The quant interview questions that are flooring experienced candidates

If you're an experienced quant applying for a new role in an investment bank, hedge fund or trading firm, you might presume that you'll be able to walk through the interview process. Not necessarily.

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Dirk Bester is a PhD quant with interview experience at firms including Goldman Sachs, JPMorgan, Squarepoint Capital, Two Sigma and Winton Capital, and has previously written a comprehensive interview guide for quant jobs in finance. He doesn't actively interview for jobs anymore, but speaks to a lot of people who do. Bester says there are two topics that are "really growing:" machine learning, and linear regression.

Helpfully, Bester's quant interview guide itself has a section on regression theory, a framework for modelling the relationships between variables. We've listed some of the questions below. In the guide, he says "linear and logistic regression make up the most prevalent models encountered not only in interviews, but also in practice."

If you're interviewing for quant roles, it will also help if you have specialist knowledge of Python and/or C++. The growth of machine learning (ML) questions necessitates knowledge in PyTorch, or other specialized languages/libraries. 

The format of interviews is changing. Bester says "places that require ML work will usually give you a take home exercise with either some sort of prediction problem, or a classification problem."  This can be a double-edged sword: while there's less immediate time pressure, you'll be expected to provide a higher quality answer and may be pressured into spending far longer on the problem than the one or two hours the interviewer suggests it will take.

If you get one of these take home projects, Bester says they're most likely looking to see if "you can clean data and either use regression or standard libraries that do random forests."

Questions can also vary depending on which field of quant finance you want to work. In high-frequency trading, you'll need to prove you can write low latency code, usually in C++; a popular technique you'll be asked to demonstrate in these kinds of interview is lock-free programming.

You'll also be likely asked the dreaded brainteasers, which Bester says are a seemingly "inevitable" part of the interview process. Giuseppe Paleologo, head of quant research at hedge fund Balyasny, says that brainteasers are "not testing your intrinsic ability to solve a puzzle, but your ability to learn about puzzles. And there is a pattern to puzzles, which can be learned."

Below are some of the more unusual questions you could expect to find in a quant interview:

Linear Regression Questions

According to interview prep site Devinterview.io, questions you could be asked on linear regression include:

• How do you interpret the coefficients of a linear regression model?
• What are the common metrics to evaluate a linear regression model's performance?
• Explain the concept of Homoscedasticity. Why is it important?
• How do you deal with missing values when preparing data for linear regression? 

Machine Learning Questions

While a few years old now, ex-Goldman Sachs quant strat Mohit Agarwal provided some machine learning questions in a quant interview question bank. These include:

• How do long short-term memory networks solve the vanishing gradient problem? Be specific, how in terms of gates?
• What is the problem with constant initialization (e.g., 0-initialization or 1-initialization) of weights in neural networks.
• How do you evaluate a model for time-series data (e.g., predicting developing heart disease in next 3 months?)
• Explain Ridge and Lasso Regression. Specifically, explain why L1 loss acts as a feature selection step and pushes the value to zero? What are the regulariziton methods in ML and DL?
• In your experience working with convolutional neural networks and deep reinforcement learning - which kind of architectures work, and which don't?

Quant Brainteasers

1. The Pirate Question

Another question that one Goldman Sachs quant via Glassdoor said they encountered was:

100 pirates stand in a circle. They start shooting alternately in a cycle such that the 1st pirate shoots the 2nd, the 3rd shoots the 4th and so on. The pirates who got shot are eliminated from the game. They continue in circles, shooting the next standing pirate, till only one pirate is left. Which position should someone stand to survive?

The Pirate Answer

The answer to (a reskinned version of) this question is provided by Nigel Coldwell, who curates a list of quant interview questions. For 100 pirates, the answer is 73.

Coldwell notes that for each full cycle, the number of players is halved. Therefore, if the number of players were a power of two, the player who shoots first would win. As soon as the number of pirates goes down to a power of two, the next person to shoot will win. In this case, the pirates go down to a power of two when there are 64 remaining at which point pirate number 73 is the next person to shoot, making them the survivor.

2. The Whisky Question

Another question from Nigel Coldwell reads as follows:

At a whisky tasting Mr Cheap works out that for every 10 used, empty, glasses he can collect, he can poor the dregs together to make a whole new glass of whisky. At the end of the day he is able to find 100 empty glasses. How many full glasses can he now drink?

The Whisky Answer

This is one of the questions designed to trap you into thinking the obvious answer, 10, when it is in fact 11. 

If Mr Cheap collects 100 glasses, their dregs will produce 10 full glasses of whisky. After drinking those ten glasses, he will then have 10 more glasses from which to pour the dregs, resulting in an additional glass.

3. The airplane seating question 

Bester says he was asked this question repeatedly in successive finance interviews. It's sometimes called the "drunken passenger" and goes like this:

One hundred people are in line to board a plane which has exactly 100 seats. Each passenger has a ticket assigning them to a specific seat, and the passengers board one at a time. The first person to board is drunk, picks a random seat, and sits in it. The remaining passengers board; if they find their assigned seat empty, they sit in it. If they find their seat taken, they pick a random seat to sit in. Everyone boards, and is seated. What is the probability that the final person who boards gets to sit in their assigned seat? 

The airplane seating answer:

This is a classic, and one that you've likely heard a number of times. It was popularised by books on quant interviews by Mark Joshi and Paul Wilmott, but Goldman Sachs quants via Glassdoor say they're still being asked this question in job interviews today.

Bester cites Wilmott's solution. - Start by considering just two people: the drunkard and yourself. In this case, the drunkard will sit in his correct seat 50% of the time and you will get your allocated seat. In another 50% of cases, the drunkard will sit in your seat and you will be displaced.  Then, expand this to three people: the drunkard either sits in his seat, your seat, or in the other person (Peter's) seat. The chances of him sitting your seat and his seat are the same and therefore balance out. If the drunkard sits in Peter's seat, the outcome will depend on whether Peter sits in the drunkard's seat or yours. So, there's a 50% chance that you'll get to sit in your allocated seat (and this holds however many people there are).

Quant questions of your own:

If you want to impress at a quant interview, Bester also suggests a number of questions you might want to ask yourself, partly to establish whether the team you're joining is working with the latest technologies. These include the following:

What operating systems do the team use?

What are the proportions of Windows, Apple, GNU/Linux?

What does the team use for technical documentation? LaTeX, Wiki, Word, or nothing?

What software does the team use for version control? Svn, Git, Mercurial, Team Foundation Server, or appending V1, V2, V3 to foldernames?

What programming languages does the team use? R, Python, C++, Julia, Matlab? For data analysis? For scripting? For production?

Is the team Bayesians, frequentists, or whatever gets the job done?

Are modellers expected to write the code to implement their models, or is this handled by developers? •

Is there a formal process for requesting the installation of new software libraries?

Good luck.

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