One-fund separation in incomplete markets with two assets

This paper provides a necessary and sufficient condition for one-fund separation to occur in incomplete-market economies where finitely many agents with distinct risk aversion and heterogeneous beliefs are allowed to trade two assets. The condition involves joint restrictions on risk aversion, beliefs and asset payoffs. Thus, such joint restrictions may be indispensable for fund separation in incomplete markets, which is in contrast with the preference-based and return-distribution-based approaches. When the condition for one-fund separation holds, agents could behave in equilibrium as if there were a single fund which delivers the aggregate asset payoffs in the economy. Otherwise, agents choose optimal shares in distinct proportions.