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dc.contributor.authorKachapova, F
dc.contributor.authorKachapov, I
dc.date.accessioned2013-06-07T07:24:57Z
dc.date.available2013-06-07T07:24:57Z
dc.date.copyright2012
dc.date.issued2013-06-07
dc.identifier.citationJournal of Mathematics and Statistics, vol.8(3), pp.323 - 329.
dc.identifier.issn1549-3644
dc.identifier.urihttp://hdl.handle.net/10292/5425
dc.description.abstractProblem statement: One of the problems considered in financial mathematics is finding portfolios of given financial assets that minimize risk for targeted returns. The set of such portfolios is called the envelope of the assets.Traditionally this problem is solved as a calculus minimization problem involving partial derivatives and Lagrange multipliers. Approach: In this study we describe an invariant geometric solution that uses orthogonal projection in Euclidean space of random variables. Results: The method is applied to find the efficient portfolio and feasible region of the assets and to investigate the mean-variance relation for envelope portfolios. In particular, it is shown that the graph of this relation is the right branch of a hyperbola. The method is illustrated by an example with four financial assets. Conclusion/ Recommendation: The described geometric approach can help to improve the teaching of portfolio analysis by making the concept of envelope clearer and by simplifying proofs.
dc.publisherScience Publications
dc.relation.urihttp://www.thescipub.com/abstract/10.3844/jmssp.2012.323.329
dc.rightsCompliance with the open-access policy, all content published by Science Publications offers unrestricted access, distribution, and reproduction in any medium; provided the original work is correctly cited.
dc.subjectTeaching portfolio analysis
dc.subjectEnvelope
dc.subjectEfficient frontier
dc.subjectFeasible set
dc.subjectMean-variance relation
dc.subjectEnvelope portfolio
dc.titleFinding the envelope and efficient frontier of financial assets
dc.typeJournal Article
dc.rights.accessrightsOpenAccess
dc.identifier.doi10.3844/jmssp.2012.323.329
aut.relation.endpage329
aut.relation.issue3
aut.relation.startpage323
aut.relation.volume8
pubs.elements-id113909


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