Delegated dynamic portfolio management under mean-variance preferences (original) (raw)

Equilibrium prices in the presence of delegated portfolio management

This paper analyzes the asset pricing implications of commonly used portfolio management contracts linking the compensation of fund managers to the excess return of the managed portfolio over a benchmark portfolio. The contract parameters, the extent of delegation, and equilibrium prices are all determined endogenously within the model we consider. Symmetric (fulcrum) performance fees distort the allocation of managed portfolios in a way that induces a significant and unambiguous positive effect on the prices of the assets included in the benchmark and a negative effect on the Sharpe ratios. Asymmetric performance fees have more complex effects on equilibrium prices and Sharpe ratios, with the signs of these effects fluctuating stochastically over time in response to variations in the funds’ excess performance.

Dynamic mean–variance portfolio selection with borrowing constraint

European Journal of Operational Research, 2010

This paper derives explicit closed form solutions, for the efficient frontier and optimal investment strategy, for the dynamic mean-variance portfolio selection problem under the constraint of a higher borrowing rate. The method used is the Hamilton-Jacobi-Bellman (HJB) equation in a stochastic piecewise linear-quadratic (PLQ) control framework. The results are illustrated on an example.

Dynamic Mean-Variance Asset Allocation

Review of Financial Studies, 2010

Mean-variance criteria remain prevalent in multi-period problems, and yet not much is known about their dynamically optimal policies. We provide a fully analytical characterization of the optimal dynamic mean-variance portfolios within a general incomplete-market economy, and recover a simple structure that also inherits several conventional properties of static models. We also identify a probability measure that incorporates intertemporal hedging demands and facilitates much tractability in the explicit computation of portfolios. We solve the problem by explicitly recognizing the time-inconsistency of the mean-variance criterion and deriving a recursive representation for it, which makes dynamic programming applicable. We further show that our time-consistent solution is generically different from the pre-commitment solutions in the extant literature, which maximize the mean-variance criterion at an initial date and which the investor commits to follow despite incentives to deviate. We illustrate the usefulness of our analysis by explicitly computing dynamic mean-variance portfolios under various stochastic investment opportunities in a straightforward way, which does not involve solving a Hamilton-Jacobi-Bellman differential equation. A calibration exercise shows that the mean-variance hedging demands may comprise a significant fraction of the investor's total risky asset demand.

Dynamic portfolio selection with nonlinear transaction costs

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2005

The dynamic portfolio selection problem with bankruptcy and nonlinear transaction costs is studied. The portfolio consists of a risk-free asset, and a risky asset whose price dynamics is governed by geometric Brownian motion. The investor pays transaction costs as a (piecewise linear) function of the traded volume of the risky asset. The objective is to find the stochastic controls (amounts invested in the risky and risk-free assets) that maximize the expected value of the discounted utility of terminal wealth. The problem is formulated as a non-singular stochastic optimal control problem in the sense that the necessary condition for optimality leads to explicit relations between the controls and the value function. The formulation follows along the lines of Merton (Merton 1969 Rev. Econ. Stat. 51 , 247–257; Merton 1971 J. Econ. Theory 3 , 373–413) and Bensoussan & Julien (Bensoussan & Julien 2000 Math. Finance 10 , 89–108) in the sense that the controls are the amounts of the risky...

Portfolio management with benchmark related incentives under mean reverting processes

Annals of Operations Research, 2017

We study the problem of a fund manager whose compensation depends on the relative performance with respect to a benchmark index. In particular, the fund manager's risk-taking incentives are induced by an increasing and convex relationship of fund flows to relative performance. We consider a dynamically complete market with N risky assets and the money market account, where the dynamics of the risky assets exhibit mean reversions, either in the drift or in the volatility. The manager optimizes the expected utility of the final wealth, with an objective function that is non-concave. The optimal solution is found by using the martingale approach and a concavification method. The optimal wealth and the optimal strategy are determined by solving a system of Riccati equations. We provide a semi-closed solution based on the Fourier transform.

Mean-Variance Portfolio Optimization with State-Dependent Risk Aversion

Mathematical Finance, 2014

The object of this paper is to study the mean-variance portfolio optimization in continuous time. Since this problem is time inconsistent we attack it by placing the problem within a game theoretic framework and look for subgame perfect Nash equilibrium strategies. This particular problem has already been studied in where the authors assumed a constant risk aversion parameter. This assumption leads to an equilibrium control where the dollar amount invested in the risky asset is independent of current wealth, and we argue that this result is unrealistic from an economic point of view. In order to have a more realistic model we instead study the case when the risk aversion is allowed to depend dynamically on current wealth. This is a substantially more complicated problem than the one with constant risk aversion but, using the general theory of time inconsistent control developed in [4], we provide a fairly detalied anaysis on the general case. We also study the particular case when the risk aversion is inversely proportional to wealth, and for this case we provide an analytic solution where the equilibrium dollar amount invested in the risky asset is proportional to current wealth. The equilibrium for this model thus appears more reasonable than the one for the model with constant risk aversion.

Optimal allocation of wealth for two consuming agents sharing a portfolio

We study the Merton problem of optimal consumption-investment for the case of two investors sharing a final wealth. The typical example would be a husband and wife sharing a portfolio looking to optimize the expected utility of consumption and final wealth. Each agent has different utility function and discount factor. An explicit formulation for the optimal consumptions and portfolio can be obtained in the case of a complete market. The problem is shown to be equivalent to maximizing three different utilities separately with separate initial wealths. We study a numerical example where the market price of risk is assumed to be mean reverting, and provide insights on the influence of risk aversion or discount rates on the initial optimal allocation.

MUTUAL FUND PORTFOLIO CHOICE IN THE PRESENCE OF DYNAMIC FLOWS

Mathematical Finance, 2010

We analyze the implications of dynamic flows on a mutual fund's portfolio decisions. In our model, myopic investors dynamically allocate capital between a riskless asset and an actively managed fund which charges fraction-of-fund fees. The presence of dynamic flows induces "flow hedging" portfolio distortions on the part of the fund, even though investors are myopic. Our model predicts a positive relationship between a fund's proportional fee rate and its volatility. This is a consequence of higher-fee funds holding more extreme equity positions. Although both the fund portfolio and investors' trading strategies depend on the proportional fee rate, the equilibrium value functions do not. Finally, we show that our results hold even if investors are allowed to directly trade some of the risky securities.

An optimal portfolio problem in a defaultable market

Advances in Applied Probability, 2010

We consider a portfolio optimization problem in a defaultable market. The investor can dynamically choose a consumption rate and allocate his/her wealth among three financial securities: a defaultable perpetual bond, a default-free risky asset, and a money market account. Both the default risk premium and the default intensity of the defaultable bond are assumed to rely on some stochastic factor which is described by a diffusion process. The goal is to maximize the infinite-horizon expected discounted log utility of consumption. We apply the dynamic programming principle to deduce a Hamilton-Jacobi-Bellman equation. Then an optimal Markov control policy and the optimal value function is explicitly presented in a verification theorem. Finally, a numerical analysis is presented for illustration.

An Explicit Solution for a Portfolio Selection Problem with Stochastic Volatility

Journal of Mathematical Finance, 2017

In this paper, we revisit the optimal consumption and portfolio selection problem for an investor who has access to a risk-free asset (e.g. bank account) with constant return and a risky asset (e.g. stocks) with constant expected return and stochastic volatility. The main contribution of this study is twofold. Our first objective is to provide an explicit solution for dynamic portfolio choice problems, when the volatility of the risky asset returns is driven by the Ornstein-Uhlenbeck process, for an investor with a constant relative risk aversion (CRRA). The second objective is to carry out some numerical experiments using the derived solution in order to analyze the sensitivity of the optimal weight and consumption with respect to some parameters of the model, including the expected return on risky asset, the aversion risk of the investor, the mean-reverting speed, the long-term mean of the process and the diffusion coefficient of the stochastic factor of the standard Brownian motion.