumFinance & DerivativesProgramming & DSAView →
- Identical balls, no empty boxMediumCombinatoricsView →
- Is W(t)³ a martingale?MediumStochastic ProcessesView →
- Is the random walk squared a martingale?MediumExpected ValueStochastic ProcessesView →
- Joint default rangeMediumProbabilityFinance & DerivativesView →
- Keeping two apartMediumCombinatoricsView →
- Largest eigenvalue of a rank-one updateMediumLinear AlgebraView →
- Last two digits of a powerMediumCombinatoricsBrainteasersView →
- Lattice paths in 3DMediumCombinatoricsView →
- Law of total varianceMediumConditional Probability & ExpectationExpected ValueView →
- Markov with a floorMediumStatisticsView →
- Max rectangle under a parabolaMediumCalculusView →
- Maximize x + y on the unit circleMediumLinear AlgebraCalculusView →
- Maximize xyz on a planeMediumCalculusView →
- Maximum of x^(1/x)MediumCalculusView →
- Maximum rate of increaseMediumLinear AlgebraCalculusView →
- Maximum variance on an intervalMediumRandom VariablesStatisticsView →
- Mean over variance of a nested uniformMediumProbabilityRandom VariablesView →
- Minimum of two exponentialsMediumProbabilityRandom VariablesView →
- Minimum-variance portfolio weightMediumStatisticsFinance & DerivativesView →
- Minimum-variance weightsMediumStatisticsFinance & DerivativesView →
- Monty HallMediumProbabilityConditional Probability & ExpectationView →
- Monty Hall with 100 doorsMediumProbabilityConditional Probability & ExpectationView →
- No two evens adjacentMediumCombinatoricsView →
- No two heads in a rowMediumProbabilityCombinatoricsView →
- No-arbitrage call boundsMediumFinance & DerivativesView →
- Norm of a doubly-stochastic stationary vectorMediumLinear AlgebraStochastic ProcessesView →
- Nullity of a concrete matrixMediumLinear AlgebraView →
- Number of runsMediumExpected ValueView →
- OLS slope from four pointsMediumStatisticsView →
- Odd multiples of threeMediumCombinatoricsBrainteasersView →
- Odd solutions to a sumMediumCombinatoricsView →
- One hundred animals for a thousand dollarsMediumBrainteasersView →
- One random subset inside anotherMediumProbabilityCombinatoricsView →
- Painted cube, one face showingMediumProbabilityBrainteasersView →
- Par swap rate definitionMediumFinance & DerivativesView →
- Placing operators among digitsMediumCombinatoricsView →
- Poisson thinning: exactly two large ordersMediumRandom VariablesView →
- Position of the first spadeMediumCombinatoricsExpected ValueView →
- Positive semidefinitenessMediumStatisticsLinear AlgebraView →
- Power iterationMediumLinear AlgebraProgramming & DSAView →
- Pricing a digital from a call spreadMediumFinance & DerivativesView →
- Pricing a squared payoffMediumExpected ValueMarket Making & Betting GamesView →
- Probability of three of a kindMediumProbabilityCombinatoricsView →
- Projecting onto a lineMediumLinear AlgebraView →
- Put–call parity with a dividendMediumFinance & DerivativesView →
- Quickselect average complexityMediumProgramming & DSAView →
- Rank–nullity dimension countMediumLinear AlgebraView →
- Reaching the target before ruinMediumStochastic ProcessesView →
- Reading an R²MediumStatisticsView →
- Recovering an eigenvector from its eigenvalueMediumLinear AlgebraView →
- Regions from ten linesMediumCombinatoricsBrainteasersView →
- Rehedging a book after a moveMediumFinance & DerivativesView →
- Russian roulette, re-spunMediumProbabilityConditional Probability & ExpectationView →
- 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 →
- Smallest simulable probabilityMediumProbabilityBrainteasersView →
- Spam filterMediumProbabilityConditional Probability & ExpectationView →
- Spectrum of a constant-diagonal matrixMediumLinear AlgebraView →
- Spectrum of a symmetric matrixMediumStatisticsLinear AlgebraView →
- Stationary distribution of a two-state chainMediumProbabilityStochastic ProcessesView →
- Subsets with no neighborsMediumCombinatoricsView →
- Sum and difference of perfectly correlated variablesMediumRandom VariablesStatisticsView →
- Sum of multinomial coefficientsMediumCombinatoricsView →
- Sum of squared standard normalsMediumRandom VariablesStatisticsView →
- Summing digits to a millionMediumCombinatoricsBrainteasersView →
- Swapping the regression variablesMediumStatisticsView →
- Ten dice, sum divisible by sixMediumProbabilityCombinatoricsView →
- Terms in a multinomial expansionMediumCombinatoricsView →
- The German tank problemMediumExpected ValueStatisticsView →
- The SDE of the reciprocalMediumStochastic ProcessesView →
- The cab problemMediumProbabilityConditional Probability & ExpectationView →
- The die that makes sums uniformMediumProbabilityCombinatoricsView →
- The first component to failMediumRandom VariablesView →
- The probability integral transformMediumRandom VariablesStatisticsView →
- The two black aces, side by sideMediumProbabilityCombinatoricsView →
- The two-headed coinMediumProbabilityConditional Probability & ExpectationView →
- Three mislabeled jarsMediumBrainteasersView →
- Three unlabeled teamsMediumCombinatoricsView →
- Three-four-five in Pascal's triangleMediumCombinatoricsBrainteasersView →
- Trailing zeros of 100!MediumCombinatoricsView →
- Tuning an exponential random walkMediumProbabilityStochastic ProcessesView →
- Two positive testsMediumProbabilityConditional Probability & ExpectationView →
- Two trains and a flyMediumBrainteasersView →
- Uncorrelated but dependentMediumRandom VariablesStatisticsView →
- Units digit of a random powerMediumProbabilityCombinatoricsView →
- Variance explained by a regressionMediumStatisticsLinear AlgebraView →
- Variance of a Brownian combinationMediumStochastic ProcessesView →
- Variance of a squared normalMediumRandom VariablesStatisticsView →
- Variance of a stochastic integralMediumProbabilityStochastic ProcessesView →
- Variance of a time-weighted Itô integralMediumCalculusStochastic ProcessesView →
- Variance of a two-regime returnMediumRandom VariablesStatisticsView →
- Variance of integrated Brownian motionMediumStochastic ProcessesView →
- Variance of the larger of two diceMediumRandom VariablesStatisticsView →
- Variance-minimizing hedgeMediumProbabilityStatisticsView →
- Volume of revolution of sqrt(x)MediumCalculusView →
- Weighing 1 to 40MediumBrainteasersView →
- What 'unbiased' meansMediumStatisticsView →
- What a p-value isMediumStatisticsView →
- Which coin produced two heads?MediumProbabilityConditional Probability & ExpectationView →
- Which desk books the larger dayMediumRandom VariablesStatisticsView →
- Which machine made the defect?MediumConditional Probability & ExpectationStatisticsView →
- Whose draw is larger?MediumProbabilityView →
- Why covariance matrices are PSDMediumStatisticsLinear AlgebraView →
- Why divide by n−1?MediumStatisticsView →
- Will they meet?MediumProbabilityView →
- X positive given the sum is positiveMediumProbabilityRandom VariablesView →
- x^4 coefficient of a composed seriesMediumCalculusView →
- A Fibonacci power sumHardBrainteasersView →
- A function minus its derivativeHardCalculusView →
- A half-plane, given positiveHardProbabilityRandom VariablesView →
- A second red ball from the same urnHardProbabilityConditional Probability & ExpectationView →
- A three-way race to the first headHardProbabilityRandom VariablesView →
- A void suit in bridgeHardProbabilityCombinatoricsView →
- Ages from product and sumHardCombinatoricsBrainteasersView →
- Amoeba extinctionHardProbabilityStochastic ProcessesView →
- An arithmetic-geometric seriesHardCalculusView →
- Balls into bowls, three eachHardCombinatoricsView →
- Best-of-seven underdogHardProbabilityRandom VariablesView →
- Blue-eyed islandersHardBrainteasersView →
- Branching process extinction (critical)HardProbabilityStochastic ProcessesView →
- Branching process extinction (supercritical)HardProbabilityStochastic ProcessesView →
- Connecting noodlesHardProbabilityExpected ValueView →
- Counting fives before a four and a sixHardProbabilityRandom VariablesView →
- Counting two-pair handsHardProbabilityCombinatoricsView →
- Covariance of X with Y squaredHardRandom VariablesStatisticsView →
- Covariance with a lognormal childHardConditional Probability & ExpectationRandom VariablesView →
- Dealing until kings or a king-and-aceHardCombinatoricsExpected ValueView →
- Defective stack of coinsHardCombinatoricsBrainteasersView →
- Deriving the first-price shading factorHardProbabilityExpected ValueView →
- Domino tilings of a 3×8 gridHardCombinatoricsView →
- Drunk man on a bridgeHardExpected ValueStochastic ProcessesView →
- Everyone gets one of eachHardProbabilityCombinatoricsView →
- Exactly one pairHardProbabilityCombinatoricsView →
- Expected flips for HHHHardExpected ValueStochastic ProcessesView →
- Expected flips for HTHHardExpected ValueStochastic ProcessesView →
- Expected revisits of the start stateHardExpected ValueStochastic ProcessesView →
- Filling three bins from a coin flipHardProbabilityCombinatoricsView →
- Four heads in a rowHardExpected ValueStochastic ProcessesView →
- Guessing cards from a known pileHardProbabilityExpected ValueView →
- HTH before HHTHardProbabilityRandom VariablesView →
- Handshakes at a dinner partyHardCombinatoricsBrainteasersView →
- Hats in a lineHardBrainteasersView →
- Laplace transform of a Brownian exit timeHardStochastic ProcessesView →
- Making a power of Brownian motion a martingaleHardStochastic ProcessesView →
- Mean of a mean-reverting processHardStochastic ProcessesFinance & DerivativesView →
- Median of a streamHardStatisticsProgramming & DSAView →
- Minimum coins where greedy failsHardProgramming & DSAView →
- More coins, more heads?HardProbabilityCombinatoricsView →
- One of each face before the two of heartsHardProbabilityCombinatoricsView →
- Order statistics are BetaHardRandom VariablesStatisticsView →
- Pirate gameHardMarket Making & Betting GamesView →
- Pricing an inverse floaterHardFinance & DerivativesView →
- Prisoners and the boxesHardProbabilityBrainteasersView →
- Quadratic variation of a scaled Itô integralHardCalculusStochastic ProcessesView →
- Reflected paths ending below the levelHardProbabilityStochastic ProcessesView →
- Reflecting wall first-passage timeHardExpected ValueStochastic ProcessesView →
- Rotations divisible by 37HardCombinatoricsBrainteasersView →
- Second moment of a Gaussian-kernel stochastic integralHardCalculusStochastic ProcessesView →
- Seven seated in age orderHardProbabilityCombinatoricsView →
- Smallest number with digit product 10000HardCombinatoricsBrainteasersView →
- Sums of fours and fivesHardCombinatoricsBrainteasersView →
- The all-pay auctionHardProbabilityExpected ValueView →
- The boy born on a TuesdayHardProbabilityConditional Probability & ExpectationView →
- The drunk passengerHardProbabilityConditional Probability & ExpectationView →
- The frog's single leftward hopHardProbabilityCombinatoricsView →
- The leap-frog's favorite landing spotHardProbabilityStochastic ProcessesView →
- The number with no new digitsHardBrainteasersView →
- The snow plowHardCalculusView →
- The survivor in the circleHardBrainteasersView →
- Three first-heads in non-decreasing orderHardProbabilityRandom VariablesView →
- Triangle from three independent sticksHardProbabilityCalculusView →
- Triangle that swallows the centerHardProbabilityBrainteasersView →
- Triangle with equal side sumsHardCombinatoricsBrainteasersView →
- Twelve balls, one oddHardBrainteasersView →
- Two Brownian values, both positiveHardProbabilityStochastic ProcessesView →
- Two eggs, 100 floorsHardBrainteasersView →
- Two random subsets that overlapHardProbabilityCombinatoricsView →
- Variance under random parametersHardRandom VariablesStatisticsView →
- When a power of the process is a submartingaleHardProbabilityStochastic ProcessesView →
- When a uniform ratio rounds to a squareHardProbabilityRandom VariablesView →
- World Series bettingHardExpected ValueStochastic ProcessesView →
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