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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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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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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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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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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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
I don't think assumptions 1 or 2 are necessary. Agree?
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Replying to @danrobinson @SBF_Alameda and 3 others
Actually, I think this means we can drop the no-transfers assumption too. Because there will never be a need to rebalance between pots (because each pot is always equal in value). Optimal rebalancing is done within each pot.
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And the other assumptions (to the extent I understand your assumption 4) were necessary already.
So, do we agree that if log-portfolio-wealth maximization is optimal for the full portfolio, log-pot-wealth-maximization is optimal if the portfolio is divided into pots?
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