What to Expect in a Quant Interview
Quantitative finance interviews test your ability to think under pressure, reason through ambiguous problems, and communicate solutions clearly. Questions span probability, statistics, brainteasers, mental math, and market intuition. Below are 20 of the most frequently asked questions across top firms, with concise explanations of how to approach each one.
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Probability and Expected Value
1. You flip a fair coin until you get two heads in a row. What is the expected number of flips?
Define states based on your streak of consecutive heads. Let E be the expected flips from the start, and E1 be the expected flips when you have one head in a row. Setting up the recurrence: E = 1 + 0.5*E1 + 0.5*E and E1 = 1 + 0.5*0 + 0.5*E. Solving yields E = 6.
2. You have a bag with 5 red and 3 blue balls. You draw 2 without replacement. What is the probability both are red?
P(both red) = (5/8) * (4/7) = 20/56 = 5/14. This tests basic combinatorial probability and the ability to reason about conditional draws.
3. Two players alternately roll a fair die. The first to roll a 6 wins. What is the probability the first player wins?
Player 1 wins on their first turn with probability 1/6. Otherwise, both miss (probability (5/6)^2) and the game resets. So P = 1/6 + (25/36)*P, giving P = 6/11.
4. What is the expected number of rolls of a fair die to see all six faces?
This is the coupon collector problem. The expected number is 6*(1/6 + 1/5 + 1/4 + 1/3 + 1/2 + 1/1) = 6*H(6) = 14.7 rolls.
5. A stick is broken at two random points uniformly distributed along its length. What is the probability the three pieces form a triangle?
The pieces form a triangle if and only if no piece exceeds half the total length. The probability is 1/4, which can be derived geometrically using the sample space of two uniform random variables.
Brainteasers and Logic
6. You have 12 identical-looking balls. One is heavier or lighter. You have a balance scale and 3 weighings. How do you find the odd ball and determine if it is heavy or light?
Divide into groups of 4. The first weighing identifies which group contains the odd ball and provides information about whether it is heavy or light. Subsequent weighings narrow down within that group using the constraints established.
7. How many trailing zeros does 100 factorial have?
Trailing zeros come from factors of 10 = 2 * 5. Since factors of 2 are more plentiful, count factors of 5: floor(100/5) + floor(100/25) = 20 + 4 = 24 trailing zeros.
8. You are given two ropes that each take exactly one hour to burn, but burn at non-uniform rates. How do you measure exactly 45 minutes?
Light both ends of the first rope and one end of the second rope simultaneously. When the first rope burns out (30 minutes), light the other end of the second rope. It will burn out in another 15 minutes, totaling 45 minutes.
Statistics and Estimation
9. Explain the difference between correlation and causation with a financial example.
Two stocks might be highly correlated because they belong to the same sector, but one does not cause the other to move. A confounding variable (sector-wide news) drives both. Understanding this distinction is critical when building trading models to avoid spurious signals.
10. What is the Central Limit Theorem and why does it matter in finance?
The CLT states that the sampling distribution of the mean approaches a normal distribution as sample size grows, regardless of the underlying distribution. In finance, this underpins risk models, portfolio theory, and statistical testing of trading strategies.
11. How would you estimate the number of tennis balls that fit in this room?
Estimate room dimensions (say 5m x 5m x 3m = 75 cubic meters). A tennis ball has diameter ~6.5cm, so volume ~143 cm^3. With packing efficiency of ~64%, usable space is 75,000,000 * 0.64 / 143 = roughly 335,000 balls. The interviewer cares about your structured approach more than the exact number.
Market Intuition and Finance
12. If a stock is trading at $100 and the one-year at-the-money call option is worth $12, roughly what is the implied volatility?
Using the approximation for an ATM option: C is roughly 0.4 * S * sigma * sqrt(T). So 12 = 0.4 * 100 * sigma * 1, giving sigma of approximately 30%.
13. Why might a market maker want to be delta neutral?
Delta neutrality removes directional exposure, allowing the market maker to profit from the bid-ask spread and volatility rather than from predicting market direction. This reduces risk and allows for more consistent returns.
14. Explain put-call parity.
For European options: C - P = S - K*e^(-rT). This relationship links call and put prices and must hold to prevent arbitrage. It is one of the most fundamental results in options pricing.
Coding and Algorithms
15. How would you find the median of a stream of numbers?
Maintain two heaps: a max-heap for the lower half and a min-heap for the upper half. Balance them so they differ in size by at most 1. The median is either the top of the larger heap or the average of both tops.
16. Write a function to compute the maximum drawdown of a time series.
Track the running maximum and compute the drawdown at each point as (peak - current) / peak. Return the maximum value observed. This runs in O(n) time with O(1) extra space.
Advanced Questions
17. Derive the Black-Scholes equation from first principles.
Construct a portfolio of the option and the underlying that is locally riskless. Apply Ito's lemma to the option value, set the portfolio return equal to the risk-free rate, and derive the resulting partial differential equation.
18. Explain the bias-variance tradeoff in the context of building a trading signal.
A model with too few parameters (high bias) will miss real patterns. One with too many (high variance) will overfit to noise. Cross-validation on out-of-sample data helps find the right balance for a trading signal that generalizes.
19. How would you test whether a trading strategy has genuine alpha?
Compare the strategy's risk-adjusted returns against a realistic benchmark after accounting for transaction costs, slippage, and data-snooping bias. Use bootstrap simulations or walk-forward testing to assess statistical significance.
20. What is the Kelly criterion and when would you use it?
The Kelly criterion determines the optimal fraction of capital to bet: f = (bp - q) / b, where b is the odds, p is the probability of winning, and q = 1 - p. It maximizes the long-run growth rate of capital but can be aggressive, so practitioners often use fractional Kelly.
Thorough preparation across these categories will put you in a strong position. Browse additional questions in our interview prep section.