Study programme for quant researcher interviews

[alovya]

Study programme for interviews​

Hi everyone,

I was researching how to prepare for interviews and have ended up organising a decent amount of material into a study programme that I am sharing in this post, which describes:

1. the technical skills needed during a quant interview
2. a study programme to develop these skills

To understand what the interview process is like, read the respective introductions of this primer and "Quant Job Interview Questions and Answers" (2nd edition).

Technical skills​

Note that the technical skills I'm going to describe are the bare minimum you need at the interview, but you might need even more at the job itself.

If you highlight a specific technical skill in your CV, the interviewer is likely going to ask deeper questions about it.

For example, if I claim C++ as the language of choice for one of my projects, the interviewer might ask me harder-than-usual C++ questions to prove my claim.

I've listed the technical skills you need in an interview starting from the most important as I have gathered while doing my research.

Probability
At the interview, you need to show that you have a very good grasp of foundational statistical concepts. I will list some of these concepts in the section on resources.

Note: machine/deep learning, prediction, signal analysis, signal generation, etc, are the most desirable skills right now [thread 1, thread 2].

Coding
Quants have to be able to code well. Python/R are expected, and C++ is nice to have. You need to be good enough to do LeetCode style questions; such questions are becoming more common in interviews.

Brainteasers
These are puzzles/riddles; you won't be solving brainteasers on the job, but they are frequently asked in interviews so you need to be good at them to pass.

Maths
In addition to all of the above, you will often get general maths questions.

Finance
Depending on the your experience or the role you're applying for, you might asked specific finance questions. For example, if you are applying to be an interest rate option quant, the interviewer might ask you pricing questions.

Study programme​

I haven't included specific instructions for finance questions as this will depend on which specific role you are applying for.

However, probability, coding, brainteaser and and maths questions are going to pop up in any quant role, so I have divided my study programme into two parts.

The first focusses on making on making sure you can adequately answer probability, coding and brainteaser questions.

The second part lets you take a break from those questions by including general maths and finance questions.

Still, even in the second part, you should be regularly cycling through probability, coding and brainteaser questions.

Resources​

The programme uses the following resources:

1. Primer
2. Interview manual by the late Mark Joshi
3. Jane Street guide
4. Questions from Pete Benson of UMich
5. 50 mixed questions
6. 21 mixed questions, with answers
7. Compilation from Aaron Cao

Part 1​

1. Read the introductions of (1) and (2) to understand for yourself the interview process before starting any practice questions.
2. Work through the Jane Street guide to find out the statistics concepts you have to know.
3. Go through the probability questions in (2) and (4) that aren't too difficult for you.
4. Do 5 - 10 LeetCode questions, starting with the "Easy" category.
5. Do 5 - 10 brainteasers from (4), (5) or (6).
6. Return to the probability questions you weren't able to do in (2).
7. Do 5 - 10 more LeetCode questions; at this point you might be able to start doing "Medium" category questions. Example list of questions.
8. Do 5 - 10 more brainteasers from (4), (5) or (6) (or wherever else you can find them, to be honest).
9. Return to the probability questions you weren't able to do in (4).

Part 2​

1. Go through the maths questions in (2) and (4) that aren't too difficult for you.
2. Go through the options questions in (2) and (4) that aren't too difficult for you.
3. Do at least 3 questions from each category of probability, coding and brainteasers.
4. Go through the coding questions in (2) and (4).
5. Return to the maths and options questions you weren't able to do in (2) and (4).
6. Again do at least 3 questions from each category of probability, coding and brainteasers.
7. Go through all the interview questions in (1) and the questions in the final chapter X of (2).

At the end of this programme you should be ok with handling interview questions.

If you want more complicated questions, do some of the more challenging ones in (7).

Suggestions to improve this programme are welcome and please let me know if I have said something factually incorrect.

 

[alovya]

This study guide is aimed at people looking for a role as a front office sell side quant or as a buy side quant (I talk about sell side vs buy side here). I thought I could still edit my old study guide but apparently it’s too old to edit. I'm updating the guide because when I wrote the old one I didn’t fully comprehend why preparing for quant interviews is difficult.

Why preparing for quant interviews is hard

Preparing for quant interviews is hard because there is too much study material to choose from. This makes it really hard to decide what to study.

At heart, a quant needs the following technical skills (based on this post, this post and these notes):

Maths

• Algebra
• Partial differential equations
• Numerical methods
• Financial maths
• Linear algebra

Stats

• Probability theory
• Statistics
• Stochastic processes
• Time series
• Bayesian statistics

Coding

• Python, R, C++, SQL
• Data structures and algorithms
• Objected oriented programming
• Design patterns
• Version control (GitHub, GitLab)

Please ignore the list because many of us won’t be able to cover all of these topics in detail. To decide which topics to cover, the best approach that I’ve come up with is to try and answer (and fail) interview questions as quickly as you can: failing will reveal what topics you need to study.

For example, I was feeling particularly unconfident about my probability/stats knowledge so I had a go at the questions in this PDF from Jane Street. The questions involved basic concepts but I took my time hammering them down. Then I had a go at the probability/stats questions in Mark Joshi’s book. I got completely stuck at the very first question on stochastic calculus and I needed to study it a lot more before I could hope to answer the question. I took a week (on top of my job, not full time) to understand stochastic calculus: I used books, videos and random PDFs online, and coded up a Jupyter notebook to confirm and summarise my understanding. Coding up the notebook didn’t make me an expert, but in terms of self-confidence, there is a huge difference between zero knowledge and some (albeit basic*) knowledge. Be mindful of the Dunning-Kruger effect though.

I wouldn't spend more than 30-40 hours per topic at a time: this is enough to get an idea of the basics, but not enough to waste time. For example, I think I spent 40 hours on probability/stats, including: the Jane Street PDF, studying stochastic calculus and coding up the Jupyter notebook.

I need to clarify that this doesn't mean you should spend 30-40 hours per topic overall. You should spend more than 40 hours per topic but only after studying other topics. You should revisit an old topic at a more advanced level once you have let the ideas incubate in your head and have a fresh mind.

*You will be surprised how much you learn just by hammering on the basics. Knowledge of the basics translates to other questions, and it also primes your mind for handling brainteasers. I think having your mind primed like this for quant interviews is not spoken about enough. People don't pass quant interviews only because they're quantitatively gifted, it's also because their mind is primed to handle brainteasers.

Interview prep material

Below there are links to more quant interview questions than you will (probably) ever get through. Remember: there is too much to learn. The trick is to fail at the interview questions to identify what you need to learn. Start with the interview questions in the areas that you are weakest in, e.g., I started with probability and stats as I explained above.

Personally, I would recommend starting with either the PDF by Jane Street or the PDF by Dirk Bester (because it has the most up-to-date interview questions I could find). If someone knows of newer interview questions I would appreciate it a lot if you passed them on to me so that I can update this post.

To understand what the overall interview process is like read the introduction of "Quant Job Interview Questions and Answers" by Mark Joshi.

• Books
  • Quant Interview Questions and Answers by Mark Joshi
  • Frequently Asked Questions in Quantitative Finance
  • Heard on The Street: Quantitative Questions from Wall Street Job Interviews
  • A Practical Guide To Quantitative Finance Interviews
• PDFs
  • https://www.janestreet.com/static/pdfs/trading-interview.pdf
  • QuantitativePrimer/QuantitativePrimer.pdf at master · dwcoder/QuantitativePrimer
  • https://pbenson.github.io/docs/quantTechnicalQuestions/quantTechnicalQuestions.pd
  • https://www.math.lsu.edu/~smolinsk/Quant_Interview_Prep.pdf
• Web links
  • MoneyScience: List of Sample Questions for Quant Interviews
  • Big List of Quant Interview Questions with Answers

Note on how to practise coding

From this article: these days, in quant interviews, “There are more coding questions and coding types of brainteasers. If you go for a quant finance interview today, you will be required to know a lot about algorithms and data structures. The questions you encounter are similar to the questions you get at Google or Facebook."

For what I think is a fantastic introduction to algorithms and data structures, make sure to watch this video.

Practise coding by doing LeetCode. Follow these these three articles in order:

1. How to LeetCode properly
2. 14 Patterns to Ace Any Coding Interview Question
3. Grokking the coding interview equivalent leetcode problems

 

[QR_HFT]

ok

 

[arisylafeta]

Thank you for providing such a thorough study guide. My I ask you, have you been able to land a job after 1 year?

 

[solidcypher]

thanks for this

 

[alovya]

Thank you for providing such a thorough study guide. My I ask you, have you been able to land a job after 1 year?

I didn't apply for QR jobs last year, but I plan on doing so this year, so let's see. To be honest, it might be way too difficult for me get a QR job, so my other options are to go into software engineering or to become a "research engineer".

Also, you're welcome for the study guide, but having spent some time preparing for QR interviews I think it's a stupidly overcomplicated guide... IMHO, getting a QR job really just boils down to the following three points:

1. Having something that shows you have really good STEM skills (e.g. degree from a top uni, winning maths/coding competitions, PhD with good publications, quant internships, etc); this is what gets you past the CV screening stage
2. Strong interview skills: this comes down to studying quant interview books and doing coding puzzles (like Leetcode) while knowing the following basic topics (i.e. at undergrad level) really, really well: linear algebra, multivariable calculus, probability and statistics; this gets you past the interviews
3. Having the skills to actually do the job; this could be pricing, data analysis, development, etc; this keeps you in your job

My guide is meant to address point (2) - getting strong interview skills - and I can't really help with points (1) and (3). To get strong interview skills, I'd recommend doing the following steps:

1. Learn linear algebra, multivariable calculus, probability and statistics really well*
   1. Linear algebra by 3Blue1Brown
   2. Calculus by 3Blue1Brown
   3. Linear algebra by Khan Academy
   4. Calculus by Khan Academy
   5. Probability and statistics by StatQuest
   6. Probability by brilliant.org
   7. Statistics in Introduction to Statistical Learning
   8. Tradermath or Zetamac for mental maths (moreso for trading tbh)
2. Go through quant interview books and coding puzzles**
   1. A Practical Guide to Quantitative Finance Interviews (often called the "green book")
   2. Other quant interview books (but the green book is the one I see the most)***
   3. Leetcode roadmap by Neetcode
   4. 14 patterns for coding interviews
   5. Blind 75 or Neetcode 150

The above are a large part of QR interviews: know linear algebra, multivariable calculus, probability and statistics really well, and be very familiar with quant interview/coding puzzles. Of course, you'll be asked more in-depth questions like about your research or your projects, but you should know those very well anyway since you're the one that executed them.

There's also this Reddit post summarising a lot of research about quant finance careers so that you don't waste time like I did.

Hope this helps and good luck

*3Blue1Brown is better for getting the intuition/visualisation, Khan Academy is better for learning by doing examples.
**In my last post I said you can figure out what to study by failing interview questions. You can still do this: fail the questions in the green book, which will tell you which of linear algebra/calculus/probability/stats you need to study.
***I've read that there aren't as many option pricing jobs these days compared to pre-GFC, so you don't need to go heavy on option pricing/stochastic calculus; just knowing the basics and knowing the Greeks is a good place to start. Also, skip the coding/algorithms questions which will be handled by doing Leetcode.

 

[holloja]

Thank you for your extensive study programme, Alovya!

In addition to your list of resources, I've found tradinginterview.com. It basically has all the information and tools you need to prepare, I have found it quite helpful for my preparations for the Optiver interview.

 

[kyle.nguyen]

I didn't apply for QR jobs last year, but I plan on doing so this year, so let's see. To be honest, it might be way too difficult for me get a QR job, so my other options are to go into software engineering or to become a "research engineer".

Also, you're welcome for the study guide, but having spent some time preparing for QR interviews I think it's a stupidly overcomplicated guide... IMHO, getting a QR job really just boils down to the following three points:

1. Having something that shows you have really good STEM skills (e.g. degree from a top uni, winning maths/coding competitions, PhD with good publications, quant internships, etc); this is what gets you past the CV screening stage
2. Strong interview skills: this comes down to studying quant interview books and doing coding puzzles (like Leetcode) while knowing the following basic topics (i.e. at undergrad level) really, really well: linear algebra, multivariable calculus, probability and statistics; this gets you past the interviews
3. Having the skills to actually do the job; this could be pricing, data analysis, development, etc; this keeps you in your job

My guide is meant to address point (2) - getting strong interview skills - and I can't really help with points (1) and (3). To get strong interview skills, I'd recommend doing the following steps:

1. Learn linear algebra, multivariable calculus, probability and statistics really well*
   1. Linear algebra by 3Blue1Brown
   2. Calculus by 3Blue1Brown
   3. Linear algebra by Khan Academy
   4. Calculus by Khan Academy
   5. Probability and statistics by StatQuest
   6. Probability by brilliant.org
   7. Statistics in Introduction to Statistical Learning
   8. Tradermath or Zetamac for mental maths (moreso for trading tbh)
2. Go through quant interview books and coding puzzles**
   1. A Practical Guide to Quantitative Finance Interviews (often called the "green book")
   2. Other quant interview books (but the green book is the one I see the most)***
   3. Leetcode roadmap by Neetcode
   4. 14 patterns for coding interviews
   5. Blind 75 or Neetcode 150

The above are a large part of QR interviews: know linear algebra, multivariable calculus, probability and statistics really well, and be very familiar with quant interview/coding puzzles. Of course, you'll be asked more in-depth questions like about your research or your projects, but you should know those very well anyway since you're the one that executed them.

There's also this Reddit post summarising a lot of research about quant finance careers so that you don't waste time like I did.

Hope this helps and good luck

*3Blue1Brown is better for getting the intuition/visualisation, Khan Academy is better for learning by doing examples.
**In my last post I said you can figure out what to study by failing interview questions. You can still do this: fail the questions in the green book, which will tell you which of linear algebra/calculus/probability/stats you need to study.
***I've read that there aren't as many option pricing jobs these days compared to pre-GFC, so you don't need to go heavy on option pricing/stochastic calculus; just knowing the basics and knowing the Greeks is a good place to start. Also, skip the coding/algorithms questions which will be handled by doing Leetcode.

By "Statistics in Introduction to Statistical Learning" Did you refer to Gareth James book?

 

[achirikhin]

Tech skills are important, but only partly important. There are many quant jobs on buy and sell side, in consulting and in fintech (and in other less flashy businesses like insurance), and they all require slightly different skill sets.

It is important to realise that if you do get the job as a junior quant, you will NOT be doing cool math, writing trading bots or writing math papers. You will be an apprentice for 2-3 years, learning nuts and bolts of the job. E.g. you will be learning real-life derivatives pricing by helping to investigate the PNL reports or asked to fix a bug in an undocumented C++ code from 10 years ago. That's what will happen.

That's why you are asked brain teasers at the interviews: to test your humility, not your math skills. It is known by now that your ability to differentiate x^x or implement a quicksort is necessary, but far not sufficient condition for you to be successful. A desire to become rich is, perhaps (conditioned on everything else)

 

[QuantCoach]

It is important to realise that if you do get the job as a junior quant, you will NOT be doing cool math, writing trading bots or writing math papers. You will be an apprentice for 2-3 years, learning nuts and bolts of the job. E.g. you will be learning real-life derivatives pricing by helping to investigate the PNL reports or asked to fix a bug in an undocumented C++ code from 10 years ago. That's what will happen.

Wow this makes me feel a lot better about the prop trading side. Over here within your first year you would get direct responsibility in trading a book generating $xx million PnL+ a year, within 3 years you would be considered a decently experienced QT, within 7 years be considered one of the most tenured quants on the floor, within 10 years be semi-retired. We can't justify paying students straight out of school 400k-700k to just investigate the PnL reports or fix bugs, if you can't help generate PnL (or at the bare minimum show potential of it) within your first year then you will almost certainly get fired in the prop side.

 

[achirikhin]

Wow this makes me feel a lot better about the prop trading side. Over here within your first year you would get direct responsibility in trading a book generating $xx million PnL+ a year, within 3 years you would be considered a decently experienced QT, within 7 years be considered one of the most tenured quants on the floor, within 10 years be semi-retired. We can't justify paying students straight out of school 400k-700k to just investigate the PnL reports or fix bugs, if you can't help generate PnL (or at the bare minimum show potential of it) within your first year then you will almost certainly get fired in the prop side.

I assume this is not a Friday joke.

Are you talking about traders or quants on the prop side? In any case you will not be paid 400k-700k straight out of school. This would be really dumb for an unexperienced junior to be paid so much.

In 3 years, if you work really a lot, you will have just accumulated 10k hours, i.e. learnt something to the point of being independent. So yes, as a trader you will be given a book. Saying it will generate millions does not really mean anything, the question is how much risk are you allowed to take to generate those millions.

If you are a library quant on the buy/trading side, your job will not be much different from that on the sell side. Only with much higher variance of comp.

 

[QuantCoach]

Are you talking about traders or quants on the prop side? In any case you will not be paid 400k-700k straight out of school. This would be really dumb for an unexperienced junior to be paid so much.

This is very standard comp for quant traders and quant researchers at JS/Optiver/Sig/Cit Sec/etc. Nearly all of my trainee class had zero prior experience beforehand (unless you consider USAMO/Chess GMs/etc. as relevant experience to quant) and the prop shops prefer that since it's much easier to teach a smart/eager 20 year old blank slate than people who were taught the wrong things.

As a HFT OMM, it's harder to quantify the risk we can take on in a traditional sense since we can get double digit sharpes by trading quite flat. Yeah $xx million is a bit misleading, we care much more about how much edge we take down and how much we retain. $xx million is sick if theres only $xx million edge available but it's pretty doo doo if theres $xxx million edge trading. We're also not given three years to learn something to the point of being independent, if we can't independently make important +EV decisions after our first year, we will most likely be fired. You get a lot of responsibility + owernship very quickly over here, can push things to prod within a day without going through all the bureaucratic jumps.

 

[achirikhin]

I agree that mentioned by you is the standard comp. But not for the freshmen. Why would you pay them so if they had not shown any potential? In 5 years at least, yes, maybe.

Regarding the last paragraph, yes, if you sit on the client flow you can sometimes get large sharps.

One vs 3 years, well, it is possible to simply "attach people to phones" and the fire the lower performers. This is described back in "Liar's Poker". This may look like a successful strategy in the firms subject to survivorship bias.

Good luck with all that, but whether this is a long-term sustainable strategy, only time can tell.

On the sell side, where the job is somewhat more systematically important, it does take time to learn the business. You used to be compensated by less volatile comp, well above the levels you mentioned for MDs, not even in the first tier US banks.

My personal opinion, quant/trader jobs that do not require 3+ years to master will be AI-ed away completely in the next 10 years.

 

[QuantCoach]

Because you can't get top talent anymore without providing that comp. If one competitor is putting up those numbers, the rest will follow or they will miss out. The more general lesson that we get taught is you don't win by being good, you win by being better than everyone else and if you're not first you might as well be last since there's not much share left for third of fourth place (which applied to recruiting, includes matching or outbidding new grad offers made by everyone else). This general principle is also partly why JS has been quite untouchable in the fixed income ETF space. Also we're told that in our first year we're expected to break-even with the cost of hiring us (including all the time it takes away from the senior traders to train us), but in our second year we're expected to generate $3 million+ in value for the firm (at least 5x multiple of our pay) whether it be through projects or good trading decisions.

 

[achirikhin]

I don't believe you pay that amount until you have determined you are dealing with top talent Not before few years. Or you have too much money to waste. Not good to boast about it

 

[QuantCoach]

I don't believe you pay that amount until you have determined you are dealing with top talent Not before few years. Or you have too much money to waste. Not good to boast about it

Multiple examples:

Baruch MFE usually has 1 or 2 students a year without any prior experience landing a 500k+ TC job as well.

this is the new grad JS job posting specifying no experience needed and 300k base alone (which you can expect a six figure sign on bonus and another six figure guaranteed first year performance bonus)

 

[achirikhin]

Out of how many offered?

 

[QuantCoach]

We give ~10 offers out of about ~8000 applicants, new grads mostly all get paid the same but with returning interns getting slightly higher; many top firms don't negotiate for new grad; interview is extremely open-ended questions, don't really care about what you know but how you think and problem solve

 

[achirikhin]

I mean how many actually stay till the year end to receive the paycheck

 

[QuantCoach]

I mean how many actually stay till the year end to receive the paycheck

Depends on the firm, can range between 10-40% of new grads not making it through their first year but they get to keep the base + sign on at least. Returning interns typically retain better, the new grad turover is expected to go down as several of these prop shops are now not taking on as many external new grads as they expand their intern class and look to hire from that pool instead.