The issue with that logic is that you can’t rebalance between pots. So when your pot gets in a hole, it is stuck in it
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My intuition agrees with - note that you can bet *more* than Kelly and still have positive growth rate (but less than Kelly)
So maybe we can just bet Kelly fraction + epsilon in each pot, and while the *individual* pots have lower growth rate, their *sum* might not
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i.e. E[log(X)], E[log(Y)] < E[log(Z)] does not imply that E[log((X+Y)/2)] < E[log(Z)]
Let me see if I can turn this into a proof either way
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OK so I think:
1) is wrong given his assumptions
2) if you *also* assume that there aren't two pots which have coins with *exactly* the same growth rate, is right given his assumptions
3) his assumptions are stupid
4) given good assumptions, he's wrong
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If there are two pots with the same growth rate, and you can’t rebalance between them, you think you can beat the growth rate?
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And the objectionable assumption that I’m making is the infinite time horizon, right?
And I guess the assumption “I prefer A to B if A outperforms B with probability 1” but that seems really hard to object to (apart from objecting to the infinite time horizon)
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nope, there are a lot of bad assumptions!
1) infinite time horizon
2) the prob dist of the coins: your model relies on the claim that with p --> 1, ETH > $999999999999999 eventually
3) that you can't rebalance
4) that you can't choose a better way to trade
...cont'd
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5) that you assign prob 0 to blowing out to ~$0 and staying there with an AMM
6) that you lose only epsilon to each arb
7) (that you are log-maxing but while I think that's wrong it's not *stupid*)
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8) and, yes, the thing you said it's hard to object to.
you still haven't responded to
Fair, I didn’t mean every assumption in the post about rebalancing portfolio growth, just in this separate hypo about pots. But I see why you think it’s an unrealistic scenario.
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wait but this separate hypo has to inherit all the stupid assumptions from the post about growth or else the hypo is wrong!
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