Capital allocation in financial institutions: the Euler method

Capital allocation is used for many purposes in financial institutions and for this purpose several methods are known. The aim of this paper is to review possible methods (we present six of them) and to help financial companies to choose between the methods. There are some properties that an allocation method should satisfy: full allocation, core compatibility, riskless allocation, symmetry and suitability for performance measurement (compatibility with Return on Risk Adjusted Capital calculation). If we think about practical application we should also consider simplicity of the methods. First we examine the methods from the point of view if they are satisfying core compatibility. We test this with simulation where we add to the existing literature that we test core compatibility with different assumptions on returns: on normal and t-distributed returns and also on returns generated from a copula. We find that if we measure risk by a coherent risk measure, the Expected Shortfall there are two methods satisfying core compatibility: the Euler method (that always fulfills the criteria) and cost gap method (obeys it around in about 99%). As Euler method is very easy to calculate even for many players while cost gap method becomes very complicated as the number of the players increases we examine further the properties of Euler method. We find that it fulfills all the above given criteria but symmetry and as aforementioned it is also very easy to calculate. Therefore we believe that the method might be suggested for practical applications.