macrocephalopod

I’m saying start with $100 dollars, 50 in cash and 50 in the asset. At the end of each day, observe your new allocation has shifted because of the days returns. Then, rebalance 50/50 of whatever NAV you have left into cash and the asset. This is different from your example.

That would be *exactly* the same as what I already did, except that the 'equity' variable would be multiplied by 100 to simulate starting with $100 instead of $1. It wouldn't change the overall result except that instead of ending with $0.000005 it would end with $0.0005

If we started with a stock with a *geometric* return of zero instead of *arithmetic* return zero the story would be different and you could make money (before costs) by rebalancing every day, although not at anything like the rate that you are imagining.

If a stock has arithmetic return of 0 you can just short it to harvest the vol decay because of the 1/2 sigma^2. Another way to make money from noise.

Lmao no you absolutely cannot

If you shorted the stock (even in a nice, frictionless theoretical work) the vol drag still works against you, because it's a quadratic term (i.e. it is not sensitive to sign) In the real world you would lose money even faster because *gestures at real-world frictions*

It’s the negative of a quadratic, so you can flip the sign