I am asserting that if I manage each independent portfolio in the way that maximizes log growth, and you pick some other strategy, then asymptotically I will have exponentially more wealth than you after infinity amount of time with probability 1.
Conversation
“In the way that maximizes log growth” of each portfolio individually? Then SBF can pick a different strategy which maximizes log growth of the portfolio of portfolios and he will be wealthier than you.
Imagine you have a billion coins that land heads with p=.51...
2
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)
2
1
even if you can't literally xfer $ between pots you can always have 1 pot look at the performance of the other and change its strategy based on that
1
This kind of thing is why I said this, but you told me it didn't matter
Quote Tweet
Replying to @hasufl @SBF_Alameda and 3 others
Awesome—sounds like we’ve hit on a real disagreement (although I think we have to delineate the question more formally because there are probably some underlying different assumptions around what kind of active management is allowed)
1
er ok sorry about that! you might be right.
I think the assumptions necessary for yours to hold are:
1) no xfers
2) can't see how the other is doing
3) goes on literally infinitely
4) assets grow unboundedly upwards in the median case
1
1
1
without any of these yours fails horribly though and they're each ridiculously bad assumptions to make
1
I don’t think 2 is required. Knowing about the other pots doesn’t change the strategy for each individual pot. (If each pot obeys the Kelly criterion—betting a constant proportion of its bankroll—then the total portfolio will also obey the Kelly criterion, right?)
2
1
Your scenario involves, e.g. the odds that ETH ends up worth less than $1000000000000 each being < 50% (that's what happens with unbounded exponential growth)
If instead you think that at some point ETH's positive EV growth would slow down, then an extra $1b on the side matters
1
Like I claim that if pot 1 is $600 and pot 2 is a fixed $1b in USD that will always be USD:
the asymptotic growth rate of ETH isn't still 30%/year, at some point it's ~0. This comes before 1 ETH = $1b.
So your preference function should be locally linear; you should go all ETH