ABSTRACT
In Chapter 6 it was shown that given an (absolute) capital allocation principle https://www.w3.org/1998/Math/MathML" display="inline"> K → with https://www.w3.org/1998/Math/MathML" display="inline"> K = ∑ j = 1 n K j , its relative counterpart is defined as https://www.w3.org/1998/Math/MathML" display="inline"> x → , where com-ponents are x= K i /K. This chapter is devoted to show that relative capital allocation principles can be understood as belonging to the (standard) simplex. Following a nomenclature often used by geologists, any vector of the simplex is called a composition and any set of vectors in the simplex is called compositional data. This chapter first presents the metric space structure of the simplex. Secondly, it is shown that it is possible to move forward and backwards from relative capital allocation principles to compositions and the opposite. Applications of this relationship are illustrated with the data set used all along this book. This chapter is based on the study that we carried out in Belles-Sampera et al. [2016a].
