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A bit of a definitional issue -- the interpretation is mostly wrong; the solution is the correct solution to *a* question but not to *the right question to be asking*

Dan Robinson

@danrobinson

Dec 2, 2020

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@SBF_FTX

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@SBF_Alameda

What makes it the wrong question?

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It's trying to maximize EV[log(money)] instead of EV[money]. This is probably wrong in and of itself as an assumption to make. But if you *do* want to make that assumption, then e.g. you have to consider all of your assets that don't have anything to do with the pool.

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Do you disagree with the Kelly criterion in general? en.wikipedia.org/wiki/Kelly_cri

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So: 1) it's not literally *wrong* in that it doesn't make a math error 2) I disagree in general that Kelly is the right way for people to bet because I disagree with its assumptions 3) neither 1/2 are necessary for my argument: Kelly only works if you consider *all* your money

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There are other problematic assumptions snuck in here, e.g. a) the paper assumes that you can only do one or the other forever and can't ever take profit if you don't use an AMM b) the paper assumes that exponential increase in valuation can go on forever

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E.g. see what happens to the math if you assume: a) The person is only using 25% of their money in this particular USD/coin pair and 75% outside of the system b) you only expand out ~10 years

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I think it's also worth noting that if you had tweeted "AMM skeptics should consider what utility curves make sense for them and whether there are more cost efficient ways to manage their risk, in some extremely constrained cases AMMs might be a decent choice" I wouldn't disagree

9:54 PM · Dec 2, 2020Twitter Web App

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This is a relief—I fundamentally disagree (I was worried it was a mathematical rather than a philosophical disagreement!) My log-wealth-maximization maximalism has absolutely nothing to do with differences in individual utility functions

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I think there are likely some math disagreements snuck in there as well but I'm not sure -- e.g., would you agree that none of the paper holds if you have a linear utility function? Say more about the second sentence? I'm not sure what point you're making.

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