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Quant Job Interview Questions (2009) [pdf]
- 20161112 10y agoSigh...I guess I'll be sticking with web dev.
- rahrahrah 10y agoI wouldn't be discouraged. I just had a look and parts 1 - 4 are simple maths, and everyone should know those maths anyway. Then part 5 is application of simple arithmetics (except questions 8 and 12) to options, which means if you already know arithmetics you only need to learn what an option is. What I mean is that you should be learning basics maths anyway, and when you know a bit you can solve all those questions. What a lot of people could benefit from is learning how to learn. EDIT: Thanks for downvotes guys. Should I also downvote when someone says "don't be discouraged with distributed systems, or asynchronous programming" etc? I don't know those things, so maybe I should downvote those people?
- augustt 10y agoI have a feeling you have a different definition of "simple maths" than most people.
- anamoulous 10y agoI do not see any answers for the questions, do you mind giving them to me so I can check mine?
- zootam 10y ago1. http://math.oregonstate.edu/~show/docs/256-SnowPlow.pdf http://math.oregonstate.edu/~show/docs/256-SnowPlow.pdf 2.https://www.academia.edu/16888899/The_joy_of_problem_solving https://www.academia.edu/16888899/The_joy_of_problem_solving 7. http://www.math.ucla.edu/~ronmiech/Actuarial_Review/Related_Rates/Prob03/Prob03.html http://www.math.ucla.edu/~ronmiech/Actuarial_Review/Related_...
- sk5t 10y agoI guess some of these could be considered basic math, maybe if you associate only with physicists and statisticians. The calculus / related rate problems are straightforward, but most folks will have had no familiarity with Brownian motion, matricies, and most other topics here. Hell, there is little point for > 99% of software developers to think about or use arctangent in any given year.
- nstj 10y agoWow - wish I could upvote this more than once, it's a sad day when someone suggests that some knowledge is within reach and they're downvoted because what they suggested is "too hard"
- minimaxir 10y agoYou are getting downvoted because "everyone should know those maths anyway" is dismissive (I think you meant "everyone [who is applying for a quant position] should know those maths anyway," which is more fair)
- rahrahrah 10y agoNo, I did mean everyone. Or everyone who cares about understanding the world. Or rather, everyone who cares about understanding the world they themselves should be wanting to learn more maths than just sums and multiplications. Anyway, thanks for the feedback.
- _lzell 10y ago| everyone who cares about understanding the world. Those fluent in math really need to drop this egocentric view. If you can't do matrix manipulations you aren't curious about the world? Give me a break. The breadth of topics that yield understanding of various parts of our world is vast. Do you have an early university understanding of history, politics, math, sociology, psychology, economics, law, capitalism, etc. etc. etc.
- rahrahrah 10y agoI didn't say you shouldn't learn those things, did I?
- SonOfLilit 10y agoIf you don't grok matrix manipulations (which are a very simple thing to understand: matrices are linear transformations and matrix multiplication is composition of linear transformations; for some reason this is only taught as a theorem, not as the first lesson in Linear Algebra), you're missing on a really great tool that helps us a lot in understanding almost every kind of large scale process precisely. Without this tool, we'd be back to the 18th century in math, physics, engineering, computer science... It's pretty high up there in "list of things to learn if you're curious about the world". Of course, so are history, economics, etc'
- wildlogic 10y agoHello, I'm hoping for a suggestion for some math courses that will help me understand these questions.. I only took algebra in high school and didn't go to college. Since, I've looked at a couple things (basic proofs, lambda calculus) but quickly was overwhelmed. What is a good starting point for someone who can reverse and exploit all sorts of binaries but does not know what a derivative is? Just start on Coursera? My other question is - what can I achieve with this knowledge? What use is it? What problems can I solve? I think one thing that kept me progressing learning code was I could see what I was looking to achieve and I reached it. I learned it because I wanted to understand it. When I look at math, I see something that I will never be able to understand... There is a part of me that has a strong desire to learn it but the other half tells me to leave it alone. Is it understandable in the same way programming is understandable? By learning the syntax?
- johan_larson 10y agoPart 1 is geometry, calculus and linear algebra. An advanced high-school education in mathematics would let you answer these questions. Parts 2 and 3 are probability and statistics, but they are the kind of advanced statistics that is typically only taught to math students. Second and third year university courses in probability and statistics would let you answer these questions. Part 4 is statistical mechanics, I think. That's a third-year physics course, and one of the more mathematically demanding ones, at that. Part 5 is specific to finance. The course you are looking for is probably called Mathematical Finance. The conventional route to learning all this stuff is an undergraduate degree in mathematics, with an emphasis on statistics. Now, getting there is a long road, but you have to start somewhere. You might possibly be able to learn it all on your own, but it's easy to get stuck and hard to get unstuck without a teacher to help you. If you are in the US, start by taking a couple of classes in a community college. In your case, the course you are looking for is probably called Pre-Calculus or maybe Algebra II. If things go well you can continue from there. As for what use this is, apparently you can get a good job as a quantitative financial analyst if you know this stuff.
- wildlogic 10y agoThanks a lot for the reply, really appreciated.
- sotojuan 10y agoSurely there are areas between web dev and quant that you can do and are interesting.
- binarytransform 10y agoAnd I'll be sticking with business dev. Major respect to those who crush these things.
- koder2016 10y agoIf you can come up with a profitable strategy then you can still be hired or just trade yourself. Without this there is no point being a quant. Besides quants still need developers - those integrals will not help building maintainable trading apps. I would say those questions are for recent graduates who want a junior quant role.
- Tempest1981 10y ago"Quant" = Quantitative Analyst?
- greesil 10y agoI'm having flashbacks to my qualifiers. Yeah!
- jxm262 10y agoI'm partway through the ML class on Coursera and have only recently rekindled my interest in Math. However, my background is in Accounting (undergrad and did a full years as an accountant), and Software Engineering (masters in SE and full time now for some years). Is there a path to actually move into a Quant Job given a software background, to someone who's mathematically inclined? My fear is that I load up on extra "free" math classes, teach myself through MOOC's and self study, and won't have the required degree or connections to break into the field. Is there a recommended path (or is it even possible) to make the major switch from Web Dev to Quant?
- rawnlq 10y agoStandard path as of maybe half a decade ago was to do a masters or phd in financial engineering (sometimes alternatively named computational finance). I personally believe it's hard to self-study since there's many graduate-level math prerequisites that are required if you don't want to just be a programmer. For example stochastic calculus which is the area of math around black scholes option pricing requires graduate level probability (i.e., one taught with measure theory which is itself is a graduate level class after analysis). I do know of some people who tried to put together their own curriculum though: https://www.quantstart.com/articles/How-to-Learn-Advanced-Mathematics-Without-Heading-to-University-Part-3 https://www.quantstart.com/articles/How-to-Learn-Advanced-Ma....
- thess24 10y agoIt's definitely possible with a masters in SE. There are many types of quant (see the markjoshi.com link above) - it will be easiest for you to become a quant developer with your background in software engineering. This will be much more focused on the software development side of things rather than the math/modelling side of things, but depending on the firm will give you large exposure to how the modelling side works. They are very competitive positions, but if you are a strong programmer that can prove you have knowledge of financial markets, have relevant side projects, and can understand and communicate the math behind what you build, you will have a leg up on the competition.
- jxm262 10y ago
- jxm262 10y agoI'm partway through the ML class on Coursera and have only recently rekindled my interest in Math. However, my background is in Accounting (undergrad and did a full years as an accountant), and Software Engineering (masters in SE and full time now for some years). Is there a path to actually move into a Quant Job given a software background, to someone who's mathematically inclined? My fear is that I load up on extra "free" math classes, teach myself through MOOC's and self study, and won't have the required degree or connections to break into the field. Is there a recommended path (or is it even possible) to make the major switch from Web Dev to Quant?
- thearn4 10y agoDidn't expect to see a link up to my graduate alma mater (Kent State U. mathematics department). I know Oana, if there are any questions about the problems or the course sequence that they fit into let me know.
- tnecniv 10y agoPretty sure 3.1 doesn't need knowledge of Markov Chains (even if you implicitly use them)
- akavi 10y agoI feel like solving a lot of these questions are just a matter of either domain knowledge, or not being intimidated by unfamiliar vocabulary. I'd be willing to bet that the vast majority of people who got through a college CS degree would be able to pass this after a couple months of self-study. (On that note, anyone want to chime in on what the job options would look like if someone had a CS degree and could pass this?)
- deleted 10y ago[deleted]
- raverbashing 10y agoYeah, looks like I would need a good statistics and linear algebra refresher to have a chance at it Options pricing is Black-Scholes equation and related equations
- anton_tarasenko 10y agoTo those who want to know more about quant jobs, Mark Joshi has a cheat sheet intro to the profession: http://www.markjoshi.com/downloads/advice.pdf http://www.markjoshi.com/downloads/advice.pdf Joshi co-authored the standard reference for quant interview preps called Quant Job Interview. Interview questions with solutions. It's available on Amazon. If you just wanna try brain teasers, google something like "ext:pdf quant interview". There are many of them.
- lordnacho 10y agoQuant dev here. Note there's broadly two kinds of quants. One is a derivatives quant, basically someone who spends a lot of time working out the values of derivatives. So you're looking at ito calculus and iterative methods to find the value of contracts with weird clauses (Knockouts, Cliquets, vanillas, etc), and then building spreadsheets to calculate the hedges for those trades as time goes by. The other is strategy quants. Here you're looking for some way to beat the market. So you're reading in a bunch of data from various sources and applying some sort of quite open-ended analysis on it to come up with rules for a trading system. You then build a framework for trading such systems, which can get very involved eg execution algos that read realtime market data. I started off in derivatives as a trader but quickly moved on to the other. They're both fairly deep, and both require you to know coding and math. The questions here seem to apply mostly to derivs quants, but strategy quants have found many things applicable.
- pkaye 10y agoSerious question... do people really enjoy working on this stuff? Do most quants go to work thinking it is fun to work on mathematical models to optimize financial transaction. Or is it just a job that pays really well towards long term financial independence to do what they really want?
- jdavis703 10y agoIf you like math and strategy of course it's fun (and I really don't see how someone who doesn't like these things could work as a quant). You're getting paid to use skills you have to solve puzzles essentially.
- mrchicity 10y agoYes it's an awesome job, and not just because of the money. I've worked for small shops that weren't very profitable and didn't really make a lot those years, but still loved the work. I could see derivatives pricing being boring, not as much room for creativity there. The strategy/trading quant work is like a super open-ended science problem with a constant stream of new challenges as you try to outperform yourself or the competition. FWIW, I don't think these are great questions for strategy quants. Some of the best people I've worked with a.) used very, very basic ML techniques b.) were just naturally smart/clever enough to engineer great features. and c.) had incredible attention to detail, didn't "hand wave" away the dirty work like checking/cleaning data or executing the model in practice.
- chollida1 10y agoI wrote about this a long time ago here: https://news.ycombinator.com/item?id=8698986#8699260 https://news.ycombinator.com/item?id=8698986#8699260 I think most of what I wrote is still valid. I believe the below reference: http://www.decal.org/file/2945 http://www.decal.org/file/2945 and the book Heard on teh street are also great refresher's for the type of material you'll need. https://www.amazon.ca/Heard-Street-Quantitative-Questions-Interviews/dp/097005520X https://www.amazon.ca/Heard-Street-Quantitative-Questions-In... To be honest most of this won't matter, the number one qualification for becoming a quant is a Phd from a top tier university. I'm one of the very few quants i've met that doesn't have a Phd, if you don't have one then its going to be a tough road ahead. YOu'll often hear people call themselves a quantitative developer if they come from a computer science background. That might be the most over used phrase on wall street:) It's kind of akin to calling yourself an architect, in that one firms architect is another's junior developer. The term really means nothing and is given out like water, sort of how the engineering term gets tossed around in software dev firms. I've got a pretty long back list of emails from hacker news to get through but if you have any questions about the job, please feel free to email. Just keep in mind that between year end, the US election and life a reply might take a while. EDIT sorry I see that someone used the term quant dev while I was typing. No insult intended. There are some amazing quant dev people on the street.
- WhitneyLand 10y agoYou stress the importance of having a Phd - How much of that is because it's really needed and how much of it is a filter / credibility signal?
- user5994461 10y agoYou need to learn the maths and for that there is nothing close to sitting down in a master/phd classroom for years, doing hard exercises for the whole duration of it, that could get you fired of the school if you ever get a single one wrong at an exam.
- deleted 10y ago[deleted]
- mrcactu5 10y agowhat is the background required for quants these days? I have a Master's in math but no formal training in econmics or finance. Also I graduated 10 years ago
- smallnamespace 10y agoQuickest way to look qualified at least for derivative pricing is go get an MFE.
- rq1 10y agoFor those who speak french : https://www.amazon.fr/101-quizz-banquent-Math%C3%A9matiques-ind%C3%A9pendantes/dp/2311007394/ https://www.amazon.fr/101-quizz-banquent-Math%C3%A9matiques-... by Pr. Gilles Pagès (LPMA).
- JustFinishedBSG 10y agoUnrelatedly Gilles Pagès is an awesome and humble prof
- sarang_neti 10y agoAccording to this advice https://www.quora.com/Is-stochastic-calculus-helpful-to-get-a-position-in-a-hedge-fund-investment-bank/answer/Ross-Kravitz?srid=33wJ https://www.quora.com/Is-stochastic-calculus-helpful-to-get-... these interview questions are not the most important thing
- daleroberts 10y agoPerhaps useful if you are interviewing, this is what I give to my undergraduate students. Mathematical Finance Cheat Sheet: https://github.com/daleroberts/math-finance-cheat-sheet https://github.com/daleroberts/math-finance-cheat-sheet
- kbumsik 10y agoThanks sharing this. I actually see some equation needed for my last midterm lol
- deleted 10y ago[deleted]
- johnnyAAPLseed 10y agodid it start snowing at 7:30am?
- murbard2 10y agoHere's my favorite interview question (spent 10 years as a quant, interviewed a bunch of people, most do not do well on this) We're going to play a game. You draw a random number uniformly between 0 and 1. If you like it, you can keep it. If you don't, you can have a do-over and re-draw, but then you have to keep that final result. I do the same. You do not know whether I've re-drawn and I do not know whether you've re-drawn. Decisions are made independently. We compare our numbers and the highest one wins $1. What strategy do you use? EDIT: The answer is not 0.5, it is not 0.7 either.
- philipodonnell 10y agoThis sounds like a variant of the two envelope problem: https://en.m.wikipedia.org/wiki/Two_envelopes_problem https://en.m.wikipedia.org/wiki/Two_envelopes_problem So is this one of those questions that's not possible to answer you're just trying to see how they handle the stress of the unsolvable?
- murbard2 10y agoIt isn't. There's a clear, well defined answer.
- twic 10y agoI'm just a programmer, but this seems really easy to me. What am I missing?
- SonOfLilit 10y agoSee my post. As a mathematician, maybe you're missing some interesting theory of why if the opponent has an average of 0.625 and you got 0.55 you should redraw. However, as a programmer, the first thing you're missing is running a quick Monte Carlo simulation and seeing whether your idea actually wins :-)
- simias 10y agoBut here you know the content of the "envelope" before you decide whether to switch or not. If the adversary was only allowed one pick I guess I'd only re-draw if I had less than 0.5 since statistically you'd be more likely to have a greater number than a weaker one. I'm not sure what the maths are but a simple implementation gave me an average value of about 0.625 using this strategy, so definitely an improvement over a single pick. But I have the feeling that since the adversary can chose the same strategy maybe you should be a little more aggressive and redraw if you are at 0.5? But then the adversary would do the same so I guess the solution would eventually converge to a value a little above 0.6? That'd be my guess at least.
- zump 10y agoGot an EE degree and a BSc in Math but 3.0 GPA - still possible to be a quant? Will they chuck out my resume or will I still get an interview.
- gragas 10y agoIt doesn't matter if you can't pass the interview.
- YZF 10y agoQuestions 8 and 9 remind me of a math YouTube video I saw recently about "weird" infinite series that can sometimes be solved quite easily. IIRC Consider sqrt(x+sqrt(x +... = x You need to check the series converges (this can sometimes be tricky but seems the questions tell you they converge). Then you can do this substitution for the infinite piece: sqrt(x+x) = x x^2 = 2x x^2 - 2x = 0 ... y = 1/(1+y) [IIRC there are situations where a different substitution yields a different result - I don't recall the details]
- YZF 10y agoThis is the video: "Ramanujan's infinite root and its crazy cousins" https://www.youtube.com/watch?v=leFep9yt3JY&t=687s https://www.youtube.com/watch?v=leFep9yt3JY&t=687s
- hodder 10y agoEnergy trading quant here. If anyone interviewed me with this crap I'd walk out immediately.
- laxatives 10y agoCare to elaborate? I guess those Ramanujan-like infinite series are a bit like trivia questions, right? Does anyone really have an intuition to solve something like that?
- CephalopodMD 10y agoThose are just simple tricks. the first one is 2, the second one, I haven't worked out yet, but it's x where 1/x = 1+x. Just transform those into something with the original in it (square the first, invert the second), then replace the infinite series with the variable you were looking for since you know they'll be equal.
- hodder 10y agoAbsolutely. Just heading out now, but I'll write out a response for you later on. In short, Being a quant is about either measuring risk, or making money trading. This doesn't test either.
- imh 10y agoIt's just pattern matching. How is this pattern formally defined (for the first problem)? x = sqrt(x + sqrt(x+sqrt(x...))) is informal, so the real definition is a recursion x = sqrt(x + THING), and THING = sqrt(x + THING), which is convenient, because that's just x again. So x = sqrt(x + x) = sqrt(2*x). Oftentimes with mathy stuff (but not always), if you have trouble, right out definitions for the confusing parts and work with that instead, recursing until it makes sense.
- Xcelerate 10y agoYeah. Those questions seem to be "hey have you seen this cool trick before?" I used to be excited about the American Math Competition back in high school before I realized that memorizing things like the Sophie Germain Identity, the Cauchy-Schwarz inequality, or the Chinese Remainder Theorem would get you through 99% of the problems on the exam. It doesn't test original thinking — it tests if you're "in the know".
- nsxwolf 10y agoNext time my wife starts looking at jobs for me and says "hey this quant thing looks like it pays a lot, why don't you apply?" I'll just show her this.
- princetontiger 10y agoI worked at a hedge fund for 4 years, and these math questions are irrelevant to market structure. Based on the challenge of most of these questions, I would hazard a guess and say only very recent grads would be able complete these. I'm 6 years out of Princeton, but I've forgotten how to do probably 90% of these questions. Parts 3/4/5 require some pretty specific rules that are more rote memory than anything else.
- radicality 10y agoI graduated ~3 years ago with a CS degree and while I probably could have done most of these questions from sections 1-4 at that time, now all this looks very daunting. Just figuring out how to setup the differential equation for Q1 took a long time and I could, almost physically, feel my thought processes struggling. It's just such a terrible feeling, knowing at one point in the past you would have been more speedy with something and noticing what time has done to your skills. Do any of you have any strategies for not loosing knowledge? Would re-reading textbooks every couple months be a solution? How do I decide if it's even worth - I don't necessarily _need_ this type of knowledge for what I'm doing now but loosing skills you know you once had feels awful.
- CN7R 10y agoIs there an answer key with detailed explanations to this?