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“In the way that maximizes log growth” of each portfolio individually? Then SBF can pick a different strategy which maximizes log growth of the portfolio of portfolios and he will be wealthier than you. Imagine you have a billion coins that land heads with p=.51...

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The strategy of maximizing asymptotic log growth in wealth of each pot IS the strategy that maximizes asymptotic log wealth growth of the total set of pots. (GIVEN that we cannot rebalance between pots)

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Gaussian Process

@GaussianProcess

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This seems not true? Take two pots with wealth x,y Give them independent coins with p=0.75 of heads Let m = 2p-1 Pot-Kelly says bet mx, my in each pot Portfolio-Kelly says bet min(x, (x+y)*m/(1+m^2)) in the first pot

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@GaussianProcess

This is making the assumption that the pots do not have access to the same coins, right? Why would there be an investment opportunity available to one pot that isn't available to the others? That's an extra assumption (and a fairly arbitrary one).

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@GaussianProcess

I think it's a natural assumption! you have impact on coins. You can't go arbitrarily big. At some point you have to split off some of your capital.

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Having impact on coins has nothing to do with the pots having heterogenous investment opportunities, right? You could still have each subpot just make the exact same bets the macro portfolio would make, but scaled down.

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If bets have an effect on the market, then sure, the subportfolio manager would find it useful to know how large the total portfolio is (to know how much capital is following the same strategy). But it will still be maximizing its own log wealth IN THAT CONTEXT.

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@GaussianProcess

ok fine how about your future earning potential? that's not something you can turn into ETH easily but it is something which should be inside the log

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or locked coins you have, or your house, or any number of other things that aren't ETH

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Uh sure but have we resolved the math thing? Was I right about the math?

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Replying to @SBF_FTX @danrobinson and 3 others

this is actually a math thing now

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@GaussianProcess

uh you were right that it depends on the assumptions you make, sorry about that! in order for your actualy claim to be right you need to make batshit crazy assumptions

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Replying to @danrobinson @elliot_olds and 2 others

er ok sorry about that! you might be right. I think the assumptions necessary for yours to hold are: 1) no xfers 2) can't see how the other is doing 3) goes on literally infinitely 4) assets grow unboundedly upwards in the median case

11:23 PM · Dec 3, 2020Twitter Web App

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and the original thing you said that spawned this violates those assumptions you'd have to be making to justify your later claim

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Replying to @SBF_FTX @SBF_Alameda and 3 others

Totally, it’s irrelevant. But given that you are managing this $1k as its own pot, might as well manage it well. If you robotically maximize EV for it, then it will get St. Petersburged and end up at 0 with very high probability

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So, like, I think in the real world and also in the world that we had been talking about they're not independent, but you can construct other worlds where they are independent

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er sorry about this, that was way too mean there was no reason for me to phrase it that way (I get kind of triggered by people misunderstanding Kelly)

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Appreciate it. I probably shouldn't have said blown the fuck out yesterday (I was worried it wouldn't be provocative enough. Lol) But in retrospect, I wasn't misunderstanding Kelly here, right? Kelly applies equally if you divide a portfolio into pots.

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