Abstract: This paper is part one of an homage to the seminal paper of Artzner, Delbaen, Eber, and Heath (1997) [1], who proposed a set of axioms that must be satisfied by risk measures in order to be “coherent”.

This paper does not aim to add to the knowledge of coherent risk measures, but it aims to prove that coherence matters not only for the mathematician, but also for the investment manager and his clients by constructing simple and transparent examples that show the dangers of working with incoherent risk measures. This way the author hopes to improve communication between the academic communities on one side and on the others side policy-makers and operational decision makers at financial institutions, their regulators and law-makers, who fifteen year after that paper still underestimate the importance of “thinking coherently”.

Keywords: Portfolio Selection, Personal Financial Decision Making, Coherent Risk Measures, Strategic Asset Allocation, Suitability of Investments, Value at Risk, Expected Shortfall, Global Exposure, Risk Classification, risk and reward indicator, variance, UCITS IV, FINRA 2011.