"but", they say, "X is riskier".
I don't think you'd immediately say "obviously I want you to take lim as t-->inf of returns^(1/t) and then take the EV of that and tell me"
You might, if you like Kelly! But you tried to phrase it as _obvious_ that's what you'd ask.
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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?
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(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?I would argue that geometric mean is appropriate for many reasons (for example, you otherwise get different results if you average monthly returns rather than annual returns).
But my argument does not depend on using geometric mean returns:
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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?