Comparing Mean-Variance and CVaR optimal portfolios, assuming bivariate skew-t distributed returns

Sammanfattning: In this paper we are building portfolios consisting of theS&P 500 index and a T-bond index. The portfolio weights arechosen in such a way that the risk for the portfolio is minimized.To be able to minimize the risk for a portfolio, we first have tospecify how to measure the portfolios risk. There are several waysof measuring the risk for a portfolio. In this paper we areinvestigating how the portfolio weights differ whether we measurethe portfolios risk by the variance or by the ConditionalValue-at-Risk (CVaR). To measure the risk for the portfolios wefirst estimated a two-dimensional density function for the returnsof the assets, using a skew student-t distribution. The time horizonfor each portfolio was one week. The result shows that the weightsin the S&P 500 index always were lower for the portfoliosconstructed by minimizing CVaR. The reason for this is that thedistribution for the returns of the S&P 500 index exhibits anegative skewness and has fatter tails than the returns of theT-bond index. This fact isn't taken care of when choosing weightsaccording to the variance criteria, which leads to anunderestimation of the risk associated with the S&P 500 index.The underestimation of the risk leads to an overestimation of theoptimal weights in the S&P 500 index.