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, all free to practise. The split is 13 easy, 72 medium, 5 hard. The topics that come up most are probability (22), 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 →
- Two heads given an even countEasyProbabilityConditional Probability & ExpectationView →
- 1000 bottles, one poisonedMediumBrainteasersView →
- A Cholesky diagonal entryMediumLinear AlgebraView →
- A point near the cone's baseMediumProbabilityCalculusView →
- A stationary probabilityMediumStochastic ProcessesView →
- Absorption probability on a lineMediumProbabilityStochastic ProcessesView →
- Arbitraging a mispriced forward loanMediumFinance & DerivativesView →
- Arc length of a curveMediumCalculusView →
- Arrivals before the rival streamMediumProbabilityStochastic ProcessesView →
- Backing out a correlationMediumRandom VariablesStatisticsView →
- Buyer count in a thinned arrival streamMediumProbabilityStochastic ProcessesView →
- Cheapest open-top boxMediumCalculusView →
- Coin-pile NimMediumBrainteasersMarket Making & Betting GamesView →
- Convergence of the integral of x^(-p)MediumCalculusView →
- Covariance of sum and differenceMediumRandom VariablesStatisticsView →
- Density of a sum of two uniformsMediumProbabilityRandom VariablesView →
- Derangements of four itemsMediumCombinatoricsView →
- Dice game, up to three rollsMediumExpected ValueStochastic ProcessesView →
- Diversified VaR of two positionsMediumStatisticsFinance & DerivativesView →
- Duration-plus-convexity price moveMediumFinance & DerivativesView →
- Euclid's worst-case step countMediumProgramming & DSAView →
- Expectation as a sum of tailsMediumRandom VariablesExpected ValueView →
- Expectation of −2 ln UMediumRandom VariablesCalculusView →
- Expected exponential of Brownian motionMediumStochastic ProcessesView →
- Expected maximum of three diceMediumRandom VariablesExpected ValueView →
- Expected sum of a random subsetMediumExpected ValueView →
- Fair outcome from a biased coinMediumProbabilityStatisticsView →
- First to roll a sixMediumProbabilityView →
- Five distinct ranksMediumProbabilityCombinatoricsView →
- Forward vs. futures priceMediumFinance & DerivativesView →
- Full housesMediumProbabilityCombinatoricsView →
- Gambler's ruinMediumProbabilityStochastic ProcessesView →
- Integral by substitution: 2x e^(x^2)MediumCalculusView →
- Inventory-skewed reservation priceMediumMarket Making & Betting GamesView →
- Inversions in a shuffleMediumCombinatoricsExpected ValueView →
- Joint default rangeMediumProbabilityFinance & DerivativesView →
- Larger eigenvalue of a 2×2MediumLinear AlgebraView →
- Last two digits of a powerMediumCombinatoricsBrainteasersView →
- Leibniz rule derivative at x = 1MediumCalculusView →
- Macaulay duration of a coupon bondMediumFinance & DerivativesView →
- Newton's division-free reciprocalMediumCalculusView →
- Number of runsMediumExpected ValueView →
- OLS slope from four pointsMediumStatisticsView →
- One hundred light bulbsMediumBrainteasersView →
- Order statistics of two uniformsMediumRandom VariablesStatisticsView →
- Painted cube, one face showingMediumProbabilityBrainteasersView →
- Par swap rate definitionMediumFinance & DerivativesView →
- Periodicity and limiting distributionMediumStochastic ProcessesView →
- Position of the first spadeMediumCombinatoricsExpected ValueView →
- Rate of a growing shadowMediumCalculusView →
- Reaching the target before ruinMediumStochastic ProcessesView →
- Rehedging a book after a moveMediumFinance & DerivativesView →
- Remaining life of a memoryless partMediumRandom VariablesView →
- Renewal-reward fraction of time runningMediumExpected ValueStochastic ProcessesView →
- Return time from a three-state chainMediumStochastic ProcessesView →
- Rolls until a face repeatsMediumProbabilityExpected ValueView →
- Spaced onesMediumCombinatoricsView →
- Sum of independent PoissonsMediumProbabilityRandom VariablesView →
- The Markov propertyMediumStochastic ProcessesView →
- The St. Petersburg paradoxMediumExpected ValueMarket Making & Betting GamesView →
- The painted cubeMediumBrainteasersView →
- Tiling a stripMediumCombinatoricsView →
- Two uniforms summing below a halfMediumProbabilityRandom VariablesView →
- Two uniforms summing past 1.5MediumProbabilityCalculusView →
- Variance of a compound daily totalMediumRandom VariablesView →
- Variance of a lognormalMediumRandom VariablesFinance & DerivativesView →
- Variance of coins-per-die headsMediumRandom VariablesStatisticsView →
- Volume where two cylinders crossMediumCalculusView →
- What a p-value isMediumStatisticsView →
- Where the slope is steepest downhillMediumCalculusView →
- Which deck for two reds?MediumProbabilityView →
- Whose draw is larger?MediumProbabilityView →
- Within distance d on the unit intervalMediumProbabilityCalculusView →
- Absorption in naive floating-point summationHardCalculusProgramming & DSAView →
- Defective stack of coinsHardCombinatoricsBrainteasersView →
- Expected comparisons, from first principlesHardProgramming & DSAView →
- Expected duration of a fair walkHardExpected ValueStochastic ProcessesView →
- Reflecting wall first-passage timeHardExpected ValueStochastic ProcessesView →
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