Delegated dynamic portfolio management under mean-variance preferences

Abstract

We consider a complete financial market with deterministic parameters where an investor and a fund manager have mean-variance preferences. The investor is allowed to borrow with risk-free rate and dynamically allocate his wealth in the fund provided his holdings stay nonnegative. The manager gets proportional fees instantaneously for her management services. We show that the manager can eliminate all her risk, at least in the constant coefficients case. Her own portfolio is a proportion of the amount the investor holds in the fund. The equilibrium optimal strategies are independent of the fee rate although the portfolio of each agent depends on it. An optimal fund weight is obtained by the numerical solution of a nonlinear equation and is not unique in general. In one-dimensional case, the investor's risk is inversely proportional to the weight of the risky asset in the fund. We also generalize the problem to the case of multiple managers and provide some examples.

Mutual Fund Portfolio Choice in the Presence of Dynamic Flows

“…Second, allowing for competition among mutual funds is an important and challenging extension of the model. As discussed in , the case of constant coefficients has been recently analyzed in Breton, Hugonnier, and Masmoudi (2010) and Cetin (2006), with results that are consistent with ours. Extending these results to the case in which funds are restricted to holding only equity would potentially lead to interesting insights as to how funds compete by jointly determining the fees they charge and the composition of their portfolios.…”

“…This striking result implies that the equilibrium we identify in Corollary 4.2 is also an equilibrium for the case in which there are multiple mutual funds. A similar conclusion was reached by Cetin (2006) in a model with mean variance preferences and a single risky asset. For the case of stochastic market coefficients, the situation is much more complicated, because one has to study a stochastic game between the managers where the pay‐offs are given in terms of a solution to a system of BSDEs.…”

“…This would make the problem analytically intractable. For deterministic coefficients, Cetin (2006) considers the case in which the investor and the manager have mean‐variance preferences, and solves the equilibrium numerically. He, too, finds that the value functions are independent of the fee rate.…”

Two essays in analyzing delegated portfolio management relationships through relative portfolio measures||Two essays in analyzing delegated portfolio management relationships through relative portfolio measures

“…It also suggests how we can avoid paradoxes such as Roll's critique, Roll (1977). However, anecdotes of this analysis can be found in many highly cited financial papers such as Gompers and Metrik (2001), Pastor and Stambaugh (2002a,b), Berk and Green (2004), and Cetin (2006). Even very recent papers provide conclusions based on the assumption of consistency of the relative performance optimization.…”