On investor preferences and mutual fund separation

We extend Cass and Stiglitz's analysis of preference-based mutual fund separation. We provide a complete characterization of the general K-fund separation. We show that some instances of separation with many funds can be constructed by adding inverse marginal utility functions having separation with one or a few funds. We also show that there is money separation (in which we can choose the riskless asset as one of the funds) if and only if there is a fund (which may or may not be the riskless asset) with a constant allocation as wealth changes. In general, we do not know how to write the separating utility functions in closed form, but we can do so in the special case of SAHARA utility defined by Chen et al. and for a new class of GOBI preferences introduced here.