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Lebowski


Total Posts: 66
Joined: Jun 2015
 
Posted: 2015-11-24 17:26
Hey folks. I have three semesters left in school and am wondering what upper division stats courses you'd recommend I take before I graduate. I'm looking to be as prepared as possible for a HFT/trading/trading software development career. I've already taken: intro sequence, probability, inference, regression, data mining, statistical machine learning, and have registered for stochastic processes for finance.

Here's our stats course directory:
http://bulletin.columbia.edu/columbia-college/departments-instruction/statistics/#coursestext

Also, I'm curious what math classes you feel would be best to round out my undergraduate math experience. I have taken calculus I-IV, linear algebra, a class in numerical methods, and optimization and analysis. I will need at least one more math class, but would be happy to take more. I was thinking one or more semesters of differential equations (should I take the applied or theoretic offering?), intro to higher math (or whatever the exact name is) to get a broader understanding of proofs, etc., and modern analysis I (should I look into II as well?). I believe I can register for up to two graduate business school, MAFN, or MSFE classes. Econ classes like econometrics and game theory have prohibitive prereqs, unfortunately. Aside from that, I'm not sure what classes would be most applicable, so here are some choices:

Math:
http://bulletin.columbia.edu/columbia-college/departments-instruction/mathematics/#coursestext

Additionally, I can take applied math courses:
http://apam.columbia.edu/apam-courses

And finally, they're difficult to register for, but maybe I can swing into some OR courses:
http://ieor.columbia.edu/ieor-courses-topics

I'm gonna exclude CS from this discussion for the sake of brevity and because I have my own interests there. Also, I'm open to grad school in the future, but I think I'm headed straight to work (likely in NYC if my internship goes well) at the moment. Columbia will let you take classes after you graduate, so I can always come back and take more classes if I really wish to do so.

Thanks for your time here. I'm looking forward to gaining your insight as practitioners about what courses will serve me best.

HitmanH


Total Posts: 423
Joined: Apr 2005
 
Posted: 2015-11-24 18:09
Are you interning presently in NYC? Probably I'd suggest to ask the guys you're working with.

From a firm very much in the space you're looking at (although UK based) - I'd be tempted to say that some econometrics would be good (but can see your comment), OR is good.

In terms of pure math - you're not pricing some complicated credit deriv that some private banker has invented to defraud their clients, a lot more HFT/trading is a little coarser - and getting things that work is where the focus is, not theoretical math

Lebowski


Total Posts: 66
Joined: Jun 2015
 
Posted: 2015-11-24 18:50
@HitmanH. Thanks for your reply. I have asked one guy on the desk I'm going to be working with this summer, and he said that really just more CS is the best thing I can do. My internship is doing software on a trading desk. I think my sweet spot at the moment is really software, but maybe down the road I'll be able to do more trading. The number of places you can go from undergrad straight to alpha generation are not that high, and I think software has more mobility, job security, and provides my best inroad into alpha generation roles (since the alternative routes appear to be grad school or winning a Putnam Competition).

I think econometrics would be something that would really interest me and it is unfortunate that Columbia has about 1,000 Econ majors at any given time scrambling to register for it. How does Time Series Analysis sound as a possible replacement?

I mirror your sentiment about higher math and several folks in the prop trading/HFT industry feel the same...some don't though, it's odd really. I think reading my question, it's clear I'm shifting more towards statistics, but at the same time I think the three courses I cited may be worth taking for the following reasons:
- Intro to higher math: It's just one class that will perhaps make me a lot better at reading research papers.
- Diff Eq: It's tough to respect an undergrad math degree that doesn't feature ODE. I already kinda know DEs from my numerical methods class and calculus IV, and I also know that we have computers for this, so I think this is the weakest choice of the three, but I see DE's as a prereq for a lot of grad schools, so I'm kinda scared to graduate without taking it.
- Modern Analysis: I hear a little measure theory goes a long way to understanding probability theory. My advisor also said that this is a class I should not skip if I wanna go to grad school in statistics at some point.

I'd appreciate your input on these three justifications and time series analysis. Thanks for taking the time to reply.

darkmatters


Total Posts: 66
Joined: Nov 2010
 
Posted: 2015-11-25 19:05
I'd recommend the independent research courses offered.

Lebowski


Total Posts: 66
Joined: Jun 2015
 
Posted: 2015-11-25 19:29
@darkmatters I neglected to mention this, but I had considered the same thing. Thanks for taking the time to take such a thorough look as would be necessary to stumble upon that! I spoke to my stats advisor about doing some research into order book dynamics, and he said that it sounded like a potentially valid topic and would point me to good profs to work with. I haven't really followed up, but I spoke to my general academic advisor who gave me some references for funding, which--hopefully--I shouldn't even need as I have a decent amount of market depth data and I'm sure the school does too somewhere. Solid suggestion. Book dynamics/microstructure is just a topic that interests me a lot, so I think this could be a really cool opportunity. I'll follow up and see if I can register for independent research with any of the profs into this stuff here after thanksgiving. Thanks for your reply.

darkmatters


Total Posts: 66
Joined: Nov 2010
 
Posted: 2015-11-25 19:45
Doesn't have to be on Market Microstructure. Most of the research there is crap anyway. Any research on any or the areas you linked to, especially if it is real research and not a fancy literature review (like results in a publication), is a good thing to do and will prepare you more than most courses will.

Lebowski


Total Posts: 66
Joined: Jun 2015
 
Posted: 2015-11-25 20:44
Your point on any [real] research experience being good experience is well taken. Admittedly, I probably haven't read a whole lot of research on other subjects by most standards, but a lot of microstructure research is pretty poor. I get the feeling a lot of it is just really overfit. Although I have the sense that a lot of the research is somewhat poor, I think reading is good for me at this point in my career because it helps to establish context. I've been doing some "unstructured research" of my own outside of school, so I think this topic would be a natural extension of that. I'm open to other stuff too, it just hasn't jumped out at me yet.

nuprin


Total Posts: 13
Joined: Jul 2009
 
Posted: 2015-11-26 00:32
You might want to check out "Data Analysis for Financial Engineering," offered by the IEOR department. Link with details: http://ieor.columbia.edu/data-analysis-financial-engineering

It covers Garch, ARMA, MCMC, etc. The only catch: it's for graduate FE students. But it couldn't hurt to ask for an exception from the prof and/or department administrator. If you want a contact for the latter, just ping me. And if you had any interest in the MSFE program, wanted to try a class, and stated as much, I suppose that could help your chances.

Best of luck and Happy Thanksgiving!



a路径积分


Total Posts: 77
Joined: Dec 2014
 
Posted: 2015-11-26 08:34
TBH, if you haven't done diffeqs and real analysis, it's hard to imagine how 1 additional math course will be a huge boost to your resume. You're probably right that you would want to take the CS angle.

a路径积分


Total Posts: 77
Joined: Dec 2014
 
Posted: 2015-11-26 08:34
TBH, if you haven't done diffeqs and real analysis, it's hard to imagine how 1 additional math course will be a huge boost to your resume. You're probably right that you would want to take the CS angle.

Lebowski


Total Posts: 66
Joined: Jun 2015
 
Posted: 2015-11-26 11:00
@nuprin, I'll take that into consideration. Thank you. Those classes are extremely difficult to register for, but I can petition up to two MSFE classes, so now might be a good time to do one. I see few better choices. I'll speak to my advisor after thanksgiving, have a nice holiday as well and thanks for sharing your experience here. Is there anything advantageous in taking this class over the MAFN equivalent, which I presume to be stat inference/time-series modeling G6503? I'm guessing this one will be easier to register for. No worries if you have no knowledge here, I've copy pasted the description:

STAT G6503 Statistical Inference / Time-Series Modeling

Modeling and inference for random processes, from natural sciences to finance and economics. ARMA, ARCH, GARCH and nonlinear models, parameter estimation, prediction and filtering.



@a___ yeah, per my earlier reply, these are classes I plan to take. At least one semester of diff eq and one semester of modern analysis. I may take both of each if I have time, I may not. I'll take fault for not having taken diff eq yet, but most people tend to take modern analysis their senior year. There's still some time on the clock.

While I have a practitioner here, let me ask you this: there seems to be a divide in the HFT folks I've spoken to. The majority seem to be along hitmanH's lines and maintain that higher math isn't as important as developing the skills to get the job done, which in my mind seem to indicate stuff like independent research, CS courses, and stats. There's also a few who vehemently maintain that higher math is necessary or at least fair game for interviews, etc. Why the disconnect and why do the latter feel the way they do? I've sort of put together this impression that you may have a math PhD from your replies, and you obviously hire at a HFT entity, so if you see fit to offer any insight on this, I'd appreciate it.

I'm thinking CS is my best way in. It got me my job this summer and I think it's a skill that is undeniably important in this industry. You have to understand that I'm different from you (if you did do a math PhD) in this sense. I'm the definition of selection bias. I don't really care for a PhD in math at this point in my life and I doubt my background would allow me to pursue one. I study math and stats because I'm interested in an application of them. I don't think I'll ever progress mathematically to a point that will allow me to get a job over a younger you. That's not gonna be my strength. I'm better off following my current strengths and interests and letting my career (hopefully) unfold in front of me vs. trying to become a serviceable mathematician. Does this mean I'll stop studying math and forgo my school's equivalent of real analysis? No, I'm fairly confident I'll take it. I can get good at some applications of what I've studied, learn a lot about trading, and get better at developing software that supports trading in my current situation, so I think that's the route I'm gonna go.

a路径积分


Total Posts: 77
Joined: Dec 2014
 
Posted: 2015-11-26 12:06
The reason for the divide in opinion is probably because "HFT" is a very vague term that qualifies a wide range of strategies. Another reason is that a good fraction of them are just relaying hearsay.

I don't know what kind of job you're looking for specifically, to be frank, but I know you sound very ambitious and probably want to get into a prestigious team. (And that's OK. Many people do.) My advice was really conditioned on you seeking a job at a prestigious firm rather than seeking a job at a "HFT" firm. I make a side note here that there's a substantial overlap between both categories.

I apologize if I'm wrong about your goals and you're actually only looking for jobs in HFT. In that case I would even argue that that's a worser goal, because none of us can guarantee you that it's the best field to be in 2 years from now.

Now, I'm not saying that those courses that have been listed aren't intellectually satisfying or useful... I fully agree that they are. But you need to be decisive as to whether you're trying to maximize your chances of getting a prestigious job vs trying to maximize your PnL presuming you have already landed said job vs hoping to find a happy middle ground. The problem with going down the math path for you is that most MFins/MFEs have done the classes you've named, so there's little differentiation if you're just a carbon copy.

nuprin


Total Posts: 13
Joined: Jul 2009
 
Posted: 2015-11-27 02:32
@Lebowski - I don't know the MAFN class. I am offering suggestions *if* indeed you want to taken an Econometrics course. If so, why not sign up for both? If they allow you to enroll in the IEOR class, and it suits you better, great. Otherwise, the MAFN class. Then drop the less desirable class.

I'm not going to recommend whether you do an MFE, or go into HFT, etc. But I will offer a little (unsolicited) life advice: whatever you study, I would suggest studying what's both interesting to you and relevant across multiple domains/job markets. That is, have a Plan B. Because you never know how you'll like something, until you do it. Maybe HFT is indeed your true passion. Or maybe not. Nothing wrong with either. Just my $.02.

P.S. IMHO, you're getting some excellent, honest advice on this board. EDITED TO ADD: That's a credit to the posters here.

Lebowski


Total Posts: 66
Joined: Jun 2015
 
Posted: 2015-11-30 17:28
[deleted]

Lebowski


Total Posts: 66
Joined: Jun 2015
 
Posted: 2015-11-30 17:37
Sorry for being unresponsive over the break. Thanks as always for your replies. A credit to this phorum as @nuprin mentioned.

@nuprin I appreciate your sentiment. I don't really see myself doing an MFE, but maybe an Masters in Stats or CS. I think they would offer flexibility outside of trading and could even be more marketable for prop trading jobs vs. an MFE which in my limited expertise seems to be more of a pipeline to quant roles in banks focusing on risk and pricing.

@a___ Thanks for your reply, your explanation makes sense. I'm not sure how I feel about the issue of prestige of my employer. Short term, I can tell you prestige influenced my choice this summer a lot. I wanted to get a big name on my resume for a number of reasons...training, name recognition, exit opportunities, the people I'll meet working there (all of this pretty contingent on a full time offer). As my career progresses and I feel more compelled to try to find a job that is more alpha generation than technology oriented, I would be perfectly fine with a smaller unknown firm. Some of the HFT's I've spoken to in the < 20 employee range seem to do just fine and have what I would consider a more relaxed workplace environment. I'm open to a lot of things though.

Lebowski


Total Posts: 66
Joined: Jun 2015
 
Posted: 2015-11-30 17:39
[deleted]

Lebowski


Total Posts: 66
Joined: Jun 2015
 
Posted: 2015-11-30 17:41
[deleted]
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