Quantitative Researcher Interview Questions

Showing 1–26 of 26 results

• DRWHard·Quantitative Researcher
  Expected Dart Score for a Bivariate Normal Throw with Ring Scoring

  Calculate the expected score of a dart throw modeled by a zero-mean bivariate normal distribution with circular scoring rings, calibrated using a known hit probability inside the inner ring.

  Statistics & MathOnsiteProbabilityBivariate NormalExpected Value
• DRWHard·Quantitative Researcher
  Expected Rounds Until a Shopping-Cart Line Empties Under Random Transfers

  Tests modeling discrete-time Markov chains, formulating hitting-time difference equations, and solving symmetric random walk absorption problems analytically.

  Statistics & MathOnsiteMarkov ChainsProbabilityRandom Walk
• DRWHard·Quantitative Researcher
  Expected Tosses Until HHT Given HHT Appears Before HTH

  Calculate the probability that the coin sequence HHT appears before HTH in repeated fair tosses, and find the conditional expected number of tosses until termination given that HHT appears first.

  Statistics & MathOnsiteprobabilitymarkov-chainsconditional-expectation
• DRWHard·Quantitative Researcher
  Expected Winnings in a Random-Walk Money Collection Game on 45 Stones

  Calculates a player's expected winnings in a random-walk money collection game on an odd-sized circle of stones using Gambler's Ruin and parity arguments.

  Statistics & MathOnsiteprobabilityrandom-walkgamblers-ruin
• DRWHard·Quantitative Researcher
  Posterior Probability of a Two-Headed Coin After Three Heads

  This question tests the application of Bayes' theorem, conditional likelihoods, and posterior probability updates given sequential binary observation data.

  Statistics & MathOnsiteProbabilityBayes' TheoremQuantitative Research
• DRWHard·Quantitative Researcher
  Probability the Two Strongest Teams Meet in a 16-Team Knockout Final

  Calculate the probability that the two highest-ranked teams face each other in the championship match of a 16-team single-elimination tournament with probabilistic match outcomes.

  Statistics & MathOnsiteprobabilitycombinatoricsconditioning
• Goldman SachsMedium·Quantitative Researcher
  Estimate Pi with a Square Cardboard and a Fair Die to 5-6 Decimal Places

  Using only a square piece of cardboard and a fair six-sided die, design an experiment that estimates pi empirically, then explain how many trials 5 to 6 correct decimal places would require and how you would get there. It tests Monte Carlo design, bias versus variance, and error analysis.

  Statistics & MathTechnical Screen
• Goldman SachsMedium·Quantitative Researcher
  From Alpha Signal to Portfolio: Reliability, Regime Dependence and Entropy

  Walk through how a quantitative equity team turns a predictive signal into portfolio holdings, then explain how to judge whether the signal is reliable, whether its performance depends on the market regime, and how entropy and mutual information can be used to evaluate signals and portfolios.

  Statistics & MathTechnical Screen
• OptiverMedium·Quantitative Researcher
  Design dice betting strategy under time limit

  This question evaluates probabilistic reasoning, expected-value computation, risk management and staking-strategy concepts including Kelly-style bet sizing, confidence-interval estimation, and return–variance trade-offs in the Statistics & Math domain.

  Statistics & MathTechnical Screen
• OOtherMedium·Quantitative Researcher
  Optimal Stopping with a Ten-Sided Die and a Reset

  Derive optimal stopping thresholds for a fair ten-sided accumulation game, then account for the continuation value of a one-time zero reset.

  Statistics & MathTechnical Screen
• Point72Medium·Quantitative Researcher
  Calibrate the Risk-Aversion Parameter

  Calibrate mean-variance risk aversion to target risk and out-of-sample utility while accounting for units, scaling, constraints, and regimes.

  Statistics & MathOnline Assessment
• Point72Medium·Quantitative Researcher
  Choose Practical Portfolio Constraints

  Specify practical stat-arb constraints for neutrality, exposure, concentration, turnover, liquidity, and borrow, including feasibility checks.

  Statistics & MathOnline Assessment
• Point72Medium·Quantitative Researcher
  Derive Annualized Portfolio Volatility

  Derive portfolio volatility from factor covariance and stock-specific variance, then annualize it with consistent horizons and units.

  Statistics & MathOnline Assessment
• Point72Hard·Quantitative Researcher
  Derive the Optimal Bid in a Two-Bidder Second-Price Auction

  Two risk-neutral bidders compete for one item in a sealed-bid second-price auction. Explain the assumptions and derivation clearly, check edge cases, and show how the result changes when those assumptions no longer hold.

  Statistics & MathTechnical Screen
• Point72Medium·Quantitative Researcher
  Estimate Factor Returns and Residual Returns

  Derive weighted factor-return estimates from a sample, then compute residual returns across a larger trading universe with stable linear algebra.

  Statistics & MathOnline Assessment
• Point72Hard·Quantitative Researcher
  Find the Two Heaviest Balls with Minimum Comparisons

  There are 32 balls with distinct weights. Explain the assumptions and derivation clearly, check edge cases, and show how the result changes when those assumptions no longer hold.

  Statistics & MathTechnical Screen
• Point72Medium·Quantitative Researcher
  Formulate a Single-Period Stat-Arb Objective

  Formulate a convex single-period statistical-arbitrage objective balancing expected return against covariance risk, with consistent units.

  Statistics & MathOnline Assessment
• Point72Medium·Quantitative Researcher
  Linearize an L1 Trading Penalty

  Linearize weighted absolute trading costs with auxiliary variables, complete LP constraints, the correct objective sign, and an equivalence proof.

  Statistics & MathOnline Assessment
• Point72Medium·Quantitative Researcher
  Model Trading Frictions in Portfolio Optimization

  Extend a stat-arb objective with unit-consistent commissions, spread, slippage, market impact, turnover, borrow, and concentration costs.

  Statistics & MathOnline Assessment
• Point72Medium·Quantitative Researcher
  Prove That Lasso Can Be Written as a Quadratic Program

  Derive the Lasso quadratic-program formulation and prove equivalence, convexity, minimizer correspondence, and rank-related uniqueness.

  Statistics & MathTechnical Screen
• Point72Medium·Quantitative Researcher
  Solve Three Probability Models

  Solve three independent probability questions. Explain the assumptions and derivation clearly, check edge cases, and show how the result changes when those assumptions no longer hold.

  Statistics & MathTechnical Screen
• Virtu FinancialHard·Quantitative Researcher
  Approximate a Binomial Upper Tail with a Normal Distribution

  This question tests the application of the Normal approximation to the Binomial distribution, the use of continuity correction, and the ability to evaluate the error bounds of this approximation.

  Statistics & MathOnsiteStatisticsProbabilityNormal Approximation
• Virtu FinancialHard·Quantitative Researcher
  Approximate a Rare-Event Binomial Probability

  This problem tests the application of the Poisson approximation to binomial distributions for rare events and the evaluation of the error bounds associated with this approximation.

  Statistics & MathOnsiteProbabilityPoisson DistributionBinomial Distribution
• Virtu FinancialHard·Quantitative Researcher
  Birthday Collisions and the Closest Pair of Birthdays

  This problem tests your understanding of probability theory, specifically the generalized birthday paradox, and your ability to analyze spacing distributions of random variables.

  Statistics & MathOnsiteProbabilityStatisticsCombinatorics
• Virtu FinancialHard·Quantitative Researcher
  Compare Two Strategies for Getting Ten Consecutive Heads

  This problem tests your ability to model probability through recursion and expectation, specifically comparing the efficiency of two distinct strategies for achieving a target streak of coin tosses.

  Statistics & MathOnsiteProbabilityExpectationRecurrence
• VoleonMedium·Quantitative Researcher
  Bound R-Squared for Individual and Combined OLS Regressions

  Derive in-sample OLS R-squared bounds and the joint-model range from individual scores, including intercept assumptions, predictor correlation, and out-of-sample exceptions.

  Statistics & MathTechnical Screen