The maximum geometric mean criterion: revisiting the Markowitz–Samuelson debate: survey and analysis

Haim Levy

doi:10.1007/s10479-024-06250-8

The maximum geometric mean criterion: revisiting the Markowitz–Samuelson debate: survey and analysis

Haim Levy^*

^*Corresponding author for this work

BA Business Department

Research output: Contribution to journal › Article › peer-review

Abstract

By the Almost First-degree Stochastic Dominance (AFSD) rule, corresponding only to economically relevant preferences, for an infinite horizon the theoretical claim of both Markowitz and Samuelson is not intact. However, for the practically more relevant case of the long but finite horizon, with stocks-bonds portfolios, Markowitz empirically is right as we find that the MGM portfolio coincides with the optimal myopic portfolio for all risk aversion parameters α<1.7. For α≥1.7 the MGM portfolio dominates by AFSD rule all optimal myopic portfolios, as long as the investment horizon is 12–15 years or longer.

Original language	English
Pages (from-to)	263-284
Number of pages	22
Journal	Annals of Operations Research
Volume	346
Issue number	1
DOIs	https://doi.org/10.1007/s10479-024-06250-8
State	Published - Mar 2025

Bibliographical note

Publisher Copyright:
© The Author(s) 2024.

Keywords

Almost first-degree stochastic dominance (AFSD)
FSD-violation area
Geometric mean
Myopic preference

Access to Document

10.1007/s10479-024-06250-8

Cite this

@article{6ae3a6a37edf40acabc78f8ec92f5e80,

title = "The maximum geometric mean criterion: revisiting the Markowitz–Samuelson debate: survey and analysis",

abstract = "By the Almost First-degree Stochastic Dominance (AFSD) rule, corresponding only to economically relevant preferences, for an infinite horizon the theoretical claim of both Markowitz and Samuelson is not intact. However, for the practically more relevant case of the long but finite horizon, with stocks-bonds portfolios, Markowitz empirically is right as we find that the MGM portfolio coincides with the optimal myopic portfolio for all risk aversion parameters α<1.7. For α≥1.7 the MGM portfolio dominates by AFSD rule all optimal myopic portfolios, as long as the investment horizon is 12–15 years or longer.",

keywords = "Almost first-degree stochastic dominance (AFSD), FSD-violation area, Geometric mean, Myopic preference",

author = "Haim Levy",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2024.",

year = "2025",

month = mar,

doi = "10.1007/s10479-024-06250-8",

language = "אנגלית",

volume = "346",

pages = "263--284",

journal = "Annals of Operations Research",

issn = "0254-5330",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - The maximum geometric mean criterion

T2 - revisiting the Markowitz–Samuelson debate: survey and analysis

AU - Levy, Haim

N1 - Publisher Copyright: © The Author(s) 2024.

PY - 2025/3

Y1 - 2025/3

N2 - By the Almost First-degree Stochastic Dominance (AFSD) rule, corresponding only to economically relevant preferences, for an infinite horizon the theoretical claim of both Markowitz and Samuelson is not intact. However, for the practically more relevant case of the long but finite horizon, with stocks-bonds portfolios, Markowitz empirically is right as we find that the MGM portfolio coincides with the optimal myopic portfolio for all risk aversion parameters α<1.7. For α≥1.7 the MGM portfolio dominates by AFSD rule all optimal myopic portfolios, as long as the investment horizon is 12–15 years or longer.

AB - By the Almost First-degree Stochastic Dominance (AFSD) rule, corresponding only to economically relevant preferences, for an infinite horizon the theoretical claim of both Markowitz and Samuelson is not intact. However, for the practically more relevant case of the long but finite horizon, with stocks-bonds portfolios, Markowitz empirically is right as we find that the MGM portfolio coincides with the optimal myopic portfolio for all risk aversion parameters α<1.7. For α≥1.7 the MGM portfolio dominates by AFSD rule all optimal myopic portfolios, as long as the investment horizon is 12–15 years or longer.

KW - Almost first-degree stochastic dominance (AFSD)

KW - FSD-violation area

KW - Geometric mean

KW - Myopic preference

UR - http://www.scopus.com/inward/record.url?scp=105001075611&partnerID=8YFLogxK

U2 - 10.1007/s10479-024-06250-8

DO - 10.1007/s10479-024-06250-8

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:105001075611

SN - 0254-5330

VL - 346

SP - 263

EP - 284

JO - Annals of Operations Research

JF - Annals of Operations Research

IS - 1

ER -

The maximum geometric mean criterion: revisiting the Markowitz–Samuelson debate: survey and analysis

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this