Solve Market-Risk and Probability Questions
Company: Morgan Stanley
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: HR Screen
Answer the following quantitative interview questions for a market-risk role:
1. **Stress testing WTI and Brent**
Design a stress-testing framework for the joint behavior of WTI and Brent crude oil prices over a chosen horizon, such as 1 day or 10 days. Describe:
- what data you would use;
- how you would model each series marginally;
- how you would capture dependence between them;
- whether and why a **t-copula** is appropriate;
- how you would generate joint stress scenarios;
- how you would validate the framework and communicate its limitations.
2. **Variance of a sum of normal variables**
Let `X` and `Y` be normally distributed random variables with variances `σ_X^2` and `σ_Y^2`.
- If `X` and `Y` are independent, what is `Var(X + Y)`?
- If they are dependent with correlation `ρ`, what is `Var(X + Y)`?
3. **Monty Hall problem**
There are 3 doors. One door hides a car and the other 2 hide goats. You choose one door. The host, who knows where the car is, opens a different door that contains a goat and offers you the chance to switch to the remaining unopened door. Should you switch, and what is the probability of winning if you stay versus switch?
4. **Eight balls, one heavier**
You have 8 visually identical balls, but exactly one is heavier than the others. Using a balance scale and at most 2 weighings, give a strategy that always identifies the heavier ball.
Quick Answer: This set evaluates quantitative modeling and probabilistic reasoning skills, covering market-risk stress-testing and time-series dependence modeling (marginal models and copulas), variance and correlation properties of normal variables, conditional probability reasoning as in the Monty Hall paradox, and combinatorial/logical inference for limited-information search problems. It is in the Statistics & Math domain for Data Scientist roles and is commonly asked because it probes both conceptual understanding and practical application of probabilistic models, dependence structures, scenario generation, and model validation and communication of limitations.