Quant case studies, worked step by step

Cases
100
Traced to a firm
43
Topics
11
Hard
30
Topic
All topicsSignal research and data tasks10Options and volatility trading10Market-making games14Portfolio construction10Strategy evaluation and backtests9Execution and market microstructure8Fixed income and credit8Regression and model review8Risk measurement and limits9Statistical arbitrage and event trades8Position sizing and bankroll6
Level
AnyWarm upCoreHard
Source
AnyReported at a firmStandard
Showing 1–10 of 13 · filtered from 100Clear filters
  1. 003You make a market in a coin-flip contract paying Rs 100 on heads. One trade in four is the interviewer, who knows the outcome and trades only when it helps; the rest is balanced. What is the narrowest breakeven spread, and what does quoting 45 at 55 cost over 40 trades?Market-making gamesHardCitadel SecuritiesLondon · 2026
  2. 005A backtest shows 18% gross return at 9% volatility, turning the book over 60 times a year at an assumed 5 bps a side. Live, costs are 14 bps a side and only 70% of signals fill. Reconcile the backtest Sharpe with a live Sharpe near zero and decide what to fix first.Strategy evaluation and backtestsHardJump TradingChicago · 2018
  3. 014A contract settles at a die roll, doubled if a coin lands heads, plus 5 if a drawn card is red. Quote it, then decide whether to trade with a bot showing 9.5 bid, 10.5 offer, and whether to make or take.Market-making gamesHardOptiverAustin · 2025
  4. 017A strategy earns 25 bps gross per trade in stocks with Rs 40 crore daily volume and 2% daily volatility, with impact equal to volatility times the square root of participation. Compare running it with Rs 10 crore and with Rs 1,000 crore.Execution and market microstructureHardScotiabankToronto · 2025
  5. 029A social media sentiment signal on 150 consumer stocks goes long the top decile and short the bottom, with a 53% hit rate on two-day holds and an average move of 1.2%. Costs are 15 basis points a side and capacity is capped at 1% of daily volume. Is there a business, and how big?Signal research and data tasksHardTwo SigmaNew York · 2024
  6. 031Three assets return 6%, 9% and 12% with volatilities of 8%, 15% and 25%. Long only, at most 50% in any one, target volatility 12%. Write the optimisation problem and find approximate weights.Portfolio constructionHardBlackRockNew York · 2025
  7. 050Three players are each dealt one card from 1 to 10 without repeats, and the contract settles at the highest card. You hold a 7. Price it, then reprice after another player immediately bids 8.5.Market-making gamesHardBelvedere TradingChicago · 2022
  8. 062A bag holds four stones, each black or white, with every count of black stones from 0 to 4 equally likely. Two stones drawn without replacement are both black. Make a market on a contract paying Rs 100 if the third stone is black, then respond when the interviewer lifts your offer at 80.Market-making gamesHardCitadelNew York · 2025
  9. 067One-month implied volatility on an index is 30% and your desk forecasts 22% realised. You sell a delta-hedged at-the-money straddle on Rs 10 crore notional. Estimate the expected profit from the gamma-theta relationship, the result if realised volatility is 35% instead, and what can go wrong between hedges.Options and volatility tradingHardOld Mission CapitalChicago · 2025
  10. 075A contract settles at the sum of three cards drawn without replacement from ten cards numbered 1 to 10, at Rs 100 a point. Quote a two-way market before any card, after the first card shows 9, and after the second shows 2, keeping pace with the dealer.Market-making gamesHardOptiverChicago · 2026

Company names and figures are illustrative.