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Modular Lipschitzian and Contractive Maps Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Eigendecomposition of the Mean-Variance Portfolio Optimization Model

Authors : Fred Mayambala, Elina Rönnberg, Torbjörn Larsson

Published in: Optimization, Control, and Applications in the Information Age

Publisher: Springer International Publishing

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Abstract

We provide new insights into the mean-variance portfolio optimization problem, based on performing eigendecomposition of the covariance matrix. The result of this decomposition can be given an interpretation in terms of uncorrelated eigenportfolios. When only some of the eigenvalues and eigenvectors are used, the resulting mean-variance problem is an approximation of the original one. A solution to the approximation yields lower and upper bounds on the original mean-variance problem; these bounds are tight if sufficiently many eigenvalues and eigenvectors are used in the approximation. Even tighter bounds are obtained through the use of a linearized error term of the unused eigenvalues and eigenvectors.
We provide theoretical results for the upper bounding quality of the approximate problem and the cardinality of the portfolio obtained, and also numerical illustrations of these results. Finally, we propose an ad hoc linear transformation of the mean-variance problem, which in practice significantly strengthens the bounds obtained from the approximate mean-variance problem.

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Metadata
Title
Eigendecomposition of the Mean-Variance Portfolio Optimization Model
Authors
Fred Mayambala
Elina Rönnberg
Torbjörn Larsson
Copyright Year
2015
Book
Optimization, Control, and Applications in the Information Age

Print ISBN: 978-3-319-18566-8

Electronic ISBN: 978-3-319-18567-5

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-18567-5_11

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