But then you aren't maintaining the invariant that you hold a number of shares equal to the current price.
> So, you will make money on a bounded random walk
Yes. If you know ahead of time what the price is going to do (even probabilistically) then you can make money. If you don't, you can't.
If you know ahead of time what the price is going to do (even probabilistically) then you can make money. Exactly, you pick a model and make money ‘if’ reality fits that model. However, fast dumb models can make lots of money and complexity adds risks.
Anyway, many people get stuck with the idea you need the smartest people in the room while ignoring how much it costs to have the ‘smartest people’ in the room. Arguably, many companies are simply doing this to attract investors not because it maximizes returns as managing money is a great way to make money.
Sure, and they can also lose a lot of money.
> complexity adds risks
Not necessarily. Modern portfolio theory is a lot more complex than (say) buying and holding a single stock. But it's a lot less risky.
> you need the smartest people in the room
Maybe you don't need the smartest people in the room, but it helps not to have too many stupid ones. The real problem is that it can be really hard to tell which is which.
The reason this is not 'optimal' is if the price moves up to far you have sold every stock and run out, also you need a reserve to handle the price moving close to zero and if the stock goes bust you now own a lot of worthless stock.
PS: So, you will make money on a bounded random walk, but potentially far less money than holding the stock. In the end all this does is trade unbound potential gains for a finite income stream. Which is what all algo provide there effectively choosing which game to play in Vegas or shifting risk around etc.