Why does the portfolio optimization mean-variance model require the covariance matrix to be positive-definite? Does this requirement have to do with the need to be able to invert the matrix during optimization?
How is positive-definiteness achieved? Does it happen because all matrix elements (variance and covariance) are non-negative? In which cases do asset returns fail to make the covariance matrix positive definite? are there any known work-arounds when this happens