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.
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.