Journal of Risk

Compositional methods applied to capital allocation problems

Jaume Belles-Sampera, Montserrat Guillen and Miguel Santolino

  • Capital allocation principles can be interpreted as composition data.
  • Compositional methods coherent with the relative scale of compositions are applied.
  • Capital allocation principles can be then ranked based on their distances.
  • The simplicial arithmetic mean is computed to average capital allocation principles.


In this paper, we examine the relationship between capital allocation problems and compositional data, ie, information that refers to the parts of a whole conveying relative information. We show that capital allocation principles can be interpreted as compositions. The natural geometry and vector space structure of compositional data are used to operate with capital allocation solutions. The distance and average that are appropriated in the geometric structure of compositions are presented. We demonstrate that these two concepts can be used to compare capital allocation principles and merge them. An illustration is provided to show how the distance between capital allocation solutions and the average of these solutions can be computed, and interpreted, by risk managers in practice.

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