(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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1) Run it as many times as you want and try to get a positive return.
2) There's no simulation. We're at the advisor's office. Here reality, what do we know about this strategy's historical performance? That it has never done better than -99.999% in any year ever.
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1) sure I will, but it'll take a while :P
2) ok but you also didn't present the *real life thing* at the advisor's office.
A *closer* version would be he shows you two sets of companies:
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a) 100 which each make average 5%/year
b) 100 which average 30%/year. However these were high-vol startups! So 95 of them are bankrupt, four are up 10,000%, and one is up 1,000,000%.
He asks you to choose a stock. Which category do you choose from?
except, really, he doesn't show you any of those companies.
He and you both know exactly which company you're going to buy. He doesn't even exist in fact, because you use ftx.com/tokenized-stoc like any civilized person does, and buy the same stock everyone does.
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And, really, what strategy did that company follow: did it aim for steady annual returns, or did it accept likely failure in return for a high EV?
I pick as many stocks as I can from the second bucket (if that's allowed).
But you are making this wayyyy too easy on yourself. Get back to this example (which you picked!)
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a) if you can only pick one stock which do you pick, first or second bucket?
b) I already said I wouldn't do all-in *or* kelly on that example because EV isn't high enough.
but if you jack it up enough (so EV is higher than replacement level) then yeah I'd go all in.
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