Solution Uniqueness and Continuity of the FTSE Target Exposure Methodology
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.
