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This question is somewhat related to my previous question here but has not been addressed in any other thread. The answer in that thread hit the nail right on the head with that one line "Textbooks will go into far too much material if you plan to read them cover to cover, and hence you have little idea of when to stop reading a textbook." I want to get validation on my current approach and if there are loopholes, I'd greatly appreciate any suggestions to cover them up.

I wish to gear up towards a career in hedge funds as an arbitrage quant. I have a PhD in EE majoring in Analog IC design with 12+ years of experience in the industry. I am well versed in linear algebra from my education in engineering. The following is what I think I need to study.

Currently, I have covered the first seven chapters from Stephen Abbott's "Understanding Analysis" including all the exercises. I will be covering the eighth chapter as well.

  1. Having read through Abbott's book, I really do not see much point in going through Rudin's PMA before moving on to measure theory. Is Rudin really required before I move on?

  2. Next, I plan to study Rene Schilling's book on measure theory. As with #1 above, I really doubt if I have to go deeper into books like Billingsley's. Is it really necessary to study Billingsley's book before moving on to the next stage?

  3. Finally, I will either study Shreve's two volume books or Oksendal's book on stochastic differential equations which I learn is necessary for the type of career I am looking for.

  4. In parallel, I will pick up Python which is geared towards finance, specifically towards statistical arbitrage.

The way I see it, I can cross the three main tiers (excluding Python which is a low hanging fruit) assuming they are just

  1. Analysis from Abbott which I am mostly done with
  2. Measure theory from Rene Schilling
  3. Stochastic differential equations from either Oksendal's or Shreve's material.

The more books that get added to this list, the longer it will take for me to get to the end of it which is perfectly in line with the answer given in the thread I have pointed out in the beginning of this question. So if I am looking at the infima of all the material needed to make an entry into a hedge fund as an arbitrage quant, would that be #1, #2, and #3 mentioned above or is it more than that?

Specifically, do I have to grind through Rudin's "Principles of Mathematical Analysis" and Billingsley's "Probability and Measure" as well before I get started with stochastic differential equations?

TryingHardToBecomeAGoodPrSlvr
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    You need to program basic trading strategies if you want to become an algorithmic trading type quant. I am a mathematician turned quant - the most important skill is to be able to program a trading strategy and work with and clean data. My whole day is usually spent in front of the computer testing and cleaning things, not in front of the whiteboard. – rubikscube09 May 21 '21 at 16:50
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    You seriously don't need to study any of these books (I read all of these as part of my mathematics education, and they were very interesting, but ultimately fruitless for 1. finding a job in the field 2. Performing duties for said job)\ – rubikscube09 May 21 '21 at 16:51
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    Focus on programming in python and analyzing and using time-series data. Focus on how you would build and rigorously test a trading strategy. Focus on how you would test things for statistical significance. It is these sorts of skills that are not very theoretically demanding at all, that are ultimately important to being the kind of quant you want to be. – rubikscube09 May 21 '21 at 16:53
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    Things like time-series books (for example, Tsay's book, whose class I also took) don't require you understanding the ins and outs of real analysis to understand (it helps with technical details - not in practice) - for god's sake, there were MBA students in the course! Just a strong understanding of probability and statistics – rubikscube09 May 21 '21 at 16:56
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    TLDR - Pick up an econometrics book + time series book, and learn to program with data as much as you can! – rubikscube09 May 21 '21 at 17:00
  • Thanks a bunch for your feedback. On the one hand, I read some articles where they list a bazillion things to know (like for instance Numerical Linear Algebra, stochastic DE, statistical inference, etc). It is overwhelming. On top of that, they mention a lot of programming skills. I mean do research arbitrage quants at hedge funds know everything on earth? – TryingHardToBecomeAGoodPrSlvr May 21 '21 at 17:02
  • I agree with rubikscube09 on the coding part. Essentially, that's your best bet at convincing the firm, that you're really good at something. Also agree with Brian - you won't stack up well against a PhD in Probability no matter what book on Stochastic Calculus you read. I disagree with rubkiscube09 on coding up a strategy - I never felt it as a compelling argument to hire someone. So I'd say if you can demonstrate you're very good at coding + basic statistics (nothing fancy, linear regression, normalization), you'd have a good shot at it. – LazyCat May 21 '21 at 17:04
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    I agree with you - it's a very broad skillset that requires learning of economics, computer science, mathematics and statistics. Deficiency in any of those can be problematic, but they have a lot of overlap so it's doable. Ultimately you need to be able to actually do the job, which at the end of the day is coding + statistics, so I'd focus on those. A good site to practice these things combined is kaggle – rubikscube09 May 21 '21 at 17:05
  • @LazyCat yes I agree, no trading strategy you write will impress anyone, but it seems like a good way to apply some of the statistics you learned. If I interview someone, I'd be more interested in them trying (and obviously failing) at building a strategy, than if they just did conv-neural-nets on cats and dogs and presented that as experience. But it all depends I guess. – rubikscube09 May 21 '21 at 17:06
  • @rubikscube09 Thanks for letting me know about kaggle. I had not heard about it before. So do you suggest I don't even bother with any of the books I have mentioned? I really want to give it a good shot to get into a role of an arbitrage quant and from all I read over the internet, stochastic differential equations seems to be the minimum requirement for them to even sniff at my resume. While the coding part is obviously what is needed for me to deliver the goods, isn't SDE (and measure theory etc) kinda of minimum requirement as well? – TryingHardToBecomeAGoodPrSlvr May 21 '21 at 17:10
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    @TryingHardToBecomeAGoodPrSlvr SDE and measure theory are necessary to rigorously understand options pricing, not much else. Frankly, you don't even need measure theory, unless you want to rigorously learn about Ito-Calculus and Progressively Measurable processes and how every continuous martingale is a time-change of Brownian motion. And ultimately, I'd wager none of that really matters at the end of the day, even for options pricing, unless you're writing academic papers. If you want a job like this you need to write code and be able to do statistics with data - not write proofs. – rubikscube09 May 21 '21 at 17:13
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    @rubikscube09 Ok. I am going to focus on econometrics and Python. Tsay has a book on Time Series and I guess that's what you were referring to. I'll take a look at that. – TryingHardToBecomeAGoodPrSlvr May 21 '21 at 17:24
  • @rubikscube09 we're on the same page regarding "conv-neural-nets on cats and dogs" .. – LazyCat May 21 '21 at 19:41

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I get this question frequently from academic types, and happily for you, the path does not involve any of those books.

The major gaps in your knowledge, from the point of view of statistical arbitrage, are not mathematical. Most or all of them are not even statistical. Rather, they are gaps in knowledge about arbitrage, and how to take part in it.

PhDs with more than enough skill in measure theory, control theory, SDEs, PDEs etc are a dime-a-dozen. Hiring managers are more concerned about whether a candidate can actually use those skills in a meaningful way -- nobody will assign 1-3 other employees to implement ideas from some rookie math primadonna who does not even know the markets.

Hiring managers will be more interested in whether you have actually done some trading (say, in personal accounts). And they will be much more interested in how much coding skill you can demonstrate.

Brian B
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  • That's comforting. However, isn't this a chicken and egg problem for someone like me who is wanting to make an entry into this field? That is how can I show trading experience before I get my first break as an arbitrage quant at a hedge fund? Can you please suggest ways I can actually get trading experience as a newbie? – TryingHardToBecomeAGoodPrSlvr May 21 '21 at 14:19
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    @TryingHardToBecomeAGoodPrSlvr - Try to write (program) a trading strategy, and a framework (write a backtesting library) to test such trading strategy. Fail because the strategy will almost surely not work. Try again, rinse and repeat :) – rubikscube09 May 21 '21 at 16:54
  • @rubikscube09 My apologies for the really late response. I somehow missed seeing it. I am doing something which is in line with your suggestion. Brian B also kinda mentions the same thing in his comment "Hiring managers will be more interested in whether you have actually done some trading (say, in personal accounts)" ... a way to break out of the chicken and egg problem. It's a shame though, that I'll be getting into this endeavor by myself. Most of my life, I have worked in groups with a mentor which was a lot of fun :) – TryingHardToBecomeAGoodPrSlvr Sep 25 '21 at 07:56
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    No worries - again, the emphasis isn't on writing a successful strategy by yourself. Everyone knows that's impossible. But showing you tried, and learned something from it is key. – rubikscube09 Sep 25 '21 at 14:49
  • @rubikscube09 Thanks for sharing all the information and for your encouragement! I greatly appreciate it. – TryingHardToBecomeAGoodPrSlvr Sep 26 '21 at 08:11