The Properties of Downside Risk Measures

A close formal relationship between poverty measurement and the measurement of downside risk was established by Breitmeyer et al. (1999). Moreover, they show that well-known requirements for poverty measures can motivate reasonable properties of downside risk measures, too. We build on their work by transforming a number of poverty measures into (new) downside risk measures. Also, we test these measures (as well as some previously suggested ones) with respect to their axioms. This sometimes is a tedious task, but is simplified considerably for decomposable measures for which we prove some fairly general features. A table summarizes the tests and can serve as a useful tool for anybody who is concerned with downside risk, e.g. risk managers, investors or regulators