Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market

The purpose of this paper is to demonstrate that a portfolio optimization model using the L 1 risk (mean absolute deviation risk) function can remove most of the difficulties associated with the classical Markowitz's model while maintaining its advantages over equilibrium models. In particular, the L 1 risk model leads to a linear program instead of a quadratic program, so that a large-scale optimization problem consisting of more than 1,000 stocks may be solved on a real time basis. Numerical experiments using the historical data of NIKKEI 225 stocks show that the L 1 risk model generates a portfolio quite similar to that of the Markowitz's model within a fraction of time required to solve the latter.