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.

Generalized Systematic Risk

We generalize the concept of .systematic risk to a broad class of risk measures potentially accounting for high distribution moments, downside risk, rare disasters, as well as other risk attributes. We offer two different approaches. First is an equilibrium framework generalizing the Capital Asset Pricing Model, two-fund separation, and the security market line. Second is an axiomatic approach resulting in a systematic risk measure as the unique solution to a risk allocation problem. Both approaches lead to similar results extending the traditional beta to capture multiple dimensions of risk. The results lend themselves naturally to empirical investigation.