dc.contributor.author Kachapova, F dc.contributor.author Kachapov, I dc.date.accessioned 2013-06-07T07:24:57Z dc.date.available 2013-06-07T07:24:57Z dc.date.copyright 2012 dc.date.issued 2013-06-07 dc.identifier.citation Journal of Mathematics and Statistics, vol.8(3), pp.323 - 329. dc.identifier.issn 1549-3644 dc.identifier.uri http://hdl.handle.net/10292/5425 dc.description.abstract Problem 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.publisher Science Publications dc.relation.uri http://www.thescipub.com/abstract/10.3844/jmssp.2012.323.329 dc.rights Compliance 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.subject Teaching portfolio analysis dc.subject Envelope dc.subject Efficient frontier dc.subject Feasible set dc.subject Mean-variance relation dc.subject Envelope portfolio dc.title Finding the envelope and efficient frontier of financial assets dc.type Journal Article dc.rights.accessrights OpenAccess dc.identifier.doi 10.3844/jmssp.2012.323.329 aut.relation.endpage 329 aut.relation.issue 3 aut.relation.startpage 323 aut.relation.volume 8 pubs.elements-id 113909
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