From variance to value at risk: A unified perspective on standardized risk measures

Risk is a concept which matters to many issues in economics and finance. The range of risk measures proposed goes from classics like variance to modern approaches like Value-at-Risk (VaR). In this paper, after a short characterization of manager's intuitive notion of risk, an overview of those risk measures is given which try to measure risk in a standardized way independent of individually varying perception. Then, it is shown that all these measures including Value-at-Risk, basically, are special cases of a certain well-known family of risk measures. From this point of view, the most critical features of each measure, particularly of VaR, become immediately evident.