On Investor Preferences and Mutual Fund Separation

We extend Cass and Stiglitz’s analysis of preference-based mutual fund separation. We show that high degrees of fund separation can be constructed by adding inverse marginal utility functions exhibiting lower degrees of separation. However, this method does not allow us to find all utility functions satisfying fund separation. In general, we do not know how to write the primal utility functions in these models 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. We show that there is money separation (in which the riskless asset can be one of the funds) if and only if there is a fund (which may not be the riskless asset) with a constant allocation as wealth changes.