Portfolio Optimization : On Risk Measures and Estimation Techniques

Abstract

This thesis focuses on the risk measure in the Markowitz algorithm. We discuss why assuming normality is unrealistic, and why the unconditional sample covariance matrix is an inappropriate input for the algorithm. We compare the minimum variance portfolio of Markowitz to the minimum CVaR portfolio, and discuss how the use of GARCH and Copula models can improve upon the precision of the risk estimate. We compare these techniques in two real data applications. Our results suggest that GARCH, and Copula and GARCH in combination outperform the sample estimates if sample correlation is low, and that minimizing variance or CVaR gives very similar results. Keywords: GARCH, Copula, Portfolio Optimization, Modern Portfolio Theory, Risk Measures, Coherent Risk Measures, Conditional Value-at-Risk, Risk Management.