Finally caught up on crypto twitter A few thoughts on this AMM debate:

1) The math itself seems plausible based on volatility harvesting results (though I haven't checked the details). The interpretation is a little optimistic though imo. 1/7 https://twitter.com/SBF_Alameda/status/1334247283081138178

2) Kelly criterion (max E[log V]) makes sense in context of an entire portfolio and effectively heavily penalizes possibilities of portfolio wipeouts. But when only modeling a component of a portfolio, it makes less sense. 2/7

To illustrate, a Kelly optimal portfolio could very well be: keep x% in safe assets w/ the rest spread over very risky bets. You wouldn't want to Kelly maximize each of the very risky bets. In effect, the safe x% removes the heavily penalized wipeout possibilities itself. 3/7

3) The results assume nice GBM. When you have less well-behaved processes, like jumps, the story may be very different. I suspect jumps are where AMM rebalancing costs are especially bad b/c the AMM offers liquidity at all prices spanning the jump distance. 4/7

4) Kelly optimality results (when applicable--see above) are on infinite time horizon. The absence of other risks from the model (e.g., stablecoin failure risks) should lend some skepticism to interpretations. 5/7

e.g. if either assets in the AMM pool were to fail, the entire pool -> 0, which makes it (in this way at least) *more* fragile than other strategies. This doesn't invalidate the results per se, just means be skeptical of asymptotic model results. 6/7

Altogether, I do think the work is interesting, and I tend to like AMM, ergodicity economics, and rebalancing ideas. Though I don't think it's robust enough to be making investment decisions based on it 7/7