McGrath:

WAG is an American slang term in management for a "wild-assed guess", or rough estimate of a situation. Sometimes also called a SWAG, for a shitty,or stupid, wild-assed guess.

As an aside the used of the suffix '-assed' as an intensifier or characterization, particularly "wild-assed", "dumb-assed", "stupid-assed", and the like, is peculiar to the US, I believe. The only legitimate precedent I can think of is zoological nomenclature such as "blue-assed baboon", "red-tailed hawk" and "red-breasted blackbird" and the like.

A