Comment by orbifold | Hacker News Reader

Comment by orbifold | Hacker News Reader

My long standing hypothesis on Medallion is that they figured out how to apply gauge theoretic techniques to financial markets. This fits with Simons work that he did before he founded the fund. The fact that gauge theory is applicable to for example currency trading is folk knowledge in the Havard, Princeton, IAS circles (here is for example the lecture notes of a popular lecture by Maldacena that uses currency trading as an example of a gauge theory https://arxiv.org/pdf/1410.6753.pdf).

In currency trading example the curvature $F$ of the gauge connection $A$ vanishes precisely, when there is no arbitrage opportunity. Now what Chern and Simons discovered is a differential form K (https://en.wikipedia.org/wiki/Chern–Simons_form), which when taken as the action S(A) of a gauge field $A$, has a corresponding field equation $F = 0$ (i.e. in the finance case = no arbitrage). In these equations time does not enter, however there are several ways in which on can incorporate time into the picture (for a naive example see also the lecture notes). Assets in this framework live in associated vector bundles of the principal bundle defining exchange rates.

My speculative assertion is that it is possible to identify "topological invariants" which can be computed by sequences of trades, i.e. parallel transport along the gauge connection and that those can have provably positive expected return. The fact that the fund is limited to a small amount of invested capital might be related to the fact that the strategies require measurements, that would have self-interactions if they were too large.

> My long standing hypothesis on Medallion is that they figured out how to apply gauge theoretic techniques to financial markets.

No. Listen to the Talking Machines podcast with Nick Patterson (who was a senior VP in research at RennTech for a long time). To paraphrase he says that the vast majority of their strategies are no more than simple linear regression. The challenge is that even though regression is conceptually simple it still takes smart people to answer questions like "what should you be regressing", or "should you apply any transform" or "how should you clean your data" or "do you understand the process well enough to realize when results are obviously unrealistic".

The thing that makes a firm like Renaissance a league above a firm like Two Sigma is the same thing that makes Two Sigma a league above a firm like Winton. It's not mathematical gnosticism, it's plain old operational excellence. It's things like expansive reliable curated datasets, deep expertise on market structure, good execution systems, powerful research and backtesting software, good access to markets, economies of scale, talented practitioners, and excellent organizational management.

The assertions you make are not necessarily in contradiction to what I am saying. In discretised form most of the formulas I'm talking about boil down to simple linear algebra with unknown parameters. You can then use essentially linear regression to find those parameters, based on observed market data and trades you are making.

So I was talking about the "what should I be regressing" and "transformation" (you can use gauge theory to adjust for inflation and changes in exchange rate in non-obvious ways) part. There is no question that having access to enough data and operational excellent are a complementary component.

Agree with this 10x. In my experience in high frequency trading, simple always wins out.

Building a workflow around simple concepts is where the engineering challenge lies.

change of gauge just means a rescaling. of course currency is the perfect example of a change of gauge for an expository piece like that arxiv paper (it's relatable). it doesn't mean there's some fundamental relationship to gauge theory to markets. arb free here gets encoded as the curl of the connection being 0 but that's just saying you can't loop through the currencies and come out with more money. it's tautological given your identifications - you get no further insight using the gauge theory. and besides the connection is continuous and currency swaps aren't.

you make the typical mistake of someone that knows a lot of math: you go up the ladder of abstraction from an example and think that the abstraction says something about the example. it doesn't - you've just hidden the simplicity of the example under the mathematical baggage.

This was a fantastic comment, good to see misapplications of abstraction get pushback.

I highly doubt it. Most of their hires were more machine learning with speech types from IBM, rather than topologists. I doubt the topologists they did hire were being hired for their expertise in fiber bundles rather than for their general intelligence and intellectual curiosity.

I think other commenters are correct when they say HMMs and linear regression made them much of their money in the 90's. I wrote an article [0] summarizing this.

But it is always tempting to think they must be doing something esoteric and mystical at Medallion. A part of me thinks that when interviewed the employees of Medallion say they do whatever simple XYZ technique from quantopian.com/lectures just so that the reporter with a distant memory of HS math leaves them alone. Another part of me does believe that you can do simple things at scale and still make money.

[0]: https://medium.com/@ilyakavalerov/the-man-who-solved-the-mar...

My theory is that they use Hidden Markov Models to figure out something subtle about the market -- probably regimes.

I got this impressions from several of Simons interviews, and then the recent book has added more clues.

Note that the Baum-Welch algo is one of the leading algos used to solve the underlying model and Baum worked at Rentech.

There is a book that explains what Baum did (it wasn't this).

Say more.

Do you mean "The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution" which I read, or another book?

Yea I mean that book basically says that Baum wasn't interested in using his or any algorithm with trading. He just had hunches and a value system that he really believed in for what world events would do to currency prices. I think that part of the book is totally believable. Medallion didn't make a name for itself until long after Baum left.

This is compatible in so far as you need to estimate parameters to calibrate any such strategy. In the simplified model that is explained in the lecture notes I linked to, you would start with eq. 6.6 on page 25 as an Ansatz for the transition matrix in the Baum-Welch algorithm.

You should read the book. Simons had almost nothing to do with the strategy (he managed money in the 80s, he got lucky but it didn't go well generally). They tried several complex ideas, none of them worked. And the advantages they had were doing simple things well (better execution, having better data, etc.).

Well the book certainly makes it look much more mundane, Simons appears to be more of a skilled people manager and the heavy lifting was apparently done by others for the most part.

My two cents: I think you should look into the work of Mercer, not Simons ;-)

seems like you know your way around the topic, do you mind putting this into more simple English? Wikipedia on gauge theory was impenetrable from step 0 for me unfortunately

imagine all the wind on the earth's surface right now. that's a vector field or gauge (as physicists call it). there are many units that it could denominated in (meters per sec, feet per second, etc). changing from one to the other is a gauge transformation (unit change, rescaling).

okay now suppose you want to compare the wind at two points. you can't just take the vectors at those two points and take a dot product because they're not in the same vector space (each of them is in a vector space tangent to the point they're anchored at). to figure out the issue with doing this watch this video

https://youtu.be/p1tfZD2Bm0w?t=170

you have to perform parallel transport. one way to do this is to track how much moving the vector changes it (messes with its orientation). that's the connection and the covariant derivative. you can then take a look at how that connection itself changes over the surface of the earth. if it's curl free (recall curl free vector field from multivariable calculus) then you don't have eddies in your wind charts i.e. you can't get faster by going around in a loop.

absolutely none of this applies to currency or equities because the surface of the earth is smooth and curved. neither of this is true about equities or securities or currency.

This is pure crank nonsense.

Ok, but please don't post unsubstantive comments here. If you know more than others, the thing to do is to share some of what you know, so we can all learn something. If you don't want to do that, it's always an option to let others be wrong on the internet and move on. Calling names helps no one.

We've had to ask you about this before, so could you please review https://news.ycombinator.com/newsguidelines.html and use HN as intended? We'd appreciate it.

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