
Quant Job Interview Questions (2009) [pdf] - dmmalam
http://www.math.kent.edu/~oana/math60070/InterviewProblems.pdf
======
lordnacho
Quant 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
Serious 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?

~~~
lordnacho
There's some interesting things about this work:

\- You get to know something that isn't published. You find a strategy, you
don't tell anyone. Sure, you can talk about it in broad strokes (we're trend
following...) but it's pretty unlikely you'll ever tell anyone enough for them
to be able to replicate it. Except people you trust, of course.

\- You're always thinking about philosophy of science. How do I know that this
series of steps I'm doing is not just a monkey and a dartboard? Again, there
isn't going to be a specific written paper that tells you the answer.

\- At one end of it, you are working with cutting edge technology. Anything
that shaves a microsecond off the speed is useful, and you can spend a lot of
time optimising such things. I've been staring at a C++ solution that is 100%
in house. No STL.

\- At the other end, you are working with data in very modern ways. All that
ML stuff in the news is interesting to quants, because if there's one thing ML
papers are about, it's how to avoid overfitting. Just a few years ago people
in the field had not come across ML, or at least the point of view that ML
brings. Plenty of other things had already come up, though, like information
theory, time series econometrics, signal theory, and so on.

\- About derivs quants, it's not my cup of tea, but I can see how others like
it. You're basically pricing things hoping that you've noticed something the
counterpart hasn't, or hoping you've found a cheaper way to hedge than your
competitors, or simply hoping your salesman is a better salesman than the
other guy's.

~~~
DeBraid
This is good stuff, thanks for articulating your experience in the role.

------
chollida1
I 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-
In...](https://www.amazon.ca/Heard-Street-Quantitative-Questions-
Interviews/dp/097005520X)

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
You 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
You 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.

------
murbard2
Here'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.

~~~
danielvf
This seems so simple.

Decisions and draws are independent - we can ignore the other guy and just go
for the highest value. Draw the first number. If it's below 0.5, draw again,
since the odds then are that the next draw will be higher.

Is there more?

~~~
SonOfLilit
I was 100% sure that redrawing below 0.5 is optimal, but a simple simulation
disagrees:

    
    
        def tournament(a, b, n=1000):
            return sum(a() > b() for _ in xrange(n)) / n
    
        def redraw_below(c):
            x = random.random()
            if x < c:
                x = random.random()
            return x
    
        In [23]: tournament(lambda: redraw_below(0.5), lambda: redraw_below(0.6), n=10000000)
        Out[23]: 0.4948004
    
        In [24]: tournament(lambda: redraw_below(0.5), lambda: redraw_below(0.6), n=10000000)
        Out[24]: 0.4948039
    
        In [25]: tournament(lambda: redraw_below(0.5), lambda: redraw_below(0.6), n=10000000)
        Out[25]: 0.4948802
    

`redraw_below(0.5)` only beats `redraw_below(0.6)` 0.4948 of the times, very
consistently, over three sets of a million rounds.

This is despite `0.5` giving a better average (0.624 vs. 0.620).

I'll think about why, but the result is very consistent and can't be ignored.

~~~
ajkjk
It makes sense that the highest expected value doesn't necessarily indicate
the best strategy.

For example, suppose you're playing against someone who has taken the "reroll
values greater than 0.5", giving them the expected value of 0.625.

If you roll the value 0.55, you expected to lose more than half the time,
because their expected value is 0.625. So you should reroll anyway.

~~~
soVeryTired
I think this is the key. Given that the game is winner-take-all, maximising
your expected value isn't necessarily the right way to go. To take an extreme
example, suppose I had a magic strategy that gave me a value of 1 every few
throws and a lousy number most other times. That might give me a good expected
value, but I'd still lose most rounds.

So what's the right objective? Trying to beat your opponent's median score, so
that you win more than half the time?

Edit: I think you're on the right track, but I'm not sure I believe that you
will lose more than half the time if you land below your opponent's expected
value. I think that assumes their distribution of scores is non-skewed, which
is not obvious to me.

------
anton_tarasenko
To 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.

------
jxm262
I'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?

~~~
thess24
It'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
Thanks. You're reply gave me a boost of inspiration. I'm working now to learn
more of the Math and modeling side of things, but I know it's going to be a
_long_ hard road. Thanks for the link, that site seems to have some great info
- I particularly like this
[http://www.markjoshi.com/downloads/advice.pdf](http://www.markjoshi.com/downloads/advice.pdf).

I'm curious what sort of side projects I could try that others could take
notice on.

------
20161112
Sigh...I guess I'll be sticking with web dev.

~~~
rahrahrah
I 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?

~~~
minimaxir
You 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
No, 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
| 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.

~~~
SonOfLilit
If 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'

------
akavi
I 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?)

------
radicality
I 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.

------
daleroberts
Perhaps 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
Thanks sharing this. I actually see some equation needed for my last midterm
lol

------
thearn4
Didn'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.

------
Tempest1981
"Quant" = Quantitative Analyst?

~~~
snoman
Yes

------
nsxwolf
Next 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.

------
CN7R
Is there an answer key with detailed explanations to this?

------
YZF
Questions 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
This 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)

------
sarang_neti
According to this advice [https://www.quora.com/Is-stochastic-calculus-
helpful-to-get-...](https://www.quora.com/Is-stochastic-calculus-helpful-to-
get-a-position-in-a-hedge-fund-investment-bank/answer/Ross-Kravitz?srid=33wJ)
these interview questions are not the most important thing

------
rq1
For those who speak french : [https://www.amazon.fr/101-quizz-banquent-
Math%C3%A9matiques-...](https://www.amazon.fr/101-quizz-banquent-
Math%C3%A9matiques-ind%C3%A9pendantes/dp/2311007394/) by Pr. Gilles Pagès
(LPMA).

~~~
JustFinishedBSG
Unrelatedly Gilles Pagès is an awesome and humble prof

------
hodder
Energy trading quant here. If anyone interviewed me with this crap I'd walk
out immediately.

~~~
laxatives
Care 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?

~~~
imh
It'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.

------
tnecniv
Pretty sure 3.1 doesn't need knowledge of Markov Chains (even if you
implicitly use them)

------
raverbashing
Yeah, 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

------
mrcactu5
what 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
Quickest way to look qualified at least for derivative pricing is go get an
MFE.

------
greesil
I'm having flashbacks to my qualifiers. Yeah!

------
princetontiger
I 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.

------
zump
Got 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
It doesn't matter if you can't pass the interview.

