I wonder what mathematical topics I should study to have an investment strategy similar like Jim Simons'.
What sort of mathematics does Jim Simons use for his hedge fund?
- Thread starter helpme_please
- Start date
Addition and subtraction. Occasionally multiplication and division (but that's only for their most advanced strategies).
LOL! Tough room.
Simons always claimed some sort of "mathmatical" formula. Wouldn't be surprised to find out it was just "faster front-running".
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If you didn't ace every single math class throughout your school years and get a 99%tile on the math portion of standardized exams, then the question is moot.
I think, probably trading strategy could be the only practical use/ application of this Complex maths below:
Q https://en.wikipedia.org/wiki/Imaginary_unit
Proper use
The imaginary unit is sometimes written √−1 in advanced mathematics contexts (as well as in less advanced popular texts). However, great care needs to be taken when manipulating formulas involving radicals. The notation is reserved either for the principal square root function, which is only defined for real x ≥ 0, or for the principal branch of the complex square root function. Attempting to apply the calculation rules of the principal (real) square root function to manipulate the principal branch of the complex square root function will produce false results:
-1 = i \cdot i = \sqrt{-1} \cdot \sqrt{-1} = \sqrt{(-1) \cdot (-1)} = \sqrt{1} = 1 (incorrect).
Attempting to correct the calculation by specifying both the positive and negative roots only produces ambiguous results:
-1 = i \cdot i = \pm \sqrt{-1} \cdot \pm \sqrt{-1} = \pm \sqrt{(-1) \cdot (-1)} = \pm \sqrt{1} = \pm 1 (ambiguous).
Similarly:
\frac{1}{i} = \frac{\sqrt{1}}{\sqrt{-1}} = \sqrt{\frac{1}{-1}} = \sqrt{\frac{-1}{1}} = \sqrt{-1} = i (incorrect).
The calculation rules
\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}
and
\frac{\sqrt{a}} {\sqrt{b}} = \sqrt{\frac{a}{b}}
are only valid for real, non-negative values of a and b.
These problems are avoided by writing and manipulating i√7, rather than expressions like √−7. For a more thorough discussion, see Square root and Branch point.
UQ
Q https://en.wikipedia.org/wiki/Imaginary_unit
Proper use
The imaginary unit is sometimes written √−1 in advanced mathematics contexts (as well as in less advanced popular texts). However, great care needs to be taken when manipulating formulas involving radicals. The notation is reserved either for the principal square root function, which is only defined for real x ≥ 0, or for the principal branch of the complex square root function. Attempting to apply the calculation rules of the principal (real) square root function to manipulate the principal branch of the complex square root function will produce false results:
-1 = i \cdot i = \sqrt{-1} \cdot \sqrt{-1} = \sqrt{(-1) \cdot (-1)} = \sqrt{1} = 1 (incorrect).
Attempting to correct the calculation by specifying both the positive and negative roots only produces ambiguous results:
-1 = i \cdot i = \pm \sqrt{-1} \cdot \pm \sqrt{-1} = \pm \sqrt{(-1) \cdot (-1)} = \pm \sqrt{1} = \pm 1 (ambiguous).
Similarly:
\frac{1}{i} = \frac{\sqrt{1}}{\sqrt{-1}} = \sqrt{\frac{1}{-1}} = \sqrt{\frac{-1}{1}} = \sqrt{-1} = i (incorrect).
The calculation rules
\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}
and
\frac{\sqrt{a}} {\sqrt{b}} = \sqrt{\frac{a}{b}}
are only valid for real, non-negative values of a and b.
These problems are avoided by writing and manipulating i√7, rather than expressions like √−7. For a more thorough discussion, see Square root and Branch point.
UQ
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Like Edward Thorp and William Eckhardt, Simons was trained as a mathematician. Like Thorp, Simons was a mathematics college professor. Unless you plan on getting a PhD in mathematics, you'll never have the math preparation that Simons has.
BUT ...
Mathematicians do tend to specialize. Like medicine, the field has grown so diverse that no one person can be an expert in all aspects of it. Find out what Simons' specialty is and that will indicate what tool(s) he brings to his trading.
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I think there is a lot of that there.
That is definitely part of his edge.
@helpme_please. I would just start by familiarizing yourself with basic probability and statistics and things like conditional probability. Next, learn to code these concepts applied towards finance. Beyond that, no-one can really guide you to the exact math he uses, as the secrets are mostly proprietary. However, I can take a stab at some things he might generally utilize.
Without looking back into details, there are a few things I've gathered from bits and pieces revealed and or slipped in the past. Although I tend to agree on the speculation that some of it is "faster front-running," there are other observations we can speculate on (just loosely regurgitating from memory, so you can look up or corroborate details if you wish).
1) A big part of his earlier success was attributed to removing an earlier partner that took a lot of risk (Axcom), and replacing him with someone who was able to control that much better (Berlekamp). That's one of the few things we all have some capability to control (risk control).
2) Earlier court proceedings and complaints from former PhD
staff, leaked that they were attempting to illegally reverse engineer POSIT order flow. They'd never admit it, but I wouldn't doubt it. An edge none of us could likely replicate. Looks like the more detailed articles were removed from web (or I couldn't find).
3) There have been recent revelations that they were unfairly and advatageously, being taxed long term gains rates for short term trades, through various tactics with their brokers. Another method none of us could likely ever replicate, but likely a huge source of Alpha.
4) Many of his early hires were HMM experts in speech processing from IBM. I wouldn't doubt that HMM or sequential modeling ( just think about modeling around finding events with stable short term temporal serial correlations ), were/are investigated or utilized. The math here is fairly complex, but there are a lot of openly available codes and learning material that allow the laymen to try to investiagate and look for edge.
two things that I heard recently in his fantastic Numberfile and TED interviews,
5) He said something along the lines of, yes, you could sort of call part of what we do Machine Learning (data mining), or searching through large bodies of data for relationships. Some of these relationships are temporal anaomolies that can be exploited for short term gains. This is a big part of where my focus has been over the years, and believe retail traders can tap into. Those who explore this route, will find that many issues and questions will surface that are more empirical than academic, and as such aren't covered very much in available literature on ML.
6) One of the things I found pretty profound and useful was when the interviewer asked if there was some complicated, advanced theory that they stumbled upon that has been withheld from the general academic community and public at large. He pretty much straight faced said no. Implying that there isn't really some super secret math formula that they are secretly deploying.
But I'd assess that they are looking at many concepts that are publicly available and scattered about, but one huge thing they are able to bring to the table is having a team of very intelligent (and no doubt detailed) experts that are able to pool their efforts together to put together a world class infastructure around some of the concepts above. That is something I most definitly miss, while working in silo, and has to be a huge advantage over what we can accomplish on our own--
*I do wish a author/journalist along the likes of Michael Covel or Scott Patterson would do some deep research and interviews with former staff or individuals around the history and success of Simons and staff. I'd be really interested to read that.
*more.
https://math.berkeley.edu/~berlek/pubs/bloomberg.pdf
Without looking back into details, there are a few things I've gathered from bits and pieces revealed and or slipped in the past. Although I tend to agree on the speculation that some of it is "faster front-running," there are other observations we can speculate on (just loosely regurgitating from memory, so you can look up or corroborate details if you wish).
1) A big part of his earlier success was attributed to removing an earlier partner that took a lot of risk (Axcom), and replacing him with someone who was able to control that much better (Berlekamp). That's one of the few things we all have some capability to control (risk control).
2) Earlier court proceedings and complaints from former PhD
staff, leaked that they were attempting to illegally reverse engineer POSIT order flow. They'd never admit it, but I wouldn't doubt it. An edge none of us could likely replicate. Looks like the more detailed articles were removed from web (or I couldn't find).
3) There have been recent revelations that they were unfairly and advatageously, being taxed long term gains rates for short term trades, through various tactics with their brokers. Another method none of us could likely ever replicate, but likely a huge source of Alpha.
4) Many of his early hires were HMM experts in speech processing from IBM. I wouldn't doubt that HMM or sequential modeling ( just think about modeling around finding events with stable short term temporal serial correlations ), were/are investigated or utilized. The math here is fairly complex, but there are a lot of openly available codes and learning material that allow the laymen to try to investiagate and look for edge.
two things that I heard recently in his fantastic Numberfile and TED interviews,
5) He said something along the lines of, yes, you could sort of call part of what we do Machine Learning (data mining), or searching through large bodies of data for relationships. Some of these relationships are temporal anaomolies that can be exploited for short term gains. This is a big part of where my focus has been over the years, and believe retail traders can tap into. Those who explore this route, will find that many issues and questions will surface that are more empirical than academic, and as such aren't covered very much in available literature on ML.
6) One of the things I found pretty profound and useful was when the interviewer asked if there was some complicated, advanced theory that they stumbled upon that has been withheld from the general academic community and public at large. He pretty much straight faced said no. Implying that there isn't really some super secret math formula that they are secretly deploying.
But I'd assess that they are looking at many concepts that are publicly available and scattered about, but one huge thing they are able to bring to the table is having a team of very intelligent (and no doubt detailed) experts that are able to pool their efforts together to put together a world class infastructure around some of the concepts above. That is something I most definitly miss, while working in silo, and has to be a huge advantage over what we can accomplish on our own--
*I do wish a author/journalist along the likes of Michael Covel or Scott Patterson would do some deep research and interviews with former staff or individuals around the history and success of Simons and staff. I'd be really interested to read that.
*more.
https://math.berkeley.edu/~berlek/pubs/bloomberg.pdf
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Thanks for the insightful reply. Probability and statistics seem like probably topics that Jim Simons used. Don't think he used esoteric stuff like differential geometry.