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

Hiroshi Konno and Hiroaki Yamazaki
Management Science
Vol. 37, No. 5 (May, 1991), pp. 519-531
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/2632458
Page Count: 13
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Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market
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Abstract

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.

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