Tunneling behaviors of two mutual funds

Abstract

In practice, the mutual fund manager charges asset based management fee as the incentives. Meanwhile, we suppose that the investor could sustainedly obtain the fixed proportions of the fund values as the rewards. In this perspective, the objectives of the investor and the manager seem to be consistent. Unfortunately, it is a common situation that the fund managers have private relations, and they transfer the assets illegally. In this paper, we study the optimal tunneling behaviors of the two fund managers to maximize the overall performance criterions. It is the first time to use two prototypes whether the management fee rates are consistent with the investment returns to study the impacts of the two factors on the tunneling behaviors. We firstly study the problem without transaction cost between funds, and it is formalized as a two-dimensional stochastic optimal control problem, whose semi-analytical solution is derived by the dynamic programming methods. Furthermore, the transaction cost is considered, and we explore the penalty method and the finite difference method to establish the numerical solutions. The results show that the well performed and high rewarded fund manager obtains most of the total assets by tunneling, and only keep the other fund at the brink of maximal withdraws for the liquidity considerations. Moreover, the well performed and low rewarded fund manager obtains most of the total assets. Being inconsistent with the instinct, the high management fee rate could neither make the fund managers work efficiently, nor induce the beneficial tunneling behaviors.