The term alpha fund is misleading because although it implies maximising alpha, it in fact usually simply means actively managed to out-perform a benchmark. The fact that funds that actually try to out-perform significantly need a label is an implicit acknowledgement that most supposedly active funds have a large element of closet tracking. The term alpha fund has also been appropriated by hedge funds, and some other funds that aim to maximise real returns.
Because fund league tables and other performance measures actually used by investors to pick funds do not actually measure alpha, there is no real motive for fund manager to maximise it. Finding managers who can consistently generate risk adjusted returns (if they exist) would probably be better for investors than simply picking the highest performers. The problem partly that the data is not always available (because the beta of a portfolio changes with every trade but the composition of most funds is only disclosed at intervals). However it is doubtful whether many investors are interested in calculating alpha in any case.
Portable alpha strategies can seperate the beta of a portfolio from its alpha, thus creating an alpha fund out of any investment with a positive alpha.