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Quant Job Interview Questions (2009) [pdf]

math.kent.edu

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Re: Quant Job Interview Questions (2009) [pdf]

#101

Post by SonOfLilit »

dreeves wrote: post #97
SonOfLilit wrote: post #89

Earlier quoted context omitted.

This... rings so right... but me and probably many other programmers here lack the math to see the explanation immediately in front of our eyes when we hear the answer. Can you please elaborate? Edit: thanks. This is convincing, but... given that we're looking for a fixed point of a process like... [bah, I lack words to describe a vague, non-rigorous intuition]... I expect that there is a convincing one-sentence expl…

Your intuition is better than mine! I crunched it out (just now edited my answer to show how) but still have no intuitive sense of why it should be the golden ratio. Would love to hear some intuition for that!

Saying "It's intuitive to me that this answer someone worked out and told me is correct" is cheating.

But generally...

The process is something like:

If you choose 0.5, then 0.625 beats you because that is the expected average of someone redrawing below 0.5. If you choose 0.625, then 0.617[2] beats you because that is the expected average of someone redrawing below 0.625. If you choose 0.618, then 0.6182 beats you...

Lets ignore those numbers for a moment and focus on the process: "Given a number to redraw below, redraw below the expected value of redrawing below that number".

Trying to find a fixed point for this kind of process, the golden ratio has some kind of... mythological fit? Like, I've heard so many stories like this that ended up with a formula involving the golden ratio...

I wouldn't necessarily expect the answer to be phi, but I would so not be surprised to find it to be some formula involving phi, a rational factor, and maybe pi (just because I have absolutely no intuition for which series happen to sum to rational factors of pi).

[2] I'm getting these numbers by simulation, it's too late for me here in Israel to do math

Re: Quant Job Interview Questions (2009) [pdf]

#102

Post by laxatives »

murbard2 wrote: post #54

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…

Just curious, can you share your role/organization and the people you typically pass and the people you typically fail in your interviews?

Re: Quant Job Interview Questions (2009) [pdf]

#103

Post by SonOfLilit »

SonOfLilit wrote: post #101
dreeves wrote: post #97

Earlier quoted context omitted.

Your intuition is better than mine! I crunched it out (just now edited my answer to show how) but still have no intuitive sense of why it should be the golden ratio. Would love to hear some intuition for that!

Saying "It's intuitive to me that this answer someone worked out and told me is correct" is cheating. But generally... The process is something like: If you choose 0.5, then 0.625 beats you because that is the expected average of someone redrawing below 0.5. If you choose 0.625, then 0.617[2] beats you because that is the expected average of someone redrawing below 0.625. If you choose 0.618, then 0.6182 beats you...…

OK I almost got it (edit: rot13 isn't very good at scrambling one-variable equations, so read at your peril, spoilers ahead):

Jr'er ybbxvat sbe n svkrq cbvag bs "vs gur bccbarag pubbfrf gb erqenj orybj k, jr erqenj orybj uvf rkcrpgrq inyhr".

V gevrq gb qrevir gur sbezhyn sbe uvf rkcrpgrq inyhr n srj gvzrf naq nyjnlf tbg pbashfrq ba jurer V fubhyq hfr k, jurer (1-k) naq jurer 0.5, fb riraghnyyl V gevrq qrevivat gur fcrpvny pnfr jurer k=0.625 naq gung jnf rnfvre:

(1-0.625) [bqqf bs abg qenjvat ntnva] * (1 + 0.625) / 2 [rkcrpgrq inyhr va guvf pnfr] + 0.625 [bqqf bs erqenjvat] * 1 / 2 [rkcrpgrq inyhr va guvf pnfr]

Fb va trareny vg jbhyq or:

s(k) = (1 - k)(1 + k) / 2 + k / 2

Gur svkrq cbvag vf jura s(k) = k, be

(1 - k)(1 + k) / 2 + k / 2 = k

naq...

uggc://jjj.gvtre-nytroen.pbz/qevyy/(1-k)(1_k)/2_k/2=k/

Guvf tvirf n pybfr rabhtu nafjre? Fb V cebonoyl unir fbzr fznyy zvfgnxr ohg unir gur evtug vaghvgvba?

V arrq gb tb gb fyrrc, fb V'yy yrnir vg sbe gur vagrearg gb svaq zl fznyy zvfgnxr, nffhzvat gung'f jung vg vf, naq V pbafvqre zl rkcynangvba orggre orpnhfr vg erdhverf bayl uvtufpubby-yriry zngu :-)

Re: Quant Job Interview Questions (2009) [pdf]

#104

Post by CephalopodMD »

laxatives wrote: post #74
hodder wrote: post #73

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

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?

Those 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.

Re: Quant Job Interview Questions (2009) [pdf]

#105

Post by laxatives »

lordnacho wrote: post #38
pkaye wrote: post #30

Earlier quoted context omitted.

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?

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 thi…

Honestly, this is a great pitch for your line of work. It sounds like you really enjoy it.

Re: Quant Job Interview Questions (2009) [pdf]

#106

Post by laxatives »

chollida1 wrote: post #29

I wrote about this a long time ago here: 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 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... To be honest most of this won't matter, the number one qu…

Is there a reason you linked the 12e of the book? Is the 16e not the latest and greatest? It does seem like they just reprint every 2 years and increase the cost $30....

Re: Quant Job Interview Questions (2009) [pdf]

#107

Post by maverick_iceman »

mrchicity wrote: post #35
pkaye wrote: post #30

Earlier quoted context omitted.

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?

Yes 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…

I've heard the working hours are terrible with 12-14 hours workdays not at all uncommon. Is that true? Is the work pressure very high?

Re: Quant Job Interview Questions (2009) [pdf]

#108

Post by SonOfLilit »

pkaye wrote: post #30
lordnacho wrote: post #27

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 strate…

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?

Not a quant, but:

Imagine playing a huge board game with a bunch of very smart (as in, MIT math PhD smart) players that spend every waking hour trying to come up with strategies, and every time you come up with a good strategy the entire metagame of all players quickly adapts to its existence so the game stays interesting (except for some that lose before they can adapt and have to leave the game.)

Factors in a good game strategy might include fast thinking, every historical move a player played in the game, human psychology, poker-type bluffing, reverse engineering algorithms based only on their outputs, correctly predicting the future of industries and companies, headlines on the news, sentiment analysis on social networks, predictions of election results (and stuff like the Brexit referendum), as well as the complicated rules of the game itself, and Sicilian Reasoning (http://webdocs.cs.ualberta.ca/~darse/rsb-results1.html).

Some things you might do as part of a strategy: charter a fast ship to send information to your friends in another market before it becomes public, so they can buy a lot of stuff before it's price goes up; buy a donut every week in the same shop and keep track of receipt serial numbers to estimate changes in a franchise's weekly sales before anyone else knows them; use satellite imagery of Walmart parking lots and some computer vision algorithms to get a very good estimate of their sales; borrow $10Bn from your friends and use it all to sell British pounds in a very short period of time, forcing the British government to stop pinning the pound-dollar exchange rate and making $1Bn in the process; install a spy network throughout Europe so you get information on the result of the battle of Waterloo a day before the King's intelligence service, spread a rumor that Napoleon won, buy everything that got cheaper because of the rumor, then the next day sell it when the truth that he lost arrives and use the money to more or less buy everything of value in Britain.

At each point in time there is a clear tracking of scores so you can know exactly how well you're doing relative to every other player.

And the best thing is, you get paid the best salaries in the market to play this game.

I love being an entrepreneur because of how open the rules of the game are and how many creative moves I can pull off to get advantage without having to convince some judge or committee or boss that this is a good idea. Strategic quants have all this and the additional benefits of immediate feedback and a great salary with low risk.

Re: Quant Job Interview Questions (2009) [pdf]

#109

Post by DrScump »

SonOfLilit wrote: post #108
pkaye wrote: post #30

Earlier quoted context omitted.

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?

Not a quant, but: Imagine playing a huge board game with a bunch of very smart (as in, MIT math PhD smart) players that spend every waking hour trying to come up with strategies, and every time you come up with a good strategy the entire metagame of all players quickly adapts to its existence so the game stays interesting (except for some that lose before they can adapt and have to leave the game.) Factors in a good…

A good example of real-world application of the donut-receipts idea above is the German Tank Problem[0] from WW2.

[0] https://en.wikipedia.org/wiki/German_tank_problem

Re: Quant Job Interview Questions (2009) [pdf]

#110

Post by YZF »

YZF wrote: post #71

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…

This is the video: "Ramanujan's infinite root and its crazy cousins" https://www.youtube.com/watch?v=leFep9yt3JY&t=687s
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