Monetary Measurement of Risk: A Critical Overview - Part II: Coherent Measures of Risk

Abstract

In Lecesne and Roncoroni (2013), we introduce the notion of monetary measure of risk borne by any financial claim. Our presentation moves from general definitions to concrete instances, including the benchmark measure Value-at-Risk (VaR). Part II develops a treatment of the class of coherent (monetary) measures of risk put forward by Artzner et al. (1999). Our goal is to illustrate the main features of this class of measures in light of application to practical cases. In this respect, we put our focus on the ambiguity of the term “coherent” and show that the connotation of consistency it naturally embeds is more an issue of lexical interpretation than actual meaning. As an example, we show that lack of subadditivity of VaR (which prevents from it to being a “coherent” measure of risk) is more a desirable property than a drawback, as is claimed in most of existing sources in the specialized literature.