"Portfolio analysis using mathematical methods"
Authors :
MSc.Agron Gjana( Student - agron_gjana@yahoo.com)
PhD.Glediana Zeneli( Lecturer in the Department of Applied Mathematics, Faculty of Natural Sciences, University of Tirana, Albania - gledafoto@yahoo.com)
MSc.Arsen Benga( Department of Mathematics, Faculty of Engineering and Technology, American University of Middle East, Kuwait - aresenbenga@yahoo.com)
Abstract :

Abstract The portfolio with the minimum variance is that portfolio (a proper combination of asset’s weights) which, when given the risk and the return of each asset, contains the lowest possible risk level. In other words, the portfolio with a minimum variance specifies the asset weights, by which the lowest risk can be achieved, without any other conditions above the desired return level (2). So, it’s enough to identify in this case, the lowest existing diversification, since it is directly related to the variance (risk). The portfolio with a minimum variance is determined by a mathematical optimization based on changing asset weights to reach the lowest possible diversification level. This includes the possibility that some of the weights are zero, so some assets from the portfolio can be eliminated. Portfolio with minimal variance is very important in this portfolio analysis because it has the lowest level of risk reachable from assets that the manager has available. This risk level may result lower than market risk, due to the effects of diversification. Another advantage is the non-inclusion of assets, which do not meet our diversification needs. So if investing in an asset does not reduce the overall portfolio risk, we simply decide to put it out. The minimum variance portfolio serves as an assessor of diversification opportunities.

Key Words :
Portfolio minimum variance Lagrange function