As I counted, Chicago has 49 trustees besides the president, of whom 19 are undergraduate alumni, 3 received PhDs (but only one of those was not also an undergraduate), and 7 (not counting the president) did not attend the university. (Maybe 6; one is a Lab alum. Hard to complain about that on a board this size.) The Chicago board is absolutely dominated by MBA (21) and Law alums (8) (significant overlap with the undergraduates there, too), and by financial types (well over half). There are lots of non-financial business people, too, which I think is good, and a variety of nonprofit types.
The contrast with the Yale board is really striking. The Yale board has 16 members other than the president, and all (and the president, too) have Yale degrees: 11 undergraduates, 3 pure PhDs (plus the president), one JD, and one MBA. A couple of the undergraduates have a professional degree from Yale, too. Only 8 of them are financial types, and that includes at least one decidedly old-school banker.