er something like EV($_{t+!})/EV($_t)
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That’s rate of growth of expected value of wealth. Maximizing EV at each step maximizes that.
But Kelly doesn’t just maximize rate of growth of log wealth. It maximizes expected rate of growth of WEALTH, full stop.
I think this might be the heart of our conceptual disagreement.
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To be more precise, time-average rate of growth:
EV[($_t / $_0)^(1/t)]
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hm ok so I agree with time-average rate of growth, but not sure I agree with rate of growth
like all-in also maximizes EV[$_t/$_0] for all t
idk mostly I guess this is a silly debate, we're just arguing over how to define "rate of growth" :P
(FWIW I'd use EV(t)-EV(t-1) :P)
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Time-average rate of return is just another way of saying annualized rate of return, right?
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You wouldn’t rather invest your money with an asset manager where you expect a 5% annualized rate of return to one where you expect a 3% annualized rate of return?
Your reaction would be “I might be interested in the 3% rate, although only if it’s RISKIER”?
That seems unusual.
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er again this is all a language debate, but again I think your doing something pretty nonstandard and biased here
so like what do you mean by "expect at 5% annualized rate of return"?
For each year, all-in has a higher expected rate of return!
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so to be clear:
(Expected rate of return) annually: all-in wins
Expected (annual rate of return): kelly wins
Expected return: all-in wins
Median return: kelly wins
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I don't think this is a language debate!
But yes I agree with those four summaries, if you replace median with "every percentile" :)
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also I very much think it's a language debate when you phrase it like this: twitter.com/danrobinson/st
Let's say you go to your advisor. They say:
"do you want X with an expected return of 50% in 5 years or Y with an expected return of 25% in 5 years?"
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Replying to @danrobinson @SBF_Alameda and 3 others
You wouldn’t rather invest your money with an asset manager where you expect a 5% annualized rate of return to one where you expect a 3% annualized rate of return?
Your reaction would be “I might be interested in the 3% rate, although only if it’s RISKIER”?
That seems unusual.
"but", they say, "X is riskier".
I don't think you'd immediately say "obviously I want you to take lim as t-->inf of returns^(1/t) and then take the EV of that and tell me"
You might, if you like Kelly! But you tried to phrase it as _obvious_ that's what you'd ask.
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How do I try to learn what some fund's expected returns are? I'll probably at least look at historical returns, right? (NOT 👏 INVESTING 👏ADVICE)
Suppose there is 50 years of history. I compute historical returns by averaging the actual annual returns, right?
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