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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wait if you compute the historical returns by averaging the actual annual returns then you would favor all-in, not kelly!
in order to favor kelly you'd have to be *geometrically meaning* the annual returns, not averaging them
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Sure! Let's suppose you look at historical annual average rates of return for the past 55 years of all-in on a coin flip:
1965: 100%
1966: 100%
1967: 100%
1968: -100%
1969: 0%
1970: 0%
1971: 0%
1972: 0%
...
2020: 0%
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you're cheating with those 0's! it's actually 0/0 which is undefined.
so, fine, so I do a 99.99999% coinflip. Now it will work.
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whatever, take your pick.
for instance: let's say you wager X to win X (so even odds) but it's a 60/40 weighted coin.
I claim that wagering 99% of your money each year produces pretty a pretty good average of your yearly returns.
OK!! I show you a historical returns chart that looks like this:
docs.google.com/spreadsheets/d
Are you excited to invest?
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eh at 7%/year it's borderline--but I wouldn't be interested in kelly investing either really.
But let's say that it were 85/15 instead, or--if you want--still 60/40 but also I got paid on 3:1 odds.
Then, the answer is.....
....yes, I would be!
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