If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)
3. Open Threads should be posted in Discussion, and not Main.
4. Open Threads should start on Monday, and end on Sunday.
Oh, I thought we were talking about reality. EMH claims to describe reality, doesn't it?
As to toy models, if I get to define what classes of investors exist and what do they do, I can demonstrate pretty much anything. Of course it's possible to set up a world where "a suitably defined investor cannot make money but can lose money".
And deep OOM options are diversifiable -- there is a great deal of different markets in the world.