The Requirement of a Positive Definite Covariance Matrix of Security Returns for Mean-Variance Portfolio Analysis: A Pedagogic Illustration
This study considers, from a pedagogic perspective, a crucial requirement for the covariance matrix of security returns in mean-variance portfolio analysis. Although the requirement that the covariance matrix be positive definite is fundamental in modern finance, it has not received any attention...
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| Format: | Article |
| Language: | English |
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McMaster University
2010-07-01
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| Series: | Spreadsheets in Education |
| Subjects: | |
| Online Access: | http://epublications.bond.edu.au/ejsie/vol4/iss1/4 |
| _version_ | 1797972943150514176 |
|---|---|
| author | Clarence C. Y. Kwan |
| author_facet | Clarence C. Y. Kwan |
| author_sort | Clarence C. Y. Kwan |
| collection | DOAJ |
| description | This study considers, from a pedagogic perspective, a crucial requirement for the covariance matrix of security returns in mean-variance portfolio analysis. Although the requirement that the covariance matrix be positive definite is fundamental in modern finance, it has not received any attention in standard investment textbooks. Being unaware of the requirement could cause confusion for students over some strange portfolio results that are based on seemingly reasonable input parameters. This study considers the requirement both informally and analytically. Electronic spreadsheet tools for constrained optimization and basic matrix operations are utilized to illustrate the various concepts involved. |
| first_indexed | 2024-04-11T03:56:22Z |
| format | Article |
| id | doaj.art-82c958b2e8fb47da849482c4a0479a3a |
| institution | Directory Open Access Journal |
| issn | 1448-6156 |
| language | English |
| last_indexed | 2024-04-11T03:56:22Z |
| publishDate | 2010-07-01 |
| publisher | McMaster University |
| record_format | Article |
| series | Spreadsheets in Education |
| spelling | doaj.art-82c958b2e8fb47da849482c4a0479a3a2023-01-02T00:35:27ZengMcMaster UniversitySpreadsheets in Education1448-61562010-07-01411078The Requirement of a Positive Definite Covariance Matrix of Security Returns for Mean-Variance Portfolio Analysis: A Pedagogic IllustrationClarence C. Y. KwanThis study considers, from a pedagogic perspective, a crucial requirement for the covariance matrix of security returns in mean-variance portfolio analysis. Although the requirement that the covariance matrix be positive definite is fundamental in modern finance, it has not received any attention in standard investment textbooks. Being unaware of the requirement could cause confusion for students over some strange portfolio results that are based on seemingly reasonable input parameters. This study considers the requirement both informally and analytically. Electronic spreadsheet tools for constrained optimization and basic matrix operations are utilized to illustrate the various concepts involved.http://epublications.bond.edu.au/ejsie/vol4/iss1/4Mean-Variance Portfolio AnalysisPositive Definite Covariance MatrixExcel Illustration |
| spellingShingle | Clarence C. Y. Kwan The Requirement of a Positive Definite Covariance Matrix of Security Returns for Mean-Variance Portfolio Analysis: A Pedagogic Illustration Spreadsheets in Education Mean-Variance Portfolio Analysis Positive Definite Covariance Matrix Excel Illustration |
| title | The Requirement of a Positive Definite Covariance Matrix of Security Returns for Mean-Variance Portfolio Analysis: A Pedagogic Illustration |
| title_full | The Requirement of a Positive Definite Covariance Matrix of Security Returns for Mean-Variance Portfolio Analysis: A Pedagogic Illustration |
| title_fullStr | The Requirement of a Positive Definite Covariance Matrix of Security Returns for Mean-Variance Portfolio Analysis: A Pedagogic Illustration |
| title_full_unstemmed | The Requirement of a Positive Definite Covariance Matrix of Security Returns for Mean-Variance Portfolio Analysis: A Pedagogic Illustration |
| title_short | The Requirement of a Positive Definite Covariance Matrix of Security Returns for Mean-Variance Portfolio Analysis: A Pedagogic Illustration |
| title_sort | requirement of a positive definite covariance matrix of security returns for mean variance portfolio analysis a pedagogic illustration |
| topic | Mean-Variance Portfolio Analysis Positive Definite Covariance Matrix Excel Illustration |
| url | http://epublications.bond.edu.au/ejsie/vol4/iss1/4 |
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