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In a Quantitative Interview, the goal is to determine your ability to think through quantitative concepts. The questions will often relate to some form of mathematics, statistics, econometrics or computer programming. You may or may not be asked finance specific questions, though a basic understanding of key concepts would be helpful.
In this interview, you should not expect to (immediately, or even eventually) know the answer to every analytical question. A good interviewer will quickly find your frontier of knowledge, and push you past that point to determine how you would think and react in a novel situation. They are looking to see if you know how to think analytically, evaluate the situation, come up with plausible explanations and substantiate your arguments.
When you get a question, make sure you fully understand the scenario. If there are terms that you are unfamiliar with, ask them for the definitions and check your understanding. Take a short time to think through the situation, and then start talking about your thought process. Be certain to explain your thought process, and make note of any assumptions that you are using. Often, you will have some guidance towards the correct approach, and you should make note of such hints and run with them. If you realize that you have made an error, point it out, backtrack your argument, fix it, and then proceed.
After arriving at your answer, look back at your assumptions / guesses, and explain what are the points at which you could have introduced errors or false reasoning. Try to quantify the extent of the error, so that you can give a reasonable confidence interval for the true answer.
Show your work
The whole purpose of this interview is to demonstrate how you think. The answer is of low importance, and they value the method / approaches taken (just like in math!).
Actively talk about what you are thinking. If you are uncertain about the path, you can say that you are exploring different possibilities first. Ask questions to clarify the scenario.
This also allows you to easily identify mistakes that you made, and fix them.
Ask questions to clarify
If you need various pieces of information but do not know, ask for help. If it's a numerical value, you could replace it with a variable and state what your best approximation for it would be.
An interviewer might steer you away from dead ends, so watch out for his body language.
Pay attention to hints
More often than not, the interviewer already knows the answer to the problem, and will offer you hints to proceed when you are stuck.
Watch their body language for signs. If they are nodding their heads and , that is likely a sign that you are alright. If they have arched eyebrows, head is tilted back, or are looking away, then it could mean that you are off the track.
Identify potential errors
At the end, it would be helpful to explain your assumptions and why they are valid / a simplification.
When you estimate your variables, also include your belief about the size of the error. This will allow you to determine the final error (just like in Physics error analysis!) Identify potential corner cases and state how you would adjust / account for them.
Be prepared for follow-on questions
Since the goal is to identify your ability to adapt, you could be asked how your answer will change as the inputs change. You should work through what you have already done, and identify the areas where your reasoning should be updated, and then give the new final answer.
Ability to explain
- Assume that I am a layman and don't understand the field. Explain to me [complex project that you worked on]. What were the main problems and how were they solved?
- Explain what you did in your previous position.
- What is your speciality in [a particular field]?
Familiarity with trading
- What do you think makes a good trader?
- Are you risk adverse or risk loving? Why?
- What have you traded and what is your returns?
- Is it possible to consistently outperform the [index benchmark]?
Understanding of statistics
- What is a lognormal distribution?
- What is a Monte Carlo Simulation?
- What is Bayes' Theorem, and how is it used?
- What is the probability that breaking a stick into 3 pieces form a triangle?
- What is the probability of a (stationary) Brownian motion hitting 1 before -2?
- How can we distinguish between correlation and causation?
Understanding of programming
- What is the order of complexity of this algorithm?
- How would you implement the code for this project?
- Is there a faster way to run this program?
- What is a virtual constructor in C++?
- What are the differences between [two programming languages]?
Understanding of finance concepts
- What is the difference between future and forward contracts?
- What is the difference between historical volatility and implied volatility?
- What happens to an options vega as volatility increases?
- What are the assumptions in Black-Scholes?
- The price of a stock is $10. It has a 60% probability of increasing to $12, and a 40% probability of decreasing to $8. What is the price of the $10 call for this time period?
Estimation / Deductive Reasoning
- How many buildings of at least ten stories are there in [city]?
- How much water is used in California on a daily basis?