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

Abstract

The purpose of this paper is to demonstrate that a portfolio optimization model using the L1 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 L1 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 L1 risk model generates a portfolio quite similar to that of the Markowitz's model within a fraction of time required to solve the latter.