Performance Measurement When Return Distributions Are Nonsymmetric

By Stephens, Alan; Proffitt, Dennis | Quarterly Journal of Business and Economics, Autumn 1991 | Go to article overview

Performance Measurement When Return Distributions Are Nonsymmetric


Stephens, Alan, Proffitt, Dennis, Quarterly Journal of Business and Economics


Performance Measurement When Return Distributions are Nonsymmetric

Alan & Stephens Utah State University

Dennis Proffitt(*) Grand Canyon University

Abstract

This paper arugues that to ignore higher moments of utility one must do

so on the basis of economic arguments (normal returns or quadratic

utility) or empirical evidence demonstrating that higher moments are

not important to investors. Extending the work of Prakash and Bear

(1986), a generalized performance evaluation model is presented that

allows for multiple moments of utility. The evaluation models are

applied to the returns of internationally diversified mutual funds. The

results indicate that ignoring higher moments of utility has significant

impact upon the performance rankings of these funds.

Introduction

Modern portfolio construction often involves attempts by portfolio managers to modify the return distributions of their portfolios. For example, Bookstaber and Clarke (1983) have shown that the returns on portfolios of common stocks can be modified substantially using a variety of option strategies. In addition, international funds with highly skewed return distributions offer their investors risk reduction possibilities through their low covariance of returns with domestic securities (Proffitt and Seitz, 1983).

If return distributions are nonsymmetrical and investors value skewness, as argued by Arditti (1967), then traditional performance measures are inadequate. To address the problem of defining performance in the face of nonsymmetric distributions, Prakash and Bear (1986) (hereafter PB) developed measures that recognized skewness of return distributions. The PB formulas were developed on the basis of the Kraus and Litzenberger (1976) (hereafter KL) skewness preference model.

This paper demonstrates that the KL three moment model is a special case of Rubinstein's (1973) parameter preference model. In the KL model, higher moments were ignored, as they were not behaviorally justified. Without entering this controversy of whether more than three moments are behaviorally justified, a performance measure based on n-moments is developed. This general performance measure has, as special cases, the Treynor and PB performance measures.

One of the desirable attributes of the general performance model is that it readily is adaptable to a form that is useful in empirical tests. (1) The application of the performance measures is illustrated with an analysis of internationally diversified mutual funds. Research concerning internationally diversified mutual funds continually encounters problems with the performance measurement of these funds relative to domestic funds using traditional techniques. Because internationally diversified funds have skewed and flattened return distributions, performance problems of international funds may be addressed using the general model of performance measurement. Performance ranking based on three or higher moments are essentially the same for internationally diversified funds, while those based on two moments differ significantly with the ranking achieved using PB measures. Thus, this paper not only empirically applies the PB measures to a set of internationally diversified funds, but also (albeit indirectly) tests the validity of the higher moments CAPM.

Development of the Model

By stating utility as a Taylor series expansion of an individual's expected wealth, Rubinstein (1973) developed the fundamental theorem of parameter preference security valuation. This model, which is a state-independent, state-preference model in which probability data are summarized by central moments, states: [Mathematical Expression Omitted]

where: [Mathematical Expression Omitted]

[U.sub.i] = an individual's continuously differentiable utility of wealth

function;

[E. …

The rest of this article is only available to active members of Questia

Sign up now for a free, 1-day trial and receive full access to:

  • Questia's entire collection
  • Automatic bibliography creation
  • More helpful research tools like notes, citations, and highlights
  • Ad-free environment

Already a member? Log in now.

Notes for this article

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Items saved from this article

This article has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this article

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
Notes
Cite this article

Cited article

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited article

Performance Measurement When Return Distributions Are Nonsymmetric
Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this article

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Full screen

matching results for page

Cited passage

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited passage

Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.

For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

Already a member? Log in now.