Enhancing Markowitz model: inspection of correlations and tail covariances

Information contained in the correlation matrix of the nancial products plays a crucial in order to construct portfolios as well as the tail e ects of asset returns. Structure hidden in the correlation matrix can be revealed appealing to hierarchcal clustering algorithms and spectral methods individually, or through a combination of them. Furthermore, covariance as a mesure of portfolio risk does not distinguish downside from upside risk. . The work shows the state of the art of asset allocation models which enhances Markowitz portfolios focusing on Minimum Spanning Tree and Random Matrix Theory used to extract information from correlations and on di erent measures of portfolio risk accounting for asymmetry in the risk.