Quant Research Stats 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 want a math-focused interview for quant research roles. Can you run me through a statistics-heavy mock interview and then give me a score on analytical rigor? I'm a second-year undergrad in the UK on a student visa, so I want feedback that is realistic for trading firms.
Absolutely. I will keep this at the level of a quant research interview and focus on expectation, variance, hypothesis testing, and model validation.
First question: suppose X and Y are independent random variables with finite variance. How would you express E[X+Y], Var(X+Y), and what changes if they are not independent? Please talk through the reasoning, not just the formulas.
For the expectation, E[X+Y] equals E[X] plus E[Y] by linearity. For the variance, if they are independent, Var(X+Y) is Var(X) plus Var(Y). If they are not independent, then I think you add a covariance term, so Var(X+Y) = Var(X) + Var(Y) + 2 Cov(X,Y). The expectation part does not need independence.
Good. That is correct and the separation between linearity of expectation and the dependence requirement for variance is exactly the kind of distinction interviewers look for.
Follow-up: imagine you estimate the mean daily return of a strategy from 40 observations and get a positive sample mean. How would you test whether the true mean return is greater than zero? Please state the null and alternative hypotheses, the test statistic, and one limitation of the test in this setting.
I would set H0 as the true mean return being less than or equal to zero, and H1 as the true mean return being greater than zero. If the sample standard deviation is s, then the test statistic is something like t = x-bar divided by s over square root of n. With 40 observations, I would compare it to a t distribution with 39 degrees of freedom. A limitation is that returns may not be normal, especially with heavy tails, so the t-test may be unreliable. Also, if the data has autocorrelation, the standard error could be wrong.
Strong answer. You identified the one-sided test, the t-statistic, and two important real-world issues: non-normality and autocorrelation. That is materially better than a purely textbook answer.
Next question: suppose a model predicts next-day returns. You split the data into training and test sets and get an excellent in-sample fit but poor out-of-sample performance. What are the most likely causes, and how would you validate the model more carefully before trusting it in a trading context?
The most likely cause is overfitting. The model may be capturing noise in the training set rather than a real signal. It could also be data leakage if future information accidentally enters the features. To validate it better, I would use a proper time-series split, not random shuffling, because returns are ordered in time. I would check performance across multiple market regimes, verify that features are available at prediction time, and compare against a simple benchmark. I would also look at stability of coefficients and transaction cost sensitivity.
Excellent. That is the right trading-firm mindset: detect overfitting, prevent leakage, preserve time order, and check robustness under costs and regime changes.
Final assessment: analytical rigor 8.5 out of 10. Your probability and hypothesis-testing answers were technically correct, and your validation discussion was very strong. To reach a top-tier quant research level, tighten the language around test assumptions and be ready to discuss whether a t-test remains valid under heteroskedasticity or serial correlation. Overall, this would read as a credible second-year candidate with solid quantitative instincts.