Quant Finance Interview Drill
This conversation was generated using Cook'd AI's career assistant and reviewed by Fallon Han from our editorial team for accuracy.
I am a third-year math undergrad targeting hedge fund internships at a quantitative multi-manager in Hong Kong. I am on a dependent visa, so I need a highly technical mock interview that feels realistic. Please start with a probability puzzle and then keep narrowing into quantitative reasoning. I want concise answers and pressure on the logic.
Great. I will run this like a real hedge fund screen: short prompts, no filler, and each answer should be tight. We will begin with a probability puzzle, then move into conditional expectation, estimation, and a quick statistics question. If you hesitate, I will push for cleaner reasoning.
First question: You have two fair coins and one biased coin that lands heads with probability 3/4. You pick one coin at random, flip it once, and get heads. What is the probability you picked the biased coin? Give the result and the key steps only.
By Bayes, P(biased | H) = P(H | biased)P(biased) / P(H). That is (3/4)(1/3) over ((1/2)(2/3) + (3/4)(1/3)) = 1/4 over 7/12 = 3/7.
Correct. Now I want the same level of precision, but with a small twist.
Second question: Suppose X and Y are independent standard normals. What is the distribution of X plus Y, and why does that matter for portfolio intuition? Keep it to two sentences.
X plus Y is normal with mean 0 and variance 2, because the sum of independent normals is normal and variances add. For portfolio intuition, independent sources of risk still aggregate, so diversification reduces relative noise only if positions are not perfectly correlated.
Good. Now I am going to make it more interview-like.
Third question: A fund strategy has monthly returns with sample mean 1.2 percent, sample standard deviation 4 percent, and 36 observations. Assume returns are approximately normal. Estimate the t-statistic for testing whether the mean return is zero, and tell me whether this is strong evidence. No long explanation.
t is 0.012 divided by (0.04 over sqrt(36)), so 0.012 over 0.006 = 2.0. That is moderate evidence, but not overwhelming; it is around the usual borderline significance range.
Reasonable. Now let us narrow into hedge fund style estimation.
Fourth question: You observe a trading signal that is correct 55 percent of the time over 200 independent trials. Roughly how wide is the 95 percent confidence interval for the true hit rate, and what does that imply for a PM deciding whether to trust it? Give an approximate interval and the interpretation.
Standard error is sqrt(p(1-p)/n), about sqrt(0.55 times 0.45 over 200), which is about 0.035. A 95 percent interval is roughly 0.55 plus or minus 0.07, so about 48 percent to 62 percent. That means the signal could still be close to random, so a PM should be cautious and look for robustness.
Good. Final question, and I want concise reasoning with no detour.
You are given three boxes. Box A has 2 red and 1 blue ball. Box B has 1 red and 2 blue balls. Box C has 3 red balls. You pick a box at random, then draw one ball. If the ball is red, which box is most likely, and why? Then tell me how you would communicate this under pressure in an interview room in Hong Kong.