What Quant Trader Interviews Actually Test
Quant trader interviews differ from quant researcher and quant developer interviews in that they test decision-making under uncertainty in adversarial settings. The interviewer isn't just asking whether you can compute an expected value - they're watching whether you commit to a price, adjust when shown new information, and stay calm when challenged. The arithmetic is fast; the mindset is everything.
This guide collects 25 worked examples from recent SIG, Optiver, IMC, Akuna, Citadel Securities, Jane Street and Hudson River Trading trader interviews. For broader context, see our quant trader career guide, options market making guide, and quant interview questions hub.
Section 1: Market Making Games (Questions 1-7)
1. Sum of two dice
"I roll two dice; I'll pay you the sum in dollars. Make me a market."
Answer: Expected value is 7. A reasonable starting market: 6 at 8 (bid 6, ask 8). The interviewer will likely trade with you. If they buy at 8, suspect they have information (maybe they've seen the dice already in this scenario) and tighten/skew. If they refuse to trade, they may think your prices are too tight.
2. Median of five dice
"I roll five dice; I'll pay you the median value in dollars. Make me a market."
Answer: By symmetry, expected median is 3.5. A reasonable starting market: 3 at 4. If pressed for a tighter market: 3.25 at 3.75.
3. Number of red marbles
"I have 100 marbles, some red, some blue. I'll pay you the number of red marbles in dollars. Make me a market."
Answer: With no information, the expected number is 50 (uniform prior). Bid 45, ask 55. Critical: if the interviewer trades repeatedly on one side, they have information. Adjust aggressively - if they sell at 55 multiple times, lower your prices to maybe 30 at 40.
4. Coin flip until heads
"I flip a fair coin until I get a head. I'll pay you the number of flips. Make me a market."
Answer: Expected number is 2. Bid 1.5, ask 2.5. Be aware: distribution has long right tail (rare large payoffs). Some candidates skew their prices low to reflect skew aversion.
5. Random integer 1 to 100
"I pick a random integer from 1 to 100. I'll pay you that integer in dollars. Make me a market."
Answer: Expected value is 50.5. Bid 47, ask 54. If asked tighter: 49 at 52.
6. Information asymmetry
"I'm thinking of a number between 1 and 100. I'll pay you that number minus your bid (if you buy) or your ask minus that number (if you sell). What price do you offer?"
Answer: This is a winner's curse problem. Anyone willing to buy at price P only does so because the actual number is < P. Bid significantly below 50.5 to compensate - maybe 30 or 35 - and ask significantly above. The optimal solution depends on the interviewer's strategy assumption.
7. Card draw
"I'll draw 5 cards from a standard deck (with replacement). I'll pay you the number of hearts. Make me a market."
Answer: Each card has 1/4 chance of being a heart. Expected hearts: 1.25. Bid 1, ask 1.5.
Section 2: Options Theory (Questions 8-14)
8. ATM call vega
"You're long an at-the-money 1-year call on a $100 stock. Implied vol drops 1 point. What happens to your P&L per share?"
Answer: Vega for an ATM 1-year option ≈ (S \sqrt{T} / 25 ≈ 100 / 25 = 4) per vol point. So you lose roughly $4 per share. (More precisely: vega for ATM is (S \sqrt{T/2π} \approx 0.4 \cdot S) per vol point, so $40 per share for a 100-point notional - check the units the interviewer expects.)
9. Put-call parity
"Stock at $100, 1-year ATM call worth $10. What's the 1-year ATM put worth, assuming 5% interest rates?"
Answer: Put-call parity: (C - P = S - K e^{-rT}). (10 - P = 100 - 100 \cdot e^{-0.05}) ≈ 100 - 95.12 = 4.88. So P ≈ $5.12.
10. Delta intuition
"You're long an ATM call. Stock moves up $1. P&L?"
Answer: Delta of ATM call ≈ 0.5. So P&L ≈ +$0.50. As stock moves up further, delta increases (gamma effect), so P&L is convex - subsequent up-moves help more than equivalent down-moves hurt.
11. Gamma scalping
"How does a market maker make money on gamma when the stock moves?"
Answer: Long gamma + delta-hedged = profit from realised vol. As stock moves, your delta drifts (because of gamma); you re-hedge by buying low / selling high in the underlying. The accumulated re-hedging trades capture realised vol; your option position pays implied vol via theta. If realised vol > implied vol, you profit.
12. Straddle pricing
"What does a 1-year ATM straddle on a $100 stock cost if implied vol is 30%?"
Answer: Approximation: (0.8 \cdot S \cdot σ \sqrt{T}) for ATM straddle = (0.8 \cdot 100 \cdot 0.30 \cdot 1) = $24. The exact value depends on Black-Scholes details but this approximation is within 5%.
13. Volatility surface intuition
"Why might OTM put implied vol be higher than ATM implied vol on the S&P 500?"
Answer: "Volatility skew" or "smile." Reasons: (1) Market participants have crash-protection demand (drive up OTM put prices). (2) Realised distributions have heavier left tails than lognormal. (3) Leverage effect - vol rises when stocks fall, so OTM puts capture more vol. (4) Risk premium: option sellers demand compensation for tail risk.
14. Theta on a calendar spread
"You sell a 30-day ATM call and buy a 60-day ATM call. What's your theta?"
Answer: Theta on the short option is more negative (it decays faster as expiry approaches). Theta on the long option is less negative. So your net position is positive theta - you make money from the passage of time. The trade-off: you're short vega differentially.
Section 3: Market Microstructure (Questions 15-20)
15. Bid-ask spread components
"Why does a market maker quote a bid-ask spread? What three things make it up?"
Answer: (1) Order processing costs (exchange fees, capital, infrastructure). (2) Inventory holding cost (you're taking risk while you hold the position). (3) Adverse selection (your counterparty might know something you don't; spread compensates for the risk that a trade is informed). For more detail see our bid-ask spread explained guide.
16. Why limit orders cluster at round numbers
"Why do you see a lot of limit orders at $100, $99.50, etc., but few at $99.43?"
Answer: Behavioural - retail and institutional traders gravitate to round numbers as natural "anchor" prices. Market makers can sometimes profit by slightly undercutting these clusters.
17. Adverse selection
"You're a market maker. Suddenly everyone wants to buy at your offer. What do you do?"
Answer: Suspect informed flow. Widen the spread; raise the offer. If buying continues, raise more aggressively. The cost of being slow to update is being run over by the news (you sell at $50 just before the stock jumps to $52).
18. Latency
"Why does a high-frequency market maker care about microseconds?"
Answer: Two reasons: (1) Inventory management - if a market moves and you don't update quickly, your standing quotes get adversely selected. (2) Queue priority - on most exchanges, time-priority within a price level matters; faster updates get more fills at the same price.
19. Maker-taker fees
"On a maker-taker exchange, market makers earn a rebate per share traded. Why might a market maker quote tighter than the natural fair value spread?"
Answer: The rebate effectively subsidises tighter pricing. If the rebate is 0.3 cents/share and the natural fair spread is 1 cent, a market maker can quote a 0.7 cent spread and still break even on the spread + collect the rebate. This pushes effective spreads below what would be sustainable in a pure trading-cost model.
20. Slippage and impact
"You want to buy 100,000 shares of a stock that trades 10,000 shares per minute on average. What's your expected slippage versus the current price?"
Answer: Significantly more than the bid-ask spread. Rule of thumb (Almgren-Chriss): impact ≈ (σ \sqrt{V/AV}) where V is your trade size, AV is daily average volume, σ is daily volatility. For 100K vs ~5M daily, with σ=2%, slippage ≈ 2% × √(0.02) ≈ 30 bps. Real impact varies; this is just a starting estimate.
Section 4: Real Trading Scenarios (Questions 21-25)
21. Position sizing
"You have a strategy with expected return 5%, std dev 15%. How much of your portfolio do you allocate?"
Answer: Kelly criterion for sizing: (f = μ/σ²) for log utility. With μ=0.05, σ²=0.0225, f = 2.22 - i.e., 222% of capital, which is leveraged. In practice, use 0.25 to 0.5 of full Kelly (so 50% to 110% allocation) due to estimation error and the discomfort of full Kelly drawdowns.
22. Stop loss vs trailing stop
"You're long a stock at $100. Should you set a stop at $90 or use a 10% trailing stop? What's the difference?"
Answer: Fixed stop locks in a maximum loss but doesn't protect gains. Trailing stop adjusts as the stock moves up - protects gains but can stop you out on volatility around your trailing level. Choice depends on whether you believe you have skill in entry timing (use fixed stop, capture mean-reversion) or trend-following (use trailing).
23. Risk limits
"Your firm gives you a risk limit of $100K daily VaR. You're allowed to take any position. What constraints does this place on you?"
Answer: Daily VaR is typically 95% or 99%. With $100K 95% VaR, your daily P&L should breach $-100K only ~13 times per year. Position size depends on volatility - you can hold a much larger notional in low-vol assets. The interviewer wants to see you ask "what's the volatility" and "is it 95% or 99%?"
24. Why your strategy isn't working
"You designed a market-making strategy that backtested with Sharpe 3. In live trading, Sharpe is 0.5. Possible reasons?"
Answer: Order: (1) Backtest assumed you got fills you wouldn't have gotten in reality (passive fills are not free). (2) Adverse selection on real fills (you're being filled mostly by informed flow). (3) Execution latency means you're queue-disadvantaged. (4) Your fair-value model is wrong about specific situations. (5) Transaction costs higher than assumed (rebates, fees, impact).
25. Decision under uncertainty
"You see a quote of 10 at 11. You think fair value is 10.4. Do you buy at 11 or sell at 10?"
Answer: Neither - both are negative expected value. Buy at 11: pay 11 for fair value 10.4 = -$0.6 per share. Sell at 10: receive 10 for fair value 10.4 = -$0.4 per share. Best action: stand aside or post your own quote (e.g., bid 10.3). The interviewer wants to see you compute carefully and not be drawn into a losing trade just because a market exists.
How to Use This Guide
For trader-track preparation, drill the market-making games (Section 1) until you can quote prices in 5 seconds. Practice with a study partner who tries to "trade" with your prices and observe whether you adjust. The market-making sections of SIG, Optiver, IMC and Citadel Securities Super Days are essentially extended versions of these.
For broader prep:
- Quant interview questions hub
- Quant trader career guide
- Options market making guide
- Greeks and volatility in options
For firm-specific trader interview content:
Practise the questions Quant Trader Interview Questions: 25 Real Examples 2026 actually asks
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