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

Research output: Journal PublicationsJournal Article (refereed)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 languageEnglish
Article number112251
JournalChaos, Solitons and Fractals
Volume161
Early online date15 Jun 2022
DOIs
Publication statusPublished - Aug 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022

Funding

The authors would like to thank Wei-han Liu for his helpful comments and Alice Richardson from Statistical Support Network (Australian National University) for her helpful advice. 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.

Keywords

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

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