macrocephalopod

Well, I'd like to think I'm not a moron, and it wasn't clear to me the arithmetic mean was 0 until you explicitly said so. Maybe that was immediately clear to non-morons before you said so?

Mean zero is the *best case* for the strategy I described! If mean > 0 then a reversion strategy is short more often than long so it would lose money. If mean < 0 then a reversion strategy is long more than it is short so it would lose money.

This is such a weird argument to be having. I literally generated some random data and people want to tell me you can develop profitable trading strategies for it. Is this what going insane feels like?

Sometimes the real world feels insane. If you generated completely random zero-mean R and *multiplied* (1+R) by itself repeatedly - you'd have complete noise that you could become incredibly rich off of. Sorry, but it's true. Don't kill the messenger.

Please, describe what the strategy here is, then go and simulate it. It will *at best* be flat.

Please do. Of course, this is gross of tcost. Please keep that in mind. But you can make money.

Gross of tcost is fine. I’m still waiting for a description of the strategy though?

Here's the strat. Let's say we have a portfolio of 50% cash / 50% your simulated stock. At the end of each day, rebalance this portfolio back to 50/50. Basically, you buy more stock if it goes down and sell some if it went up that day. Let me know the returns you see.