Conversation

Replying to

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

Quote Tweet

Dan Robinson

@danrobinson

Dec 3, 2020

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

Replying to

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

Replying to

I don't think assumptions 1 or 2 are necessary. Agree?

Quote Tweet

Dan Robinson

@danrobinson

Dec 3, 2020

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.

Replying to

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?

Replying to

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

Replying to

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

Replying to

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?

Replying to

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"

Replying to

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.

Replying to

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

Replying to

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.)

11:47 PM · Dec 3, 2020Twitter Web App

Replying to

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."

Replying to

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

Quote Tweet

Dan Robinson

@danrobinson

Dec 3, 2020

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

Show replies