Fuzzy Semi-absolute Deviation Portfolio Rebalancing Model

In 1952, Markowitz published his pioneering work which laid the foundation of modern portfolio analysis. Markowitz’s model has served as a basis for development of the modern financial theory over the past five decades. However, contrary to its theoretical reputation, it is not used extensively to construct portfolios at a large-scale. One of the most important reasons for this is the computational difficulty associated with solving a large-scale quadratic programming problem with a dense covariance matrix. Konno and Yamazaki used the absolute deviation risk function to replace the risk function in Markowitz’s model and formulated a mean absolute deviation portfolio optimization model. It turns out that the mean absolute deviation model maintains the favorable properties of Markowitz’s model and removes most of the principal difficulties in solving Markowitz’s model. Simaan provided a thorough comparison of the mean variance model and the mean absolute deviation model. Furthermore, Speranza used the semi-absolute deviation to measure the risk and formulated a portfolio selection model.

In this study, we consider the liquidity angle, and we propose a linear programming model for portfolio rebalancing, after considering transaction costs; based on the fuzzy decision theory, a portfolio rebalancing model with transaction costs is proposed.