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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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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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)
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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Ok....
This was fun. Everybody have a beer and go to bed now.
*interested in hearing more about the last sentence 👀
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Heh
This is a classic trap for people who know a decent amount of math, get swayed by a sexy-sounding sentence, and fail to go back and critical examine it.
I think it was maybe the most accurate predictor of whether someone at Jane Street was/would become a good trader.
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