Absolutely not. All long term growth rates are geometric. There is no other kind.
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Replying to
uhhhh how are you defining growth rate?
"Growth rates refer to the percentage change of a specific variable within a specific time period"
from the first link: investopedia.com/terms/g/growth
I'd interpret that as lim t --> inf EV[ W_{t+1}/W_t ]
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That isn't a rate. it's the total growth. You have to scale it a period of time to make it a rate:
lim t --> inf EV[ (W_{t+1}/W_t)^(1/t) ]
That formula is the geometric return.
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Replying to
why exactly are you raising it to the 1/t power?
you're not taking W_{t+1}/W_0 there so I'm not sure why you should be raising to the 1/t, you're still just looking at growth in one time period!
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anyway, whatever, we're just fighting over how to define words now
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Were not there is an enormous difference between the two
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If you really believe this, though......
say you have 2 choices.
(a) doubles every year
(b) triples every year; but with probability 1/10^t each year causes 20^t torture to everyone on earth
which would you choose?
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That's quite an example. Are you trying to put a value on torture?
A.
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Replying to
But note that (b) has this property you've been talking about--it maximizes long-run geometric growth rate no matter how much of a hit you put for the unlikely torture; this is the symmetric scenario to the classic kelly one, where you ignore unlikely outcomes with large effects
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(or alternately you decide that if there is any chance at all that you end up having net done harm, all the analytical tools break down because they can't handle a negative number