The analysis of the impact of fee structures on a fund’s portfolio choice decisions have previously been typically studied in a setting in which the manager receives an exogenously prespecified amount of money to manage for an exogenously prespecified time period. Even models in which investors do make allocation decisions have mostly been restricted to a setting in which investors flexibility is reduced to deciding what fraction of the wealth to delegate to the management of the fund at the initial date. Once this initial decision is made the investor is unable to neither delegate additional funds to the fund to manage at a later date nor withdraw part of the money under the fund’s management.

The important innovation of our paper is that we allow the investor to move money in and out of the fund dynamically. to this end, we study a dynamic continuous time economy with two agents: a small investor and a fund manager. the small investor implicitly faces high transaction costs that preclude him from trading directly in the equity market. While he is precluded from holding equity directly, he can invest money in a mutual fund. Specifically, he is permitted to dynamically allocate his money between a mutual fund and a locally riskless bond, where we impose the natural restriction that the investor can not short the fund. the fund manager, on the other hand, is allowed to trade dynamically in both the stocks and the bond. We allow the manager to select the fund portfolio strategy and at the same time to trade on his own account.

Our objective is to understand how enabling an investors to dynamically rebalance between the fund and the bond impacts the dynamic trading strategy of the fund. We focus our analysis on the case of fraction of funds fees, whereby the manager receives an instantaneous fee that is a fixed proportion of the assets under management. as of 1995, approximately 98% of all mutual funds were using fraction of fund fees without any performance based incentives. It is important to emphasize from the outset that we are not taking a stance on whether this is the form of the optimal contract in our setting, but instead rely on its widespread use by mutual funds as the motivation for our analysis.

In order to focus on the impact of flows in and out of the fund on the manager’s choice of a fund portfolio, while maintaining a tractable setup, we make the following simplifying assumptions. First, both agents have complete information about financial markets. second, agents observe the actions of each other. third, from the perspective of the fund manager markets are complete. forth, while only mild regularity conditions are imposed on the manager’s utility function, the small investor is assumed to have a log utility function.

We further assume that while both agents observe the actions of each other, the fund manager is strategic where as the investor is not. Specifically, when the investor determines his portfolio he takes the fund strategy as given. On the other hand, when the fund manager selects the fund’s trading strategy he takes into account what would be the investor’s reaction to such a strategy.

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