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.
Kwan, Clarence C. Y.
"The Requirement of a Positive Definite Covariance Matrix of Security Returns for Mean-Variance Portfolio Analysis: A Pedagogic Illustration,"
Spreadsheets in Education (eJSiE):
1, Article 4.
Available at: http://epublications.bond.edu.au/ejsie/vol4/iss1/4