Solve stress testing and probability

Q: Solve stress testing and probability

This question evaluates proficiency in statistical modeling and probabilistic reasoning, spanning risk-stress testing, marginal and dependence modeling (including copulas), variance and distributional properties, conditional probability paradoxes, and combinatorial logic puzzles.

Q: How do I approach Statistics & Math interview questions?

Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

Q: What difficulty level is this interview question?

This is a medium difficulty Statistics & Math question, commonly asked during HR Screen rounds at Morgan Stanley.

Q: What role is this question designed for?

This question is commonly asked for Data Scientist candidates at Morgan Stanley during technical interviews.

Question

A quantitative interviewer asks several statistics and probability questions.

Commodity stress testing. You manage risk for positions exposed to WTI and Brent crude. Describe a framework to stress test the portfolio. Assume you have historical daily returns for both series and want to generate joint downside scenarios over a 10-day horizon. Explain how you would model the marginals, dependence structure, and tail risk. If you use a t-copula, explain the workflow and why it may be preferable to a Gaussian copula.
Variance of a sum. Let X and Y be normally distributed random variables with means mu_X and mu_Y , standard deviations sigma_X and sigma_Y , and correlation rho .
- What is Var(X + Y) when X and Y are independent?
- What is Var(X + Y) when they are dependent?
- Under what condition is X + Y itself normally distributed?
Monty Hall. There are three doors, one hides a car and two hide goats. You pick one door. The host, who knows the location of the car, opens one of the remaining doors and always reveals a goat. You may stay or switch. What strategy maximizes the chance of winning, and what is that probability?
Eight balls puzzle. You have eight visually identical balls, and exactly one is heavier than the other seven. Using a balance scale at most two times, describe a strategy that always identifies the heavier ball.

Solve stress testing and probability

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