(This point, unlike the other one, leans on the infinite-time-horizon assumption)
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It relies on a number of things, and e.g. means that any not-infinitely-repeatable process is irrelevant
(which is one reason I think the backdrop scenario kelly is usually presented in is not a helpful one to try to think about)
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er also they *do* have an impact on your asymptotic wealth growth rate!
just not your asymptotic *log* wealth growth rate
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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!
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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