>Presumably they failed to pay much more than that. I don't know how much, I doubt it would be possible to calculate.
The exact amount is what the IRS figures out before damages are applied.
>I kinda doubt that this could be accurately assessed by Levin
Once someone starts to believe things that suit them without evidence they generally stop listening to actual evidence. This is exactly that pattern: an investigate, and likely the IRS also, did do an investigation likely of hundreds to thousands of man hours, reached the above conclusion, and you, an internet poster googling for a few minutes, disbelieves them?
Financial News London, a pretty solid source on such things states "Current and former executives of hedge fund Renaissance Technologies will personally pay as much as $7bn in back taxes, interest and penalties to settle a long-running dispute with the Internal Revenue Service, the firm said, a tax settlement that may be the largest in history." [1] I think I'll trust their (and similar financial research places) on the characterization of the payment, especially since the standard for back payment has always been back taxes + penalties + interest. The IRS doesn't just play around, especially when something this high profile is at stake.
>nearly half of that magic was tax fraud.
What? Provide your napkin math. I just presented numbers that show this "half" to be far out of reality.
If you're a programmer, simply set up a simple model (I just did that) and compute expected with or without paying that 7B over the past 30 years. The returns are vastly more than "half". Did you just claim half from any numerical checking, or just guessed it?
>Lastly I'd like to point out this linear, it's not like they would have returned 39% in a universe where they paid that $7
The naive compound growth is T=P(1+r)^n, which is exactly linear. Double the principal P, double the outcome. Taxes aren't paid on value, only on profit, and if you check the math (it's pretty easy), taking X % each year or at the end of profits is exactly the same number.
The practical reason profits are taxes yearly to to provide smoother income for govt and to get some of the profit before things tank and there is none left.
In real investment, this actually becomes sublinear, as the more invested in a market, the lower percent returns, since the ability to grow is an S-curve (as is all things), not an exponential. Buffet, for example, has talked exteneively about this.
This sublinear fact is also why Renaissance famously kicked out lots of early external investors - the funds under management were not able to grow since there was too much for the opportunities they chased.
So I do agree it's not linear - it's sublinear.
[1] https://www.fnlondon.com/articles/hedge-fund-renaissance-tec...