Prop Trading Interview Questions for Quant Researchers
The same round is marked differently depending on the seat you are interviewing for. This is the prop trading set as it applies to quant researchers.
90 questions, 35 of them free to practise right now. The split is 13 easy, 72 medium, 5 hard. The topics that come up most are probability (21), calculus (18), random variables (15), statistics (15).
- A race between two small-angle ratesEasyCalculusView →
- A two-sigma tail probabilityEasyRandom VariablesStatisticsView →
- Chi-square test for a varianceEasyStatisticsView →
- Correlation of two event indicatorsEasyProbabilityStatisticsView →
- Paid a dollar or the drawEasyExpected ValueStatisticsView →
- R-squared when you duplicate every pointEasyStatisticsView →
- Regressing with zero covarianceEasyRandom VariablesStatisticsView →
- Ripple on a pondEasyCalculusView →
- Sharing your weekday of birthEasyProbabilityView →
- Sharpe of two combined uncorrelated strategiesEasyStatisticsFinance & DerivativesView →
- Slope of a product at a special pointEasyCalculusView →
- Three-one strings with matching endpointsEasyCombinatoricsView →
- 1000 bottles, one poisonedMediumBrainteasersView →
- A Cholesky diagonal entryMediumLinear AlgebraView →
- A point near the cone's baseMediumProbabilityCalculusView →
- Coin-pile NimMediumBrainteasersMarket Making & Betting GamesView →
- Covariance of sum and differenceMediumRandom VariablesStatisticsView →
- Density of a sum of two uniformsMediumProbabilityRandom VariablesView →
- Dice game, up to three rollsMediumExpected ValueStochastic ProcessesView →
- Expectation as a sum of tailsMediumRandom VariablesExpected ValueView →
- Fair outcome from a biased coinMediumProbabilityStatisticsView →
- Full housesMediumProbabilityCombinatoricsView →
- Gambler's ruinMediumProbabilityStochastic ProcessesView →
- Newton's division-free reciprocalMediumCalculusView →
- Number of runsMediumExpected ValueView →
- OLS slope from four pointsMediumStatisticsView →
- One hundred light bulbsMediumBrainteasersView →
- Order statistics of two uniformsMediumRandom VariablesStatisticsView →
- Rate of a growing shadowMediumCalculusView →
- Rehedging a book after a moveMediumFinance & DerivativesView →
- Sum of independent PoissonsMediumProbabilityRandom VariablesView →
- Tiling a stripMediumCombinatoricsView →
- Volume where two cylinders crossMediumCalculusView →
- Which deck for two reds?MediumProbabilityView →
- Whose draw is larger?MediumProbabilityView →
- Two heads given an even countEasyProbabilityConditional Probability & Expectation Premium
- A stationary probabilityMediumStochastic Processes Premium
- Absorption probability on a lineMediumProbabilityStochastic Processes Premium
- Arbitraging a mispriced forward loanMediumFinance & Derivatives Premium
- Arc length of a curveMediumCalculus Premium
- Arrivals before the rival streamMediumProbabilityStochastic Processes Premium
- Backing out a correlationMediumRandom VariablesStatistics Premium
- Buyer count in a thinned arrival streamMediumProbabilityStochastic Processes Premium
- Cheapest open-top boxMediumCalculus Premium
- Convergence of the integral of x^(-p)MediumCalculus Premium
- Cutting a cubeMediumBrainteasers Premium
- Derangements of four itemsMediumCombinatorics Premium
- Diversified VaR of two positionsMediumStatisticsFinance & Derivatives Premium
- Duration-plus-convexity price moveMediumFinance & Derivatives Premium
- Euclid's worst-case step countMediumProgramming & DSA Premium
- Expectation of −2 ln UMediumRandom VariablesCalculus Premium
- Expected exponential of Brownian motionMediumStochastic Processes Premium
- Expected maximum of three diceMediumRandom VariablesExpected Value Premium
- Expected sum of a random subsetMediumExpected Value Premium
- First to roll a sixMediumProbability Premium
- Five distinct ranksMediumProbabilityCombinatorics Premium
- Forward vs. futures priceMediumFinance & Derivatives Premium
- Integral by substitution: 2x e^(x^2)MediumCalculus Premium
- Inventory-skewed reservation priceMediumMarket Making & Betting Games Premium
- Inversions in a shuffleMediumCombinatoricsExpected Value Premium
- Joint default rangeMediumProbabilityFinance & Derivatives Premium
- Larger eigenvalue of a 2×2MediumLinear Algebra Premium
- Last two digits of a powerMediumCombinatoricsBrainteasers Premium
- Leibniz rule derivative at x = 1MediumCalculus Premium
- Macaulay duration of a coupon bondMediumFinance & Derivatives Premium
- Par swap rate definitionMediumFinance & Derivatives Premium
- Periodicity and limiting distributionMediumStochastic Processes Premium
- Position of the first spadeMediumCombinatoricsExpected Value Premium
- Reaching the target before ruinMediumStochastic Processes Premium
- Remaining life of a memoryless partMediumRandom Variables Premium
- Renewal-reward fraction of time runningMediumExpected ValueStochastic Processes Premium
- Return time from a three-state chainMediumStochastic Processes Premium
- Rolls until a face repeatsMediumProbabilityExpected Value Premium
- Spaced onesMediumCombinatorics Premium
- The Markov propertyMediumStochastic Processes Premium
- The St. Petersburg paradoxMediumExpected ValueMarket Making & Betting Games Premium
- The painted cubeMediumBrainteasers Premium
- Two uniforms summing below a halfMediumProbabilityRandom Variables Premium
- Two uniforms summing past 1.5MediumProbabilityCalculus Premium
- Variance of a compound daily totalMediumRandom Variables Premium
- Variance of a lognormalMediumRandom VariablesFinance & Derivatives Premium
- Variance of coins-per-die headsMediumRandom VariablesStatistics Premium
- What a p-value isMediumStatistics Premium
- Where the slope is steepest downhillMediumCalculus Premium
- Within distance d on the unit intervalMediumProbabilityCalculus Premium
- Absorption in naive floating-point summationHardCalculusProgramming & DSA Premium
- Defective stack of coinsHardCombinatoricsBrainteasers Premium
- Expected comparisons, from first principlesHardProgramming & DSA Premium
- Expected duration of a fair walkHardExpected ValueStochastic Processes Premium
- Reflecting wall first-passage timeHardExpected ValueStochastic Processes Premium
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