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Generalized distance to a simplex and a new geometrical method for portfolio optimization

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  • Fr'ed'eric Butin

Abstract

Risk aversion plays a significant and central role in investors' decisions in the process of developing a portfolio. In this framework of portfolio optimization 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 generalized Euclidean distance to a standard simplex. With this new approach, we are able to 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 in order to determine which convex combination of the CAC 40 stocks possesses the lowest risk: not only we get a very low risk compared to the index, but we also get a return rate that is almost three times better than the one of the index.

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  • Fr'ed'eric Butin, 2020. "Generalized distance to a simplex and a new geometrical method for portfolio optimization," Papers 2009.08826, arXiv.org.
    • Handle: RePEc:arx:papers:2009.08826
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    References listed on IDEAS

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    1. Jón Daníelsson & Bjørn Jorgensen & Casper Vries & Xiaoguang Yang, 2008. "Optimal portfolio allocation under the probabilistic VaR constraint and incentives for financial innovation," Annals of Finance, Springer, vol. 4(3), pages 345-367, July.
    2. William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
    3. Hanene Ben Salah & Mohamed Chaouch & Ali Gannoun & Christian Peretti & Abdelwahed Trabelsi, 2018. "Mean and median-based nonparametric estimation of returns in mean-downside risk portfolio frontier," Annals of Operations Research, Springer, vol. 262(2), pages 653-681, March.
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