That’s what you look at when you look at returns, right? Some standard unit of time? When you look at historical returns for funds you don’t look at it “per coin flip”
I agree it is arbitrary (one reason geometric mean, which is scale invariant, is better)
Conversation
ok so this question is a bit weird because the upside cases are about equal to the number of atoms in the universe so I think I object to the hypothetical?
but anyway, this will have higher average almost surely *if you run for enough years*!
In particular, something like 10^60
1
So yeah, in the long run, 99% still has higher arithmetic average annual returns if you're flipping 365 times per year almost surely, as (number of years) goes to infinity!
But if you instead only have ~60 years then you'll find weird "not in the infinite limit" results.
1
1
1) !! Now taking the limit as time approaches infinity is appropriate?
2) This is not correct. EV[annual return] is negative. As t approaches infinity, arithmetic mean of annual return will be negative
1
1) idk, I think this whole thing is ridiculous! But you seem to want to insist on infinite time horizons; so be it.
2) ok so what do you think the EV of the return for the first year is: positive or negative?
1
Yeah, I guess I’m wrong on the infinite timeframe. (Although I’d argue that it doesn’t make sense to do that here).
But still: look at your spreadsheet. Current wealth is zero and annual return is -99.99% no matter how much you refresh.
1
1
er obviously "no matter how much you refresh" is false
also, though, yes, I agree, this is all ridiculous! It was ridiculous for you to write a paper premised on infinite timeframes that doesn't hold on reasonable time frames in the first place, but now we're here.
2
1
3
If you guys keep this up you are not gonna leave any content for the podcast :(
1
2
don't worry we still haven't gotten past yelling about Kelly; we still have the whoel rest of the debate to go ;)