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.

Torrente, M., Uberti, P. (2023). A rescaling technique to improve numerical stability of portfolio optimization problems. SOFT COMPUTING, 27(18), 12831-12842 [10.1007/s00500-021-06543-1].

A rescaling technique to improve numerical stability of portfolio optimization problems

Uberti, Pierpaolo
2023

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.
Articolo in rivista - Articolo scientifico
Asset allocation; Matrix conditioning; Numerical stability; Portfolio optimization;
English
8-gen-2022
2023
27
18
12831
12842
reserved
Torrente, M., Uberti, P. (2023). A rescaling technique to improve numerical stability of portfolio optimization problems. SOFT COMPUTING, 27(18), 12831-12842 [10.1007/s00500-021-06543-1].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/394015
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