That's the time-average growth rate, right?
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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?
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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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