Central moments, stochastic dominance, moment rule, and diversification with an application

Raymond H. Chan; Sheung-Chi Chow; Xu Guo; Wing-Keung Wong

doi:10.1016/j.chaos.2022.112251

Central moments, stochastic dominance, moment rule, and diversification with an application

Raymond H. Chan, Sheung-Chi Chow, Xu Guo, Wing-Keung Wong^*

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

4 Citations (Scopus)

Abstract

In this paper, we first develop some properties to state the relationships among central moments, stochastic dominance (SD), risk-seeking stochastic dominance (RSD), and integrals for the general utility functions and the polynomial utility functions of both risk averters and risk seekers. We then introduce the moment rule and establish some necessary and/or sufficient conditions between stochastic dominance and the moment rule for the general utility functions and the polynomial utility functions of both risk averters and risk seekers without imposing the same-location-scale-family condition. Thereafter, we apply the moment rules to develop some properties of portfolio diversification for the general utility functions and the polynomial utility functions for both risk averters and risk seekers. The findings in our paper enable academics and practitioners to draw preferences of both risk averters and risk seekers on their choices of portfolios or assets by using different moments. We illustrate this by using the moment rule tests to compare excess return of 49 industry portfolios from Kenneth French's online data library.

Original language	English
Article number	112251
Journal	Chaos, Solitons and Fractals
Volume	161
Online published	15 Jun 2022
DOIs	https://doi.org/10.1016/j.chaos.2022.112251
Publication status	Published - Aug 2022

Funding

The second author would like to thank Simon GRANT, Timothy KAM, and Shu-Kam LEE for their continuous guidance and encouragement. The fourth author would like to thank Robert B. Miller and Howard E. Thompson for their continuous guidance and encouragement. This research has been partially supported by grants from the City University of Hong Kong, Australian National University, the Hang Seng University of Hong Kong, Asia University, China Medical University Hospital, the Research Grants Council of Hong Kong (project numbers UGC/IDS14/15 and 12500915), and Ministry of Science and Technology (MOST), R.O.C.

Research Keywords

Central moments
Expected-utility maximization
Investment behaviors
Moment rule
Risk aversion
Risk seeking
Stochastic dominance

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10.1016/j.chaos.2022.112251

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title = "Central moments, stochastic dominance, moment rule, and diversification with an application",

abstract = "In this paper, we first develop some properties to state the relationships among central moments, stochastic dominance (SD), risk-seeking stochastic dominance (RSD), and integrals for the general utility functions and the polynomial utility functions of both risk averters and risk seekers. We then introduce the moment rule and establish some necessary and/or sufficient conditions between stochastic dominance and the moment rule for the general utility functions and the polynomial utility functions of both risk averters and risk seekers without imposing the same-location-scale-family condition. Thereafter, we apply the moment rules to develop some properties of portfolio diversification for the general utility functions and the polynomial utility functions for both risk averters and risk seekers. The findings in our paper enable academics and practitioners to draw preferences of both risk averters and risk seekers on their choices of portfolios or assets by using different moments. We illustrate this by using the moment rule tests to compare excess return of 49 industry portfolios from Kenneth French's online data library.",

keywords = "Central moments, Expected-utility maximization, Investment behaviors, Moment rule, Risk aversion, Risk seeking, Stochastic dominance",

author = "Chan, {Raymond H.} and Sheung-Chi Chow and Xu Guo and Wing-Keung Wong",

year = "2022",

month = aug,

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TY - JOUR

T1 - Central moments, stochastic dominance, moment rule, and diversification with an application

AU - Chan, Raymond H.

AU - Chow, Sheung-Chi

AU - Guo, Xu

AU - Wong, Wing-Keung

PY - 2022/8

Y1 - 2022/8

N2 - In this paper, we first develop some properties to state the relationships among central moments, stochastic dominance (SD), risk-seeking stochastic dominance (RSD), and integrals for the general utility functions and the polynomial utility functions of both risk averters and risk seekers. We then introduce the moment rule and establish some necessary and/or sufficient conditions between stochastic dominance and the moment rule for the general utility functions and the polynomial utility functions of both risk averters and risk seekers without imposing the same-location-scale-family condition. Thereafter, we apply the moment rules to develop some properties of portfolio diversification for the general utility functions and the polynomial utility functions for both risk averters and risk seekers. The findings in our paper enable academics and practitioners to draw preferences of both risk averters and risk seekers on their choices of portfolios or assets by using different moments. We illustrate this by using the moment rule tests to compare excess return of 49 industry portfolios from Kenneth French's online data library.

AB - In this paper, we first develop some properties to state the relationships among central moments, stochastic dominance (SD), risk-seeking stochastic dominance (RSD), and integrals for the general utility functions and the polynomial utility functions of both risk averters and risk seekers. We then introduce the moment rule and establish some necessary and/or sufficient conditions between stochastic dominance and the moment rule for the general utility functions and the polynomial utility functions of both risk averters and risk seekers without imposing the same-location-scale-family condition. Thereafter, we apply the moment rules to develop some properties of portfolio diversification for the general utility functions and the polynomial utility functions for both risk averters and risk seekers. The findings in our paper enable academics and practitioners to draw preferences of both risk averters and risk seekers on their choices of portfolios or assets by using different moments. We illustrate this by using the moment rule tests to compare excess return of 49 industry portfolios from Kenneth French's online data library.

KW - Central moments

KW - Expected-utility maximization

KW - Investment behaviors

KW - Moment rule

KW - Risk aversion

KW - Risk seeking

KW - Stochastic dominance

UR - http://www.scopus.com/inward/record.url?scp=85132223537&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85132223537&origin=recordpage

U2 - 10.1016/j.chaos.2022.112251

DO - 10.1016/j.chaos.2022.112251

M3 - RGC 21 - Publication in refereed journal

SN - 0960-0779

VL - 161

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

M1 - 112251

ER -

Central moments, stochastic dominance, moment rule, and diversification with an application

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GRF: New theory on portfolio optimization and stochastic dominance with applications

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Central moments, stochastic dominance, moment rule, and diversification with an application

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GRF: New theory on portfolio optimization and stochastic dominance with applications

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