Computing optimal mean/downside risk frontiers: The role of ellipiticity

Hall, AD; Satchell, SE

Computing optimal mean/downside risk frontiers: The role of ellipiticity

Hall, AD

Satchell, SE

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Publisher:: Elsevier
Publication Type:: Chapter
Citation:: Optimizing Optimization: The Next Generation of Optimization Applications and Theory, 2010, 1st, pp. 179 - 199
Issue Date:: 2010-01

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Field	Value	Language
dc.contributor.author	Hall, AD https://orcid.org/0000-0002-9724-951X	en_US
dc.contributor.author	Satchell, SE	en_US
dc.contributor.editor	Satchell, S	en_US
dc.date.issued	2010-01	en_US
dc.identifier.citation	Optimizing Optimization: The Next Generation of Optimization Applications and Theory, 2010, 1st, pp. 179 - 199	en_US
dc.identifier.isbn	978-0-12-374952-9	en_US
dc.identifier.uri	http://hdl.handle.net/10453/14348
dc.description.abstract	The purpose of this chapter is to analyze and calculate optimal mean/downside risk frontiers for financial portfolios. Focusing on the twO important cases of mean/value at risk and mean/semivariance, we compute analytic expressions for the optimal frontier in the two asset case, where the returns follow an arbitrary (nonnormal) distribution. Our analysis highlights the role of the normality/ellipticity assumption in this area of research. Formulae for mean/variance, mean/expected loss, and meanlsemistandard deviation frontiers are presented under normality/ellipticity. Computational issues are discussed and two propositions that facilitate computation are provided. Finally, the methodology is extended to nonelliptical distributions where simulation procedures are introduced. These can be presented jointly with our analytical approach to give portfolio managers deeper insights into the properties of optimal portfolios.	en_US
dc.publisher	Elsevier	en_US
dc.relation.ispartof	Optimizing Optimization: The Next Generation of Optimization Applications and Theory	en_US
dc.title	Computing optimal mean/downside risk frontiers: The role of ellipiticity	en_US
dc.type	Chapter
utslib.location	USA	en_US
utslib.for	150202 Financial Econometrics	en_US
utslib.citation.edition	1st	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Business
utslib.copyright.status	closed_access
pubs.consider-herdc	true	en_US
pubs.edition	1st	en_US
pubs.place-of-publication	USA	en_US

Abstract:

The purpose of this chapter is to analyze and calculate optimal mean/downside risk frontiers for financial portfolios. Focusing on the twO important cases of mean/value at risk and mean/semivariance, we compute analytic expressions for the optimal frontier in the two asset case, where the returns follow an arbitrary (nonnormal) distribution. Our analysis highlights the role of the normality/ellipticity assumption in this area of research. Formulae for mean/variance, mean/expected loss, and meanlsemistandard deviation frontiers are presented under normality/ellipticity. Computational issues are discussed and two propositions that facilitate computation are provided. Finally, the methodology is extended to nonelliptical distributions where simulation procedures are introduced. These can be presented jointly with our analytical approach to give portfolio managers deeper insights into the properties of optimal portfolios.

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http://hdl.handle.net/10453/14348