Only if you only flip the coin once a year.
If you flip the coin once a day, then the arithmetic mean returns will almost always be worse, right?
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er sorry actually could you describe the coin that you're saying I'm flipping once per day?
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I might have been making different assumptions than you.
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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"
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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What's the actual claim either of you are making? Maybe set up like this:
I have a sequence W_0=1, W_1, ..., W_T of year-end wealths
I get to W_i from W_{i-1} through some sequence of bets
My annual returns are X_i = W_i / W_{i-1} (maybe -1)
My annualized return is E[W_T^1/T]
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