Portfolio optimization: historical value at risk vs expected shortfall

Abstract

The main objective of this thesis is to compare the weightings of different efficient portfolios by using two different approaches to measure the risk: Historical Value at Risk (HVaR) and Expected Shortfall (ES) both for confidence levels of 95 % and 90%. In addition, the results of this study will be compared with the results obtained in previous works. Based on the results obtained in the present study, we can surely confirm that: the weights of the efficient portfolios evaluated by HVaR have a more erratic behavior than those evaluated by ES; assets which expected return is higher have an upward trend in the evolution of weightings; Es is more similar to Markowitz in trend weights than HVaR; the similarity in the evolution of the weights according to Markowitz does not imply that they are also similar according to HVaR.