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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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@GaussianProcess

what do you mean "were necessary already"? necessary for what?

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For log-wealth-optimization to be optimal at the portfolio level

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@GaussianProcess

uh why? I mean I don't think log-wealth-optimization is optimal in the first place so technically I agree I guess you're saying that really you're doing some "I want percentiles to be high" model and so that's only equivalent to log-wealth-opt under certain assumptions?

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hm ok so I think my conclusion here is that we were, in fact, not disagreeing on the math -- we were just disagreeing on the assumptions though as I understand it your assumptions now include "thinks such that my personal preference function would be equivalent to log-wealth"

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Uh I'm trying to resolve a very specific sub-point: that if you divide a portfolio into pots, then the strategy of optimizing the log wealth of each pot is also the strategy that optimizes the log wealth of the portfolio.

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The only new assumption that it depends on AFAICT is that the investment opportunities are divisible.

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@GaussianProcess

Uh I think this also requires a lot of "old" assumptions that I also disagree with and was not making but I do think your sub-point is correct given the unstated assumptions you were making! (Which, again, I disagree with.)

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Hate to zoom in on this rabbit hole but what old assumptions does it require? "There is a portfolio construction P that optimizes EV(log wealth). If you split it into N pots, each pot can just be P scaled down by N. This optimizes both pot log wealth and portfolio log wealth."

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@GaussianProcess

the context was about a paper you co-wrote that used a uniswap pool as one pot, so that can't be an example of what you just said b/c you don't have fractional houses in it e.g. also right before this you said twitter.com/danrobinson/st Roth IRAs also don't have fractional houses

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Replying to @danrobinson @ArthurB and 3 others

The model doesn't assume that the portfolio is all of your wealth, but it does assume that it never interacts with the rest of your wealth. More realistic in some cases (like a Roth IRA) than others

11:58 PM · Dec 3, 2020Twitter Web App

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and *also* this where you implied that $1k could be its own pot which is also not consistent with it having fractional parts of your future earning potential and also your kitchen sink in it

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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 I object to "each pot can just be P scaled down by N" as a possible let alone obvious assumption given the context of the discussion and many of your previous statements in it

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