Mean Variance Optimization of Portfolios

The Mean-Variance Portfolio Theory continues to be the cardinal tool for much of portfolio management. Traditional concerted literature on the Mean-Variance theory can be segmented almost exclusively into (i) chapters in books that provide simply a write up on the theory and (ii) books that contain a purely mathematical analysis without emphasizing the financial implications and interpretations. The fallout of this mutually exclusive segmentation is that both segments cover MeanVariance portfolio theory only marginally i.e. in the asymptote rather than as a mainstream course. The coverage is, nowhere near adequate for a student to get acquainted with the intricacies of the theory and hence, appreciate its nuances. This article fights that trend by covering in detail the topics that are thrown by the wayside in the traditional coverage. We look at a comprehensive mathematical analysis of the two security problem in risk return space, obtain several interesting mathematical results and follow up each of them with their interpretation and explanations in financial markets. We, then, extend the framework to three security dynamics and again elucidate some intriguing mathematical inferences.