Equivalence of linear deviation about the mean and mean absolute deviation about the mean objective functions

Authors:
C.M Kenyon;S Savage;B Ball
Affiliations:
EES, Austin Product Center - Research, Schlumberger, 8311 North FM 620, Austin, TX 78726, USA;Department of EES/OR, Stanford University, USA;MIT, MA, USA
Venue:
Operations Research Letters
Year:
1999

Citing 8
Cited 0

Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market

Management Science
A reformulation of a mean-absolute deviation portfolio optimization model

Management Science
Asymmetric risk measures and tracking models for portfolio optimization under uncertainty

Annals of Operations Research
Mean-absolute deviation portfolio optimization for mortgage-backed securities

Annals of Operations Research
Estimation risk in portfolio selection: the mean variance model versus the mean absolute deviation model

Management Science
Concepts, Technical Issues, and Uses of the Russell-Yasuda Kasai Financial Planning Model

Operations Research
Formulation of the Russell-Yasuda Kasai Financial Planning Model

Operations Research
Lindo an Optimization Modeling System/Book and Macintosh Disk

Lindo an Optimization Modeling System/Book and Macintosh Disk

Quantified Score

Hi-index	0.00

Visualization

Abstract

Konno (Oper. Res. Soc. Japan 33 (1990) 139-156). introduced a piecewise linear objective function for portfolio optimization to measure the deviation from a mean return. An apparently asymmetric objective function can be obtained by changing the gradients either side of the mean. However, we show that when the linear deviations are taken relative to the mean, any two piece linear objective function is equivalent to the mean absolute deviation, which is symmetric. Equivalent is used here to mean that one function is proportional to the other. Also we show that emphasizing upside risk is exactly equal to emphasizing downside risk when these are taken relative to the mean. No distributional assumptions are required beyond the existence of the first moment. In this case an investor changing from upside to downside risk would not change his solution at all, despite what the investor intended to achieve.