Why are they better?
This still requires the same kind of explanation as 'they are simply better at investing than anyone in the world'
My immediate impression was that this was not a coincidence. Having talked to many other hedge funds over the years, I've come to realize that this is even more anomalous than it seemed at the time. While you will sometimes find a person on the cutting edge of these kinds of mathematics at other funds it tends to be an isolated case. Many hedge funds have boringly simplistic approaches to signal discovery. People overestimate how widely distributed and available this kind of expertise is.
Renaissance are not better at investing per se, they are better at signal discovery than anyone else and invested heavily in maintaining that (meta-)edge over the years, the investing part is relatively mechanical after the signal is discovered.
Usually if a company has secret sauce, someone will leave and spin off on their own. Even Google can't retain everyone. So unless I'm missing something, any explanation has to account for why this hasn't occurred here.
Really high comp is another.
Perhaps a bigger deal is the fact that they actively return money over the roughly $10BN fund value, implying that the strategy doesn't work past that point. A competitor would then be stuck in a zero-sum game battling for a slice of a fixed pie rather than being able to grow the market.
Possible explanation: there aren't any other firms founded by as great mathematicians as the founders of Renaissance. I saw a quote online attributed to them, something like: "We hire the A-grade mathematicians. Most other firms hire B and C grade mathematicians, and don't even know the A grade exists". This fits my experience, as a D-grade mathematician working in finance. Never heard of significant mathematical prizewinning researchers working at any of the firms I know (lots of maths olympians, but there's a huge difference between winning a maths olympiad and conducting groundbreaking mathematical research).
If you look at AHL, they have lots of people who know the maths. They have their own institute at Oxford ffs (the number of people who don't have PHds from Oxbridge there is small), and they have crap performance, year-in, year-out.
It is a typical flaw of human nature to assume that when someone else does something extraordinary that they have some secret knowledge you don't. People on here talking about discrete topology and all kinds of craziness...read the book, one of the big early advantages that RenTech had was they sent some guy down to the Fed to transcribe by hand data that no-one else had. Another example is their stat arb strategy didn't work for years, until they worked out how to get good execution.
I am not saying that it is only this but if you read the book, there are several instances where RenTech try to apply something complex and it doesn't work...and the success they have is after doing something simple, marginally better than anyone else...again, to a certain kind of person, this simplicity is offensive but it is also why most people with technical backgrounds get destroyed by the market.
Also, one thing that is kind of unclear. Simons had almost nothing to do with the perf. By the early 90s, he wasn't personally active anymore (he was spending most of his time on venture capital). The step change was hiring Brown and Mercer (again, two guys who clearly knew the maths but had spent most of their time in industry). Ppl assume that Simons is in the boiler room doing all kinds of crazy technical stuff...he wasn't (most of the time that he ran the fund, it didn't do well at all).
Figuring out things nobody else can is the hard way to achieve. Figuring out what you don't know and never betting on it is an alternative way that doesn't require being a genius.
I don't think it is only knowing what you don't know either. That is a component but people from academia are rarely overconfident, the opposite is usually true (they tend to react badly under pressure). These people have a "circle of competence", they know what they don't know...but they don't really have anything else. All these places are churning massive resources into education, into human capital...is that working? It clearly works in some places and not others. I am just very cautious of the "know what you don't know" argument because it tends towards thinking everyone should be specialists...and I don't think the world works that way.
You can have low confidence and discount the value of things you know, while still assuming you know things you don't.
I'm skeptical. There are a lot of smart mathematicians, and given that the incentive is billions in profit, there is no way you can maintain that kind of competitive advantage over decades. Again, we're not talking about a company stumbling on a massively profitable, but undiscovered space. In that case, yes, as a first-mover you'll make billions. But you can't maintain that for decades as others will move in.
The other item that makes it kind of crazy is that nobody actually knows how they are doing it in, even in theory. Take the example of Google's search monopoly. They were one of the first to create a specific kind of search product that led them to billions in profit. Two decades later, they still maintain that competitive lead and the product is still highly profitable, but nobody is confused as to how they actually do it even if only Google knows the nitty-gritty details of the infrastructure or algorithms that back this product up. The Medallion Fund might as well be magic since nobody can explain the mechanism by which they maintain their outlier status.
This explanation shows why Medallion's high returns are possible, and also why Medallion not actually better than Renaissance's overall average performance (that is, could not be replicated as an indepdent spin of without the rest of Renaissance to extract value from), beyond an acconting illusion to make ordinary wages look like investing.
It's not at all surprising that this could be how Medallian works, since that's just an application hedging, which is Renaissance's core business.