Solution Uniqueness and Continuity of the FTSE Target Exposure Methodology

Abstract

The Target Exposure methodology FTSE derives a portfolio allocation of assets each being exposed to multiple factors We show that given a set of model parameters and active exposures of the assets to the factors there exists at most one allocation of the assets The means to prove this result are i mathematical induction on the number of factors and ii a statistical argument averaging the overall exposures of each asset to the considered factors The model has been set to a system of non-linear exponential functions and the goal is to prove the existence of at most one solution of this system as well as its continuity The theoretical result derived in this paper provides additional insight into the well-adopted Target Exposure methodology and furthers the understanding of this portfolio construction framework that in many cases is favored for its weighting transparency