Are you saying that I take the same coin that gives 60% +99%, 40% -99% each year, and then try to like guess what full time graph produces that yearly result?
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No, I’m saying you take that same coin, but you get to flip it every day. So every day a +99% or (somewhat less likely) a -99%. It’s great news for you: EV(wealth) grows 365 times as fast.
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sweet!
yeah ok I'm pretty sure this is gonna be great
I'll whip up a spreadsheet
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er ok wait nvm we have another different assumption now
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I suspect you think I'm going to measure something I'm going to say is silly, like "flip a coin once a day, arbitrarily group into years in a way that can't be meaningful, for each year compute end/start-1, then average those together"
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That’s what you look at when you look at returns, right? Some standard unit of time? When you look at historical returns for funds you don’t look at it “per coin flip”
I agree it is arbitrary (one reason geometric mean, which is scale invariant, is better)
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ok so this question is a bit weird because the upside cases are about equal to the number of atoms in the universe so I think I object to the hypothetical?
but anyway, this will have higher average almost surely *if you run for enough years*!
In particular, something like 10^60
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So yeah, in the long run, 99% still has higher arithmetic average annual returns if you're flipping 365 times per year almost surely, as (number of years) goes to infinity!
But if you instead only have ~60 years then you'll find weird "not in the infinite limit" results.
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1) !! Now taking the limit as time approaches infinity is appropriate?
2) This is not correct. EV[annual return] is negative. As t approaches infinity, arithmetic mean of annual return will be negative
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1) idk, I think this whole thing is ridiculous! But you seem to want to insist on infinite time horizons; so be it.
2) ok so what do you think the EV of the return for the first year is: positive or negative?
so let's say you start with $1.
a) do you think EV($ after 1 year) is more or less than 1?
b) do you think EV($ after 1 day) is more or less than 1?