Markowitz's portfolio selection theory is one of the pillars of theoretical finance. This formulation has an inherent instability once the mean and variance are replaced by their sample counterparts. The problem is amplified when the number of assets is large and the sample covariance is singular or nearly singular. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in effect, very far from optimal with respect to the average risk. The paper starts with a general introduction to Markowitz’s portfolio theory and then discusses further developments and a few notable works in the area and later moves on to discuss the need for regularization and points out a few existing methods for regularization. After which a formulation of the optimal portfolio selection is presented and ends with a few numerical examples.
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Operations Research
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Rutgers University Electronic Theses and Dissertations
Rutgers University. Graduate School - New Brunswick
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