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and

And it is not actually true for the linear case, at least if it isn’t your last chance to use your capital to make more money ever

Replying to

and

No, what

is saying makes total sense to me in the linear case. Your CFMM is no better off rebalancing if you want to maximize a linear objective. It's just a completely uninteresting case.

Replying to

and

I don’t agree. If your utility function is linear, you will almost surely be happier in the long run by maximizing log wealth growth at each step than maximizing expected value of wealth

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and

Yep, I'm with Dan here. One way to view the question: EV measures what happens when you make a ton of bets in parallel. EV of log measures what happens when you compound a bunch of bets over time. The reason is that multiplying <-> adding logs, so law of large numbers works

Replying to

and

Another way to look at it: maximizing EV(wealth) at the expense of log wealth results in the long run in some EXTREMELY HAPPY people in some possible worlds—but you are vanishingly unlikely to get to live in such a world. It’s like utility monsters in ethics. Probability monster

Replying to

and

I actually agree with all of that. Here, by definition, you're asking "what maximizes EV[wealth]?" In the world

@SBF_Alameda

is (I think) referring to, I can always construct an LP with less than or equal linear loss than the zero-fee LP.

Replying to

Maybe the discontinuity at that fee introduces the confusion? At (not approaching) a zero fee, it can be proven trivially.

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and

Agreed, at zero fee you always do worse being an LP, and that discontinuity is key. The only thing I'd add regards your previous tweet: we're not really asking about EV[Wealth], because EV actually doesn't tell us what will happen over time (!!) See ergodicityeconomics.com/lecture-notes/

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and

Yes, totally agree. That said, EV[wealth] is still a well-defined objective function. And you can prove that the smallest fee that maximizes the objective is exactly enough to preclude rebalancing.

Replying to

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My point here is that having a utility function that is linear in wealth does not mean that your utility function is linear in EV(wealth)

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yes it very much does imply that; that's how math works

11:30 PM · Dec 2, 2020Twitter Web App

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I think you think I'm objecting to the first step (EV[wealth]-maximizing -> EV[utility]-maximizing when utility linear in wealth) when actually I'm objecting to the latter step (EV[utility]-maximizing -> utility-maximizing)

Replying to

It is a tautology that I prefer having greater utility to having less. It is NOT a tautology that I prefer a strategy with higher EV(utility) to one with lower