"Beyond Markowitz: Building the Optimal Portfolio Using Non-Elliptical Asset Return Distributions"

Modern Portfolio Theory (MPT) assumes a multivariate Normal distribution for the financial asset returns. However, statistical data show fat-tailed and asymmetric financial asset return distributions. Consequently, for monitoring and managing professionaly the relevant market risk of large financial portfolios, banks have to handle with a new coherent risk measure: Conditional Value-at-Risk (CVaR).This relevant and tractable measure has been defined as the conditional mean of portfolios losses exceeding Value-at-Risk (VaR). When the uncertainty is modelled by generation of a finite number of Monte Carlo or historical scenarios for the portfolio asste log-returns, the complex problem of stochastic optimisation may be solved using a linear programming technique. Following the example of Rockafellar and Urayasev (2000), we build the efficient portfolio frontier minimizing the CVaR. However, differently from the cited authors, in this work we aim to verify whether the portfolio efficient compositions for CVaR may change assuming different methodologies of asset log-return scenario generation or, in other words, assuming diverse distributional assumptions regarding to the relevant market risk factors.