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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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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how many years are we running this for?
there's nothing with constant % distribution each year that I'd invest any money in at all for 60 years: either the EV is < 100%/year and I wouldn't invest, or >100%/year and after 60 years it'd be > all the money in the world
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so basically I think the "infinite horizon" approach is totally fucked for this reason (it's in all cases running simulations which usually end with more money than atoms in the universe, somehow)
But if you use 5 years instead, 50/50 each year, 6:1 payout, I'd go all in