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A rescaling technique to improve numerical stability of portfolio optimization problems.

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Title: A rescaling technique to improve numerical stability of portfolio optimization problems.
Authors: Torrente, Maria-Laura1 (AUTHOR) marialaura.torrente@economia.unige.it, Uberti, Pierpaolo1 (AUTHOR)
Source: Soft Computing - A Fusion of Foundations, Methodologies & Applications. Sep2023, Vol. 27 Issue 18, p12831-12842. 12p.
Subjects: Portfolio management (Investments), Covariance matrices, Mathematical optimization, Asset allocation, Structural components
Abstract: This paper analyzes the numerical stability of Markowitz portfolio optimization model, by identifying and studying a source of instability, that strictly depends on the mathematical structure of the optimization problem and its constraints. As a consequence, it is shown how standard portfolio optimization models can result in an unstable model also when the covariance matrix is well conditioned and the objective function is numerically stable. This depends on the fact that the linear equality constraints of the model very often suffer of almost collinearity and/or bad scaling. A theoretical approach is proposed that exploiting an equivalent formulation of the original optimization problem considerably reduces such structural component of instability. The effectiveness of the proposal is empirically certified through applications on real financial data when numerical optimization approaches are needed to compute the optimal portfolio. Gurobi and MATLAB's solvers quadprog and fmincon are compared in terms of convergence performances. [ABSTRACT FROM AUTHOR]
Copyright of Soft Computing - A Fusion of Foundations, Methodologies & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: A rescaling technique to improve numerical stability of portfolio optimization problems.
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  Data: <searchLink fieldCode="AR" term="%22Torrente%2C+Maria-Laura%22">Torrente, Maria-Laura</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> marialaura.torrente@economia.unige.it</i><br /><searchLink fieldCode="AR" term="%22Uberti%2C+Pierpaolo%22">Uberti, Pierpaolo</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="DE" term="%22Portfolio+management+%28Investments%29%22">Portfolio management (Investments)</searchLink><br /><searchLink fieldCode="DE" term="%22Covariance+matrices%22">Covariance matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Asset+allocation%22">Asset allocation</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+components%22">Structural components</searchLink>
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  Label: Abstract
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  Data: This paper analyzes the numerical stability of Markowitz portfolio optimization model, by identifying and studying a source of instability, that strictly depends on the mathematical structure of the optimization problem and its constraints. As a consequence, it is shown how standard portfolio optimization models can result in an unstable model also when the covariance matrix is well conditioned and the objective function is numerically stable. This depends on the fact that the linear equality constraints of the model very often suffer of almost collinearity and/or bad scaling. A theoretical approach is proposed that exploiting an equivalent formulation of the original optimization problem considerably reduces such structural component of instability. The effectiveness of the proposal is empirically certified through applications on real financial data when numerical optimization approaches are needed to compute the optimal portfolio. Gurobi and MATLAB's solvers quadprog and fmincon are compared in terms of convergence performances. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Soft Computing - A Fusion of Foundations, Methodologies & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00500-021-06543-1
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      – Code: eng
        Text: English
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        PageCount: 12
        StartPage: 12831
    Subjects:
      – SubjectFull: Portfolio management (Investments)
        Type: general
      – SubjectFull: Covariance matrices
        Type: general
      – SubjectFull: Mathematical optimization
        Type: general
      – SubjectFull: Asset allocation
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      – SubjectFull: Structural components
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      – TitleFull: A rescaling technique to improve numerical stability of portfolio optimization problems.
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              Text: Sep2023
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              Y: 2023
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