"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.
Conversation
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.
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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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That's what it means to invest in really early stage startups -- usually you blow out, but once in a while you become Peter Thiel.
This is the whole business model of e.g. Y Combinator, which has made all its money from a tiny fraction of its companies.
Now you might object that while each individual company looks like your spreadsheet their overall book is more of a kelly approach, and that would be reasonable!
but, ok, how about being a startup founder at y combinator? You see similar return profiles!
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