Resumen de Dynamic portfolio selection with transaction costs and estimation error
Xiaoling Mei
The last few decades have witnessed a surge in research activity in the area of multiperiod portfolio optimization due to its theoretical and practical importance. One of the main issues that researchers have confronted in the implementation of successful portfolio strategies is the consideration of transaction costs. Characterizing the optimal portfolio policy in the presence of transaction costs is an open area of research in portfolio optimization. In this dissertation, we aim to investigate the portfolio policy for a multiperiod portfolio problem with multiple risky assets and different types of transaction costs under the utility maximization framework. In particular, we study and characterize the optimal portfolio rebalancing rules for a risk-averse investor who incurs transaction costs in a discrete-time setting. We begin with an analytically tractable framework where the investor has mean-variance preference and constant investment opportunity set in the presence of different types of transaction costs. For small trades, which result in proportional transaction costs, we provide a closed-form expression for the no-trade region that confines the investor’s optimal portfolio policy for each period, and we further analyze how the size of the no-trade region changes with relevant model parameters. For large trades, which can distort prices and thus result in strictly convex costs, we show analytically that there exists a state-dependent rebalancing region for each period, such that the optimal policy at each period is to trade to its boundary. We further study the utility losses associated with ignoring transaction costs and behaving myopically with an empirical dataset. Then, we move to an analytically intractable framework where the investor has power utility preference and predictable risky asset returns in the presence of proportional transaction costs. We first consider an approximation to the model with power utility using a mean-variance problem, and we propose several approximate solutions that induce low utility losses for the mean-variance problem. Furthermore, we adapt these feasible trading strategies to the framework with power utility of intermediate consumption and study numerically the associated losses in certainty equivalent. We show that the multiperiod portfolio selection problem can be tackled through the utilization of a duality approach.
