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  4. A new geometrical method for portfolio optimization

A new geometrical method for portfolio optimization

MMC.
2021;
Volume 8, Number 3
: pp. 400–409
https://doi.org/10.23939/mmc2021.03.400
Received: March 24, 2021
Accepted: June 10, 2021

Mathematical Modeling and Computing, Vol. 8, No. 3, pp. 400–409 (2021)

Authors:
  1. F. Butin
1
Université de Lyon, Université Lyon 1, CNRS, UMR5208, Institut Camille Jordan

Risk aversion plays a significant and central role in investors’ decisions in the process of developing a portfolio.  In this portfolio optimization framework, we determine the portfolio that possesses the minimal risk by using a new geometrical method.  For this purpose, we elaborate an algorithm that enables us to compute any Euclidean distance to a standard simplex.  With this new approach, we can treat the case of portfolio optimization without short-selling in its entirety, and we also recover in geometrical terms the well-known results on portfolio optimization with allowed short-selling.  Then, we apply our results to determine which convex combination of the CAC 40 stocks possesses the lowest risk.  Thus, we not only obtain a very low risk compared to the index, but we also get a rate of return that is almost three times better than the one of the index.

portfolio optimization
short-selling
Euclidean distance to a standard simplex
geometrical approach of portfolio optimization
geometrical algorithm
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