so to be clear:
(Expected rate of return) annually: all-in wins
Expected (annual rate of return): kelly wins
Expected return: all-in wins
Median return: kelly wins
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I don't think this is a language debate!
But yes I agree with those four summaries, if you replace median with "every percentile" :)
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also I very much think it's a language debate when you phrase it like this: twitter.com/danrobinson/st
Let's say you go to your advisor. They say:
"do you want X with an expected return of 50% in 5 years or Y with an expected return of 25% in 5 years?"
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Replying to @danrobinson @SBF_Alameda and 3 others
You wouldn’t rather invest your money with an asset manager where you expect a 5% annualized rate of return to one where you expect a 3% annualized rate of return?
Your reaction would be “I might be interested in the 3% rate, although only if it’s RISKIER”?
That seems unusual.
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"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
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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