VaR Risk Measures versus Traditional Risk Measures: An Analysis and Survey

Abstract

The article presents an analysis and partial survey regarding the validity of VaR risk measures in comparison to traditional risk measures. The assumed individuals are either maximizing their expected utility or possess a lexicographic utility function. The analysis is carried out for generally distributed functions and for the normal and the log-normal distributions. The main conclusion is that although VaR is an inadequate measure under the expected utility framework, it is at least as good as other traditional risk measures. Moreover, it can be improved by modified versions such as the Accumulated VaR (Mean-Shortfall).Assuming a lexicographic expected utility adds justification to the use of AVaR as a legitimate risk measure that can be further applied in the newly proposed multi-VaR risk analysis.