(c) you are a fund, and your investors are contributing only small fractions of their wealth
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yup 's (b) is my answer!
If I were selfish I would be much more risk averse
But the scale of world problems has diminishing marginal impact on the 10b's scale
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Oh no, how did we get back to utility?
I prefer maximizing log growth of wealth to growth of EV(wealth) not because of my utility function, but because the former leads to compounding growth and the latter leads to historical charts that look like this:
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Replying to @SBF_FTX @SBF_Alameda and 3 others
OK!! I show you a historical returns chart that looks like this:
docs.google.com/spreadsheets/d
Are you excited to invest?
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You can’t get escape the concept of utility. You’re implying that you assign higher utility to returns that have one shape vs. another.
Every strategy has a probability distribution over outcomes and people differ on which probability distributions they like.
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You can say “as long as you like more money vs. less then it implies you should prefer Kelly” (for *almost* all percentiles), but this goes back to the insane infinite time assumption.
In real life the 10th percentile outcomes of Kelly tend to be pretty bad.
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They look a lot better than the 99th percentile outcomes in almost-all-in (the strategy Sam prefers)!
And law of averages kicks in over time; it doesn’t for almost-all-in.
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1) I think that and I were talking about what _we_ think, and we do believe in utility, so I don't think it's appropriate for you to respond the way you did.
2) can you please address twitter.com/SBF_Alameda/st? Percentile outcomes as a metric fails.
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I wasn’t saying you were being inconsistent with yourself
On percentiles: yes, directly optimizing median or any given percentile would probably not be coherent. But Kelly doesn’t try to do that. It just ends up doing that for all percentiles (other than 100%) eventually
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Dan: "yes, directly optimizing median or any given percentile would probably not be coherent"
Also Dan: twitter.com/danrobinson/st
Could you please, in a single tweet thread here, define what exactly it is you _are_ aiming for?
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Replying to @SBF_FTX @SBF_Alameda and @elliot_olds
No! I am not trying to maximize EV of anything!
I want to pick the strategy that beats yours 99.99% of the time. That’s my terminal goal
Kelly takes that input and spits out that I should maximize EV(log(wealth)), but that preference is the consequence, not the cause
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this is never going to get anywhere if people keep confusing the difference between a.s. and 1, and between "tends to zero" and "is zero", and stop assuming that 0/0=0.
Can we please just talk about numbers less than the number of atoms in the universe?
Also Kelly isn't defined by "almost surely" either, that's an emergent property of it in some very specific infinite scenarios.
Kelly is defined by optimizing for log(wealth)
en.wikipedia.org/wiki/Kelly_cri
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This part really is a language debate, but saying that it is defined by optimizing for log(wealth) IMO makes it sound like it’s driven by preferences about marginal utility of wealth, which it isn’t.
Would prefer “maximizing log return” or “maximizing annualized rate of return.”
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