Solution Uniqueness and Continuity of the FTSE Target Exposure Methodology

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Julien Riposo
Julien Riposo
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Yang Wang
Yang Wang

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GJSFR Volume 23 Issue F6

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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.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

Julien Riposo. 2026. \u201cSolution Uniqueness and Continuity of the FTSE Target Exposure Methodology\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 23 (GJSFR Volume 23 Issue F6): .

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Enhances research on the importance of solution uniqueness and continuity in TFSE target exposure methodology.
Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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GJSFR-F Classification: FOR CODE: 0101
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v1.2

Issue date

October 13, 2023

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English

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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.

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Solution Uniqueness and Continuity of the FTSE Target Exposure Methodology

Julien Riposo
Julien Riposo
Yang Wang
Yang Wang

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