(OK, technically, I get a more accurate result if I average LOG returns, just as we do when measuring volatility. But no funny business—I'm never looking at log wealth! And my point will still stand if we use arithmetic mean of returns.)
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So, when I do this, what number is it going to approximate?
It's going to approximate the time-average rate of growth of wealth, right?
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How do we know that Warren Buffett is a phenomenal investor?
We look at his average annual return, right? We see that he has has returned, on average >20.3% per year since he started.
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nope, not if you're averaging the returns!
to get what you're trying to call the time-average growth rate you have to *geometrically mean* the returns
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OK, and you're saying that arithmetic mean of annual returns is appropriate?
What happens if you flip the coin not once a year, but once a day? Even faster growth in EV(wealth), right?
But what happens to your arithmetic mean of annualized returns?
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(I could make the spreadsheet for you but you can probably guess that it's going to be -99.999999999%)
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if you do _one single simulation of it_ then the median result will be very negative returns!
but in fact the expected arithmetic mean of annualized returns is positive!
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But really a lot of my point is:
twitter.com/danrobinson/st
what you said there was literally false.
what you _meant_ may have been true!
But your whole point was some weird gotcha schtick involving a sentence you thought sounded bad for me.
and actually it sounds bad for you!
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Replying to @SBF_FTX @SBF_Alameda and 3 others
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?
INVESTING ADVICE)
Suppose there is 50 years of history. I compute historical returns by averaging the actual annual returns, right?1
"averaging the actual annual returns"
should have been "geometric"
It's true regardless of whether you use arithmetic or geometric, right?
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Replying to @SBF_FTX @SBF_Alameda and 3 others
OK, and you're saying that arithmetic mean of annual returns is appropriate?
What happens if you flip the coin not once a year, but once a day? Even faster growth in EV(wealth), right?
But what happens to your arithmetic mean of annualized returns?
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Nope!
The EV of the arithmetic mean of your annual returns goes up the more you can flip because each flip is positive EV.
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