Medium Trader Interview Questions
Everything asked of traders, filtered to the medium end - useful for calibrating where you actually are.
195 questions, all free to practise. The topics that come up most are probability (77), expected value (39), combinatorics (34), market making & betting games (31).
- 25 horses, 5 tracksMediumBrainteasersView →
- A 5 before a 7MediumProbabilityView →
- A convexity gap by JensenMediumRandom VariablesExpected ValueView →
- A cube root by tangent lineMediumCalculusView →
- A low medianMediumProbabilityRandom VariablesView →
- A prime sum on prime diceMediumProbabilityCombinatoricsView →
- Absorption probability on a lineMediumProbabilityStochastic ProcessesView →
- Aces in a seven-card handMediumCombinatoricsExpected ValueView →
- Adverse selection in quotingMediumMarket Making & Betting GamesView →
- An ace for everyoneMediumProbabilityCombinatoricsView →
- An ace in every pileMediumProbabilityCombinatoricsView →
- An ace in the handMediumProbabilityCombinatoricsView →
- Ants on a stickMediumBrainteasersView →
- Arbitraging a coupon bond against zerosMediumFinance & DerivativesView →
- Arbitraging a mispriced forward loanMediumFinance & DerivativesView →
- At least two sixes in five rollsMediumProbabilityRandom VariablesView →
- Backing out a correlationMediumRandom VariablesStatisticsView →
- Backing out a margin-free probabilityMediumMarket Making & Betting GamesView →
- Backing out the informed flow from imbalanceMediumMarket Making & Betting GamesView →
- Balancing six- and eight-sided diceMediumExpected ValueBrainteasersView →
- Balloon related ratesMediumCalculusView →
- Bertrand's boxMediumProbabilityConditional Probability & ExpectationView →
- Both even given an even sumMediumProbabilityConditional Probability & ExpectationView →
- Boy–girl neighbors in a lineMediumCombinatoricsExpected ValueView →
- Break-even fill quality for a resting bidMediumMarket Making & Betting GamesView →
- Break-even half-spread from toxic flowMediumProbabilityExpected ValueView →
- Break-even half-spread under adverse selectionMediumExpected ValueMarket Making & Betting GamesView →
- Bridge and torchMediumBrainteasersView →
- Buyer count in a thinned arrival streamMediumProbabilityStochastic ProcessesView →
- Calendar spread intuitionMediumFinance & DerivativesView →
- Capturing the spreadMediumMarket Making & Betting GamesView →
- Cash out or bustMediumProbabilityExpected ValueView →
- Cash-and-carry arbitrageMediumFinance & DerivativesView →
- Cats and dogs on the streetMediumBrainteasersView →
- Chords that don't crossMediumProbabilityCombinatoricsView →
- Clock hands overlapMediumBrainteasersView →
- Coin sets the number of dice rollsMediumProbabilityConditional Probability & ExpectationView →
- Coin-pile NimMediumBrainteasersMarket Making & Betting GamesView →
- Conversion arbitrage from a parity violationMediumFinance & DerivativesView →
- Correlation of overlapping sumsMediumRandom VariablesStatisticsView →
- Counting straightsMediumProbabilityCombinatoricsView →
- Cutting a cube into 27MediumBrainteasersView →
- Delta of a straddleMediumFinance & DerivativesView →
- Delta-hedge a two-leg option bookMediumFinance & DerivativesView →
- Dice game, up to three rollsMediumExpected ValueStochastic ProcessesView →
- Dice payoff via WaldMediumExpected ValueStochastic ProcessesView →
- Distributing candies with a capMediumCombinatoricsView →
- Eight coins, one lightMediumCombinatoricsBrainteasersView →
- Eight dice summing to twelveMediumProbabilityCombinatoricsView →
- Emptying the cherry bowlMediumProbabilityCombinatoricsView →
- Exactly two aces in a bridge handMediumProbabilityCombinatoricsView →
- Expected absolute difference of two diceMediumExpected ValueView →
- Expected fives before the first sixMediumProbabilityExpected ValueView →
- Expected flips for HHTMediumExpected ValueStochastic ProcessesView →
- Expected flips for HTMediumExpected ValueStochastic ProcessesView →
- Expected gap on 30-sided diceMediumProbabilityExpected ValueView →
- Expected maximum of three diceMediumRandom VariablesExpected ValueView →
- Expected maximum of two diceMediumRandom VariablesExpected ValueView →
- Expected median of three diceMediumProbabilityExpected ValueView →
- Expected minimum of two diceMediumRandom VariablesExpected ValueView →
- Expected revenue of a Vickrey auctionMediumProbabilityExpected ValueView →
- Expected value of the highest cardMediumProbabilityExpected ValueView →
- Fair price of a payout that doubles per headMediumExpected ValueMarket Making & Betting GamesView →
- Fair value after an informed buyMediumConditional Probability & ExpectationMarket Making & Betting GamesView →
- Fair value after two informed buysMediumMarket Making & Betting GamesView →
- Filling a pool with the drain openMediumBrainteasersView →
- First HH on the tenth tossMediumProbabilityCombinatoricsView →
- First consecutive repeatMediumProbabilityExpected ValueView →
- First head on an even flipMediumProbabilityView →
- First head strictly soonerMediumProbabilityRandom VariablesView →
- First to roll a sixMediumProbabilityView →
- First to three of a kind in a rowMediumProbabilityExpected ValueView →
- Five distinct ranksMediumProbabilityCombinatoricsView →
- Forward price with a cash dividendMediumFinance & DerivativesView →
- Forward vs. futures priceMediumFinance & DerivativesView →
- Four distinct birth monthsMediumProbabilityCombinatoricsView →
- Four fives before the first sixMediumProbabilityRandom VariablesView →
- Four times as long to the first headMediumProbabilityRandom VariablesView →
- Fox, goose, beans crossingMediumBrainteasersView →
- Frog in the wellMediumBrainteasersView →
- Full housesMediumProbabilityCombinatoricsView →
- Gambler's ruinMediumProbabilityStochastic ProcessesView →
- Gambler's ruin (unfair)MediumProbabilityStochastic ProcessesView →
- Gamma and rehedging P&LMediumFinance & DerivativesView →
- Gamma-scalping a round tripMediumFinance & DerivativesView →
- Grandmother's age from the digitsMediumBrainteasersView →
- Guess 2/3 of the averageMediumMarket Making & Betting GamesView →
- HT before HH in coin flipsMediumProbabilityStochastic ProcessesView →
- Heads given the ends differMediumConditional Probability & ExpectationExpected ValueView →
- Implied dividend yield from a forwardMediumFinance & DerivativesView →
- Implied vol from a straddle quoteMediumFinance & DerivativesView →
- Inventory skewMediumMarket Making & Betting GamesView →
- Inventory-skewed reservation priceMediumMarket Making & Betting GamesView →
- Keeping two apartMediumCombinatoricsView →
- Kelly sizing on an asymmetric betMediumMarket Making & Betting GamesView →
- Large sum given a sixMediumProbabilityConditional Probability & ExpectationView →
- Largest circle in a triangleMediumBrainteasersView →
- Limit of x ln x as x to 0+MediumCalculusView →
- Limit of x^100 over e^xMediumCalculusView →
- Locking a profit by hedging after the odds moveMediumExpected ValueMarket Making & Betting GamesView →
- MLE at a boundaryMediumStatisticsCalculusView →
- Marking a seasoned forwardMediumFinance & DerivativesView →
- Matching penniesMediumMarket Making & Betting GamesView →
- Maximum loss on a collarMediumFinance & DerivativesView →
- Minimum defense frequency against a betMediumProbabilityExpected ValueView →
- Monty HallMediumProbabilityConditional Probability & ExpectationView →
- Monty Hall with 100 doorsMediumProbabilityConditional Probability & ExpectationView →
- Neither die exceeds fourMediumProbabilityRandom VariablesView →
- No face card before the two of heartsMediumProbabilityCombinatoricsView →
- No-arbitrage call boundsMediumFinance & DerivativesView →
- One card each in casino warMediumProbabilityCombinatoricsView →
- One extra roll for more primesMediumProbabilityView →
- One hundred animals for a thousand dollarsMediumBrainteasersView →
- Optimal bid-ask placementMediumMarket Making & Betting GamesView →
- Optimal quote widthMediumMarket Making & Betting GamesView →
- Paid only if the last roll winsMediumExpected ValueView →
- Painted cube, one face showingMediumProbabilityBrainteasersView →
- Pair at a round tableMediumCombinatoricsView →
- Paths dodging a closed intersectionMediumCombinatoricsView →
- Pay to play with a capMediumExpected ValueMarket Making & Betting GamesView →
- Position of the first spadeMediumCombinatoricsExpected ValueView →
- Pricing a coupon bond off the spot curveMediumFinance & DerivativesView →
- Pricing a digital from a call spreadMediumFinance & DerivativesView →
- Pricing a squared payoffMediumExpected ValueMarket Making & Betting GamesView →
- Prime sumMediumProbabilityView →
- Probability of three of a kindMediumProbabilityCombinatoricsView →
- Product of two dice, doubled on doublesMediumExpected ValueMarket Making & Betting GamesView →
- Product of two uniforms above a halfMediumProbabilityRandom VariablesView →
- Profit on a bull call spreadMediumFinance & DerivativesView →
- Profit on a risk reversalMediumFinance & DerivativesView →
- Put–call parity arbitrageMediumFinance & DerivativesView →
- Put–call parity with a dividendMediumFinance & DerivativesView →
- Rare-event Poisson approximationMediumProbabilityRandom VariablesView →
- Reaching the target before ruinMediumStochastic ProcessesView →
- Reading order flowMediumMarket Making & Betting GamesView →
- Red faces on a diced cubeMediumCombinatoricsExpected ValueView →
- Rehedging a book after a moveMediumFinance & DerivativesView →
- Right angles in 12 hoursMediumBrainteasersView →
- Risk-neutral up probabilityMediumStochastic ProcessesFinance & DerivativesView →
- Rolling a 5-sided die to reach fiveMediumProbabilityExpected ValueView →
- Rolling until two rolls differ by twoMediumProbabilityExpected ValueView →
- Rolls to a six before a fiveMediumProbabilityExpected ValueView →
- Rolls to see both a 1 and a 2MediumExpected ValueView →
- Russian roulette, re-spunMediumProbabilityConditional Probability & ExpectationView →
- Scaling vega across maturitiesMediumFinance & DerivativesView →
- Second-price auction strategyMediumProbabilityMarket Making & Betting GamesView →
- Sharpe ratio in a marble gameMediumExpected ValueStatisticsView →
- Short-straddle P&L when vol stays lowMediumFinance & DerivativesView →
- Sizing a cross-book arbitrage lockMediumMarket Making & Betting GamesView →
- Sum of 10 with three diceMediumProbabilityCombinatoricsView →
- Sum of multiples of 3 or 5MediumBrainteasersView →
- Sum versus twice the differenceMediumProbabilityRandom VariablesView →
- Tennis: two sets or three?MediumProbabilityView →
- The St. Petersburg paradoxMediumExpected ValueMarket Making & Betting GamesView →
- The birthday problemMediumProbabilityCombinatoricsView →
- The gold chainMediumBrainteasersView →
- The larger die shows a 4 - what about the smaller?MediumProbabilityRandom VariablesView →
- The largest unmakeable totalMediumCombinatoricsBrainteasersView →
- The last lightbulb to burn outMediumRandom VariablesExpected ValueView →
- The missing dollarMediumBrainteasersView →
- The pile that always leaves oneMediumBrainteasersView →
- The profitable range of a short strangleMediumFinance & DerivativesView →
- The same number of tailsMediumProbabilityCombinatoricsView →
- The third shiny pennyMediumProbabilityCombinatoricsView →
- The two-headed coinMediumProbabilityConditional Probability & ExpectationView →
- The winner's curse in a bid warMediumMarket Making & Betting GamesView →
- Three dots, exactly one shared edgeMediumProbabilityCombinatoricsView →
- Three mislabeled jarsMediumBrainteasersView →
- Three ones in a rowMediumProbabilityCombinatoricsView →
- Three prisonersMediumProbabilityConditional Probability & ExpectationView →
- Three-jug measuringMediumBrainteasersView →
- Tower of Hanoi, adjacent moves onlyMediumBrainteasersView →
- Two childrenMediumProbabilityConditional Probability & ExpectationView →
- Two face cardsMediumProbabilityCombinatoricsView →
- Two guards, two doorsMediumBrainteasersView →
- Two reds in a row from a shrinking urnMediumProbabilityConditional Probability & ExpectationView →
- Two ropes, 45 minutesMediumBrainteasersView →
- Two trains and a flyMediumBrainteasersView →
- Two uniforms summing below a halfMediumProbabilityRandom VariablesView →
- Two uniforms summing past 1.5MediumProbabilityCalculusView →
- Two-sided p-value of a mean testMediumStatisticsView →
- Variance of a coin-gated payoffMediumRandom VariablesStatisticsView →
- Variance of the longer pieceMediumProbabilityRandom VariablesView →
- Volatility smile meaningMediumStatisticsFinance & DerivativesView →
- Waiting to see both facesMediumRandom VariablesStatisticsView →
- Weighing 1 to 40MediumBrainteasersView →
- When time decay reversesMediumFinance & DerivativesView →
- Which coin produced two heads?MediumProbabilityConditional Probability & ExpectationView →
- Which deck for two reds?MediumProbabilityView →
- Which desk books the larger dayMediumRandom VariablesStatisticsView →
- Width of a market under uncertaintyMediumMarket Making & Betting GamesStatisticsView →
- Wine and waterMediumBrainteasersView →
- Winner's curseMediumMarket Making & Betting GamesView →
- Winning from deuceMediumProbabilityConditional Probability & ExpectationView →
- Within distance d on the unit intervalMediumProbabilityCalculusView →
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