TL;DR: Stocks move on new information. That movement has a time-course. What else do you want to know to answer this question? Isn’t that what we mean by arbitrage in this context?
I do think arbitrage has a kind of esoteric meaning and gets in the way of this discussion. We are really trying to answer what new information moves markets and how quickly that information moves the market here in 2023. is alternative data disseminated as quickly? Maybe people buy credit card data because it take a while for retrial investors to get that information.
Some at P123 place important on finding new factors that make sense to them but are not being used by others (the equivalent of Fisher’s price to sales). We can argue it that really worked for Fisher or not (or O’shaughnessey) but some believe in that.
Even, I who likes the method more than the factors understand you have to have good factors. And the stocks need some turnover—in part because the new information eventually gets priced-in.
We have a post showing that for some models some of that movement can occur in the first day of trading on a Monday. "Next open" always the best - #47 by yuvaltaylor
Which just suggests this arbitrage can occur relatively quickly at times.
With reduced movement by Friday for some ports (on the now 5-day old information). I.e., The new information can be priced-in by Friday.
But why do we ever even sell a position? Isn’t it because, at least to some extent, the new information in our ranking system evenytually gets arbitraged way for basically every port ever created at P123?
I am not sure what more you would need to show that there CAN be arbitrage.
There has to be some arbitrage somewhere, at some point for the market to even work, I think.
Jim