Apple Split

I'm trying to wrap my head around the "efficient-markets" meaning of the Apple split. I guess the entire notion of stock splits seems to me to be in violent conflict with EMH. It seems I'm not the only one who's scratched his head over this. 

While the authors of those links are concerned chiefly with the event-study implications (positive signaling and so forth), I am more curious about how to reconcile EMH with the idea that a cheaper share price should make a stock more attractive. Surely the first splits were not conducted as a signal; they were meant to draw in more investors by making the stock easier to buy. Only later, I imagine, did market actors begin to interpret splits as a sign that a firm was prospering. 

Neil Irwin best captured the absurdity of the idea of drawing in more investors with a split:

"The logic, presumably, is that there may be people who really want to invest in Apple, yet want to do so in chunks smaller than $530, (which raises a question of why somebody who can’t come up with $530 to invest would be investing in individual stocks to begin with)."

So maybe it is just about signaling. But, even that aspect is troubling. If a firm's prospects could be measured on a one-dimensional index (call it theta (0 < theta < infinity)), firms may decide to split their stock when theta reaches a certain value theta0. Market actors will subsequently learn that a split is an indication that management believes theta=theta0, and incorporate this into their information portfolio.

Grasping and impatient firms may then try to goose their share prices by splitting at, say, 0.9theta0. This will lead firms who would have waited until theta0 to split at 0.9theta0. Market actors will then adjust their beliefs about splits to mean a firm has theta=0.9theta0. The graspers may then split at 0.8theta0. This spiral will continue until market actors begin to believe that splits have no meaningful informational value. 

Yet we still see that market actors believe splits have informational value. Is the answer that there are no impatient and grasping firms? That seems unlikely. I think the most plausible explanation for (positive) market reactions to splits is that many market actors (lone wolves and institutional investors alike) have no idea what in world a given split means, except that it means that the price will go up, so they buy (hoping they are) on the up-slope.

Irwin's post has a link to Dhar, Goetzmann, Zhu, and Moscow, which found that the lower prices created by splits attracts individual idiots and has no impact on institutional investors. Irwin cites this as Warren Buffett's reason for never splitting BRK.A. Matthew Yglesias speculates that the Apple split could be aimed at getting inclusion on the Dow index, but notes that this would not likely generate much value.

However one chooses to look at it, a meaningful impact from stock splits is generally incompatible with EMH.