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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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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"maximizing log return" is obviously equivalent to maximizing log wealth, it's just subtracting log(start_wealth) from all outcomes. Really not sure why you think that's an important thing to add!
But "maximizing annualized rate of return" is *not* kelly in general! It's only Kelly in some very specific situations.
e.g. if you only have a single coin flip ever and it's in 1 year then max annualized rate of return = max return = max linear EV != kelly
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Like what the fuck Dan. I literally just copied the definition from Wikipedia! en.wikipedia.org/wiki/Kelly_cri
And you objected to that definition, replacing it with your own which was *incorrect* in the general case.
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Perhaps the more important is the latter (annualized return), or equivalently “average log return over time.”
All equivalent. But with these latter terms it is much more obvious why you might want to optimize for them if you care about compound interest
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twitter.com/SBF_Alameda/st
to be clear I think you're not understanding correctly what Kelly is here.
You're saying we should define Kelly as a thing which is *not* Kelly but is instead the other different thing that you believe.
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Replying to @SBF_FTX @danrobinson and 4 others
But "maximizing annualized rate of return" is *not* kelly in general! It's only Kelly in some very specific situations.
e.g. if you only have a single coin flip ever and it's in 1 year then max annualized rate of return = max return = max linear EV != kelly
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