DP13127 | Optimal fund menus

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We study the optimal design of a menu of funds by a manager who is required to use linear pricing and does not observe the preferences of investors regarding one of the risky assets. The optimal menu involves bundling of assets and is explicitly constructed from the solution to a calculus of variations problem that optimizes over the indirect utilities that each type of investor receives. We show that the need to maintain incentive compatibility leads the manager to behave as a closet indexer by offering funds that are inefficiently tilted towards the asset not subject to the information friction.