I have a PhD in mathematics which I completed three years ago. The degree involved traditional coursework in various areas of abstract mathematics, the passing of a comprehensive exam and the submission and publication of a dissertation. I have also been teaching mathematics (all abstract) since finishing my degree. My expertise and therefore research has so far been limited to a very theoretical field. None of what I currently do has any direct real life application. I only have background in undergraduate statistics. I have attended graduate classes in differential equations - the one area of mathematics I have taken that I assume has applications in finance, as well as off-university workshops but only those that focus in mathematical biology.

Recently, I have taken interest in investing stocks and have been reading various resources on non-quantitative trading methods. I myself do not have any investments at the moment, but will probably start having one this year.

I only have a cursory knowledge of quantitative analysis. What I do know is that the field requires a high level of mathematical fluency, which I suppose I have given my degree, and that if I ever need to learn another field of study, I might not have a difficult time grasping the concepts. If it helps, I also have background in C, R, Mathematica, Maxima and Octave. My goal is to pursue a freelance career as a quantitative analyst on the side and slowly transition into mathematical finance as my area of research. The end goal is to still continue publishing papers (which is what my university requires of me) in applied mathematics and at the same time achieve significant financial gains as an analyst. What I am not willing to do is go back to university and get a related degree, or any form of formal classroom training. I am open to enrolling in online OCWs and pay for certifications, or self-study.

My questions are as follows: 1. First is that I need the knowledge/technical background in what I intend to pursue. Where exactly should I start? Where can I get the training? Any recommended OCWs? 2. Assuming that I am now have the requisite knowledge, how do I start practicing?

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    Use your PhD to earn, build an emergency fund and pay off student loans. Then invest in index funds with impunity. – Pete B. Jan 11 at 12:49
  • Do you know of any freelance quants? – quid Jan 11 at 19:09
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    relevant xkcd – Kevin Jan 11 at 19:43

My goal is to pursue a freelance career as a quantitative analyst on the side and slowly transition into mathematical finance as my area of research. The end goal is to still continue publishing papers (which is what my university requires of me) in applied mathematics and at the same time achieve significant financial gains as an analyst.

It seems very unlikely you can make it as a freelance "quant" without ever having worked formally as a quant analyst for some sort of trading firm. Making money in the stock market using advanced mathematics goes way beyond textbook or PhD research - there are entire departments of brilliant MIT PhDs on wall street developing proprietary algorithms for securities trading, working 100 hours a week and getting paid da big bucks. If you want to learn the field, go work at one of those shops for a few years, then try and make it on your own.

Even then, a major challenge would be that most of the advanced math that yields profit on Wall Street requires very high speed connections to the wall street data servers, to check prices, buy, and sell, all near instantaneously. And that kind of data pipeline is expensive. VERY expensive. Quant traders and automated trading algorithms often need their computers to be physically very close to the exchange computers, since the trading times are so short that the speed of light is too slow for distant computers to be useful.

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    Just in case it wasn't clear - you would be directly competing with the big departments of brilliant people. – not_a_comcast_employee Jan 12 at 10:35

Firstly, just because you have a PhD in some (probably abstract) area of math, doesn't mean you automatically have a gift for everything to do with numbers. So give up on this idea that you're sitting on a money printing machine just waiting to be plugged in. Just like you've undergone 5+ years to do your PhD, on top of 4+ years of build up during undergrad and possibly 12 years during K-12, the "market wizards" have also spent a lot of time learning about finance to get to where they are. Not to mention inborn talent (for abstract math in your case, for finance in theirs).

By your own admission your experience and knowledge of trading is minimal, so get ready to start at the beginning. The good news is, this is where your PhD will afford you some benefits:

  • You are fluent in mathematical terminology, accustomed to reading proofs and theorems, and (hopefully) comfortable applying principles given in a very abstract form. This is a huge barrier for non-math people that you won't have to overcome, so try to go for more mathematically rigorous aspects of investing like quant finance, statistical finance and academic papers on pricing/portfolio optimization theory. You will learn these much faster.
  • Your research experience should have taught you how to digest technical texts quickly, take good notes, think critically about your text, and easily spot illogical quackery. Use these skills.
  • Learn how to code and work with big datasets. Learn at least basic stats that goes with it. Luckily in finance your statistical approach is not bound by the reviewer's whims, if it works, it doesn't matter what some other professor thinks of your particular p-value calculation method. But it still has to work. More broadly, these days you can't do any useful quantitative work in trading without big data (it's all been arbitraged away, and the markets are too complex). So you have to get comfortable working with big datasets, and also obtaining them (often financial data is locked behind paywalls).
  • The latest big thing these days is AI, specifically convolutional neural networks, deep learning, machine learning generally and all that. This would be very useful to learn. Your existing math knowledge may or may not carry over much, but regardless you are in a good position in terms of fundamentals to have as good a shot as anyone to learn ML. I recommend you try to learn as much ML as you can, trying to stay focused on time series, and ideally finance/stock data. A lot of ML is pretty general, so if you learn to predict say Taxi commutes or cancer treatments, it's not that different from analyzing stocks, but when getting started it can be very helpful to learn in the appropriate domain and hearing about all the particular quirks of that domain.

As far as monetizing your PhD, there are two ways to go: You can trade yourself, or you can work for a company doing a tiny part of a big trading system very well. I highly recommend against the first option. You would be competing against some real clever dudes, who on top of experience and knowledge have immense institutional resources and connections behind them. You will likely fail. At best you could try a niche, non-traditional market like cryptocurrency, but then you have all the problems that come with that. And the big boys have all heard of crypto now, it's not 2009 anymore.

The more boring but much more promising route is to brush up your skills as much as possible and try to get a job in the industry. Some companies don't want random dudes with a PhD and a head full of dreams, they want people with finance degrees and finance experience - you'd be wasting your time talking to them. Others are willing to take promising people with good skills, but no or little finance background - this is what you're going for. They would be hiring you mainly for those skills (probably coding, data, math, stats) that they're looking for, not finance knowledge, but having finance knowledge would probably make a considerable difference during hiring, so your strategy would be to learn the practical aspects of your existing skills, learn to communicate effectively what those skills are and what your background is (the interviewer probably won't have a clue), but also as much basic finance as you have room for. Working at a company or institution will shield you from market risk, but people working on things that make a lot of money, usually also make good money themselves. You can then save some of that money and do your investment, too.

I know this might sound a tad vague, but writing an entire math to finance transition curriculum here would not be feasible, nor would it be a very helpful answer to other users because it is so dependent on the person. Good luck!


No one would invest in a hedge fund, or use a consultant, that doesn't know what its play is.

A hedge fund could certainly hire someone with potential and then a career and an expertise could develop from the position.

Here's a link to a quantitative analyst article:

https://www.bloomberg.com/news/features/2018-11-19/the-triple-jeopardy-of-ke-xu-a-chinese-hedge-fund-quant .


I would say the place to begin is to come to the really harsh realization that securities markets are not rational. As far am I'm concerned there is no amount of compute power and data that will ever exist which can predict the movement of an individual security in a known period of time. There are certainly market inefficiencies that can be uncovered at times, but time has a value (cost) and early is the same as wrong.

When you apply heat to steel the outcome is known. There is a formula, it all makes a lot of sense.

There is not a formula for the stock market, or commodities market, or forex or whatever other security. There are a lot of people who think they can find one. There are fewer who think they ever came up with one. On a long enough timeline even a formula that works will fail. The market adapts, the market existed before the treasury did, before we abandoned the gold standard. Is market data from 1950 relevant to today? Is market data from yesterday relevant to today?

Yes, to some extant finance involves numbers. But REALLY, finance is business. Business decisions are not always rational. Sometimes, 2 + 2 = 5 in a way that makes no sense and is never repeated. Sometimes 2 + 2 = 5 in a way that rightly makes no sense and eventually falls apart in a way that should have been known and could be capitalized on by the skeptics who don't follow the herd and didn't run out of money before the short position came to fruition. I think the fact that there are a lot of numbers in finance lures people in to a false sense of security that the numbers must interact with each other in a predictable manner. To some extent even theoretical math has rules that don't involve the mood someone was in when they signed an underwriting deal for a corporate bond issue.

If I could offer one piece of advice, I'd recommend that you read the book Flash Boys. This book chronicles the rise of computer driven high-frequency-trading. To give you the punchline, these shops make money by buying in one market for $1 and selling in another market for $1.001 a lot of times. It's not actually about a really fancy strategy that can identify and capitalize on a market inefficiency by simply feeding quote information to a really complicated formula.

There are various market simulators that use actual market data to facilitate testing a strategy. You may want to give that a try. If you're looking to really simply apply math to securities, you should probably focus on trading options.

I hate the comparison between financial markets and gambling, but if you don't participate in high risk activities now, finance probably isn't the profession for you.

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