Optimización robusta de portafolio empleando métodos Bayesianos
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Optimización robusta de portafolio empleando métodos Bayesianos
.

Sumario:

En este artículo se implementa un modelo de optimización robusta bayesiana para la selección óptima de un portafolio de inversión. Para ello, se extiende el modelo desarrollado por Meucci, que consiste en la incorporación del enfoque bayesiano al modelo de portafolio robusto para definir el conjunto de incerti­dumbre de tipo elipsoidal, bajo una distribución Wishart inversa. De esta for­ma, se incorpora la incertidumbre de los parámetros estimados para crear la contraparte robusta en el modelo de portafolio. El modelo propuesto utiliza una función de distribución Gamma, como generalización de la función Wishart. Los resultados confirman las conclusiones de Meucci y corroboran las propiedades atribuidas a este tipo de portafolios.... Ver más

Guardado en:

Revista ODEON

1794-1113

2346-2140

Carmona Espejo, Diego Felipe

Gamboa Hidalgo, Jhonatan

UNIVERSIDAD EXTERNADO DE COLOMBIA

10.18601/17941113.n21.05

2022-12-14

81

104

Colombia

portafolio óptimo;

métodos bayesianos;

optimización robusta

Diego Felipe Carmona Espejo, Jhonatan Gamboa Hidalgo - 2022

Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-CompartirIgual 4.0.

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spelling Optimización robusta de portafolio empleando métodos Bayesianos
Robust portfolio optimization using Bayesian methods
En este artículo se implementa un modelo de optimización robusta bayesiana para la selección óptima de un portafolio de inversión. Para ello, se extiende el modelo desarrollado por Meucci, que consiste en la incorporación del enfoque bayesiano al modelo de portafolio robusto para definir el conjunto de incerti­dumbre de tipo elipsoidal, bajo una distribución Wishart inversa. De esta for­ma, se incorpora la incertidumbre de los parámetros estimados para crear la contraparte robusta en el modelo de portafolio. El modelo propuesto utiliza una función de distribución Gamma, como generalización de la función Wishart. Los resultados confirman las conclusiones de Meucci y corroboran las propiedades atribuidas a este tipo de portafolios.
In this paper we implemented a Bayesian robust optimization model to select an optimal investment portfolio. To do that, we extended the model developed by Meucci, which consists of incorporating the Bayesian approach into the robust portfolio model in order to define an ellipsoidal-type uncertainty set under an Inverse Wishart Distribution. Thus, the uncertainty of the estimated parameters for create the robust counterpart in the portfolio model. The proposed model uses a Gamma distribution function, as a generalization of the Wishart func­tion. Results confirm Meucci’s conclusions and, it corroborates the properties attributed to those portfolios.
Carmona Espejo, Diego Felipe
Gamboa Hidalgo, Jhonatan
Optimal portfolio;
Bayesian methods;
robust optimization
portafolio óptimo;
métodos bayesianos;
optimización robusta
21
Núm. 21 , Año 2021 : Julio-Diciembre
Artículo de revista
Journal article
2022-12-14T10:23:26Z
2022-12-14T10:23:26Z
2022-12-14
application/pdf
text/html
Universidad Externado de Colombia
ODEON
1794-1113
2346-2140
https://revistas.uexternado.edu.co/index.php/odeon/article/view/8490
10.18601/17941113.n21.05
https://doi.org/10.18601/17941113.n21.05
spa
http://creativecommons.org/licenses/by-nc-sa/4.0
Diego Felipe Carmona Espejo, Jhonatan Gamboa Hidalgo - 2022
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-CompartirIgual 4.0.
81
104
Avramov, D. y Zhou, G. (2010). Bayesian portfolio analysis. Annual Review of Financial Economics, 2(1), 25-47. https://faculty.runi.ac.il/davramov/paper10.pdf
Bade, A., Frahm, G. y Jaekel, U. (2009). A general approach to Bayesian portfolio optimization. Mathematical Methods of Operations Research, 70(2), 337-356. https://doi.org/10.1007/s00186-008-0271-4
Best, M. y Grauer, R. (1991). Sensitivity analysis for mean-variance portfolio problems. Management Science, 37(8), 980-989. https://doi.org/10.1287/mnsc.37.8.980
Black, F. y Litterman, R. (1992). Global portfolio optimization. Financial Analysts Journal, 48(5), 28-43. https://doi.org/10.2469/faj.v48.n5.28
Fabozzi, F., Focardi, S., Kolm, P. y Pachamanova, D. (2007). Robust portfolio optimi¬zation and management. John Wiley & Sons.
Fama, E. y French, K. (1993). Common risk factors in the returns on stocks and bonds. Journal of financial economics, 33(1), 3-56. https://doi.org/10.1016/0304- 405X(93)90023-5
Garlappi, L., Uppal, R. y Wang, T. (2007). Portfolio selection with parameter and mo¬del uncertainty: A multi-prior approach. The Review of Financial Studies, 20(1), 41-81. https://doi.org/10.1093/rfs/hhl003
Georgantas, A. (2020). Robust Optimization Approaches for Portfolio Selection: A Computational and Comparative Analysis. Working paper. https://arxiv.org/ abs/2010.13397
Goldfarb, D. e Iyengar, G. (2003). Robust portfolio selection problems. Mathematics of Operations Research, 28(1), 1-38. https://doi.org/10.1287/moor.28.1.1.14260
Halldórsson, B. y Tütüncü, R. H. (2003). An interior-point method for a class of saddle-point problems. Journal of Optimization Theory and Applications, 116(3), 559-590. https://doi.org/10.1023/A:1023065319772
Hoffman, M., Brochu, E. y De Freitas, N. (2011). Portfolio allocation for ayesian optimi-zation. En Proceedings of the Twenty-Seventh Conference on Uncertainty in Ar¬tificial Intelligence, 327-336. https://dl.acm.org/doi/abs/10.5555/3020548.3020587
Kim, W. C., Kim, J. H., Ahn, S. H. y Fabozzi, F. J. (2013). What do robust equity port¬folio models really do? Annals of Operations Research, 205(1), 141-168. https:// doi.org/10.1007/s10479-012-1247-6
Kim, W. C., Kim, J. H. y Fabozzi, F. J. (2015). Robust Equity Portfolio Management: Formulations, Implementations, and Properties Using MATLAB. John Wiley & Sons.
Kim, J. H., Kim, W. C., Kwon, D. G. y Fabozzi, F. J. (2018). Robust equity portfo¬lio performance. Annals of Operations Research, 266(1), 293-312. https://doi. org/10.1007/s10479-017-2739-1
Lobo, M. S., Vandenberghe, L., Boyd, S. y Lebret, H. (1998). Applications of second-order cone programming. Linear Algebra and its Applications, 284(1-3), 193-228. https://doi.org/10.1016/S0024-3795(98)10032-0
Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91.
Markowitz, H. (1959). Portfolio selection: Efficient diversification of investments. New Heaven: Yale university Press.
Meucci, A. (2005). Risk and asset allocation (vol. 1). Springer.
Meucci, A. (2011). Robust Bayesian Allocation. ssrn Working paper 681553. https:// papers.ssrn.com/sol3/papers.cfm?abstract_id=681553
Michaud, R. (1998). Efficient asset management: A practical guide to stock portfolio optimization and asset allocation. Oxford University Press.
Michaud, R. y Michaud, R. (2008). Estimation error and portfolio optimization: A resampling solution. Journal of Investment Management, 6(1), 8-28.
Nesterov, Y. y Nemirovsky, A. (1993). Interior Point Polynomial Methods in Convex Programming: Theory and Algorithms. SIAM.
Pachamanova, D. y Fabozzi, F. (2012). Equity portfolio selection models in practice. En-cyclopedia of Financial Models, 1(1), 61-87. https://doi.org/10.1002/9781118182635. efm0046
Tütüncü, R. y Koenig, M. (2004). Robust asset allocation. Annals of Operations Research, 132(1), 157-187. https://doi.org/10.1023/b:anor.0000045281.41041.ed
Williams, J. (1938). The Theory of Investment Value. Harvard University Press.
Zapata, C. (2021). Optimización robusta de portafolios: conjuntos de incertidumbre y contrapartes robustas. odeon, 20, 93-121. https://doi.org/10.18601/17941113.n20.04
https://revistas.uexternado.edu.co/index.php/odeon/article/download/8490/13487
https://revistas.uexternado.edu.co/index.php/odeon/article/download/8490/13488
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Text
Publication
institution UNIVERSIDAD EXTERNADO DE COLOMBIA
thumbnail https://nuevo.metarevistas.org/UNIVERSIDADEXTERNADODECOLOMBIA/logo.png
country_str Colombia
collection Revista ODEON
title Optimización robusta de portafolio empleando métodos Bayesianos
spellingShingle Optimización robusta de portafolio empleando métodos Bayesianos
Carmona Espejo, Diego Felipe
Gamboa Hidalgo, Jhonatan
Optimal portfolio;
Bayesian methods;
robust optimization
portafolio óptimo;
métodos bayesianos;
optimización robusta
title_short Optimización robusta de portafolio empleando métodos Bayesianos
title_full Optimización robusta de portafolio empleando métodos Bayesianos
title_fullStr Optimización robusta de portafolio empleando métodos Bayesianos
title_full_unstemmed Optimización robusta de portafolio empleando métodos Bayesianos
title_sort optimización robusta de portafolio empleando métodos bayesianos
title_eng Robust portfolio optimization using Bayesian methods
description En este artículo se implementa un modelo de optimización robusta bayesiana para la selección óptima de un portafolio de inversión. Para ello, se extiende el modelo desarrollado por Meucci, que consiste en la incorporación del enfoque bayesiano al modelo de portafolio robusto para definir el conjunto de incerti­dumbre de tipo elipsoidal, bajo una distribución Wishart inversa. De esta for­ma, se incorpora la incertidumbre de los parámetros estimados para crear la contraparte robusta en el modelo de portafolio. El modelo propuesto utiliza una función de distribución Gamma, como generalización de la función Wishart. Los resultados confirman las conclusiones de Meucci y corroboran las propiedades atribuidas a este tipo de portafolios.
description_eng In this paper we implemented a Bayesian robust optimization model to select an optimal investment portfolio. To do that, we extended the model developed by Meucci, which consists of incorporating the Bayesian approach into the robust portfolio model in order to define an ellipsoidal-type uncertainty set under an Inverse Wishart Distribution. Thus, the uncertainty of the estimated parameters for create the robust counterpart in the portfolio model. The proposed model uses a Gamma distribution function, as a generalization of the Wishart func­tion. Results confirm Meucci’s conclusions and, it corroborates the properties attributed to those portfolios.
author Carmona Espejo, Diego Felipe
Gamboa Hidalgo, Jhonatan
author_facet Carmona Espejo, Diego Felipe
Gamboa Hidalgo, Jhonatan
topic Optimal portfolio;
Bayesian methods;
robust optimization
portafolio óptimo;
métodos bayesianos;
optimización robusta
topic_facet Optimal portfolio;
Bayesian methods;
robust optimization
portafolio óptimo;
métodos bayesianos;
optimización robusta
topicspa_str_mv portafolio óptimo;
métodos bayesianos;
optimización robusta
citationissue 21
citationedition Núm. 21 , Año 2021 : Julio-Diciembre
publisher Universidad Externado de Colombia
ispartofjournal ODEON
source https://revistas.uexternado.edu.co/index.php/odeon/article/view/8490
language spa
format Article
rights http://creativecommons.org/licenses/by-nc-sa/4.0
Diego Felipe Carmona Espejo, Jhonatan Gamboa Hidalgo - 2022
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-CompartirIgual 4.0.
info:eu-repo/semantics/openAccess
http://purl.org/coar/access_right/c_abf2
references Avramov, D. y Zhou, G. (2010). Bayesian portfolio analysis. Annual Review of Financial Economics, 2(1), 25-47. https://faculty.runi.ac.il/davramov/paper10.pdf
Bade, A., Frahm, G. y Jaekel, U. (2009). A general approach to Bayesian portfolio optimization. Mathematical Methods of Operations Research, 70(2), 337-356. https://doi.org/10.1007/s00186-008-0271-4
Best, M. y Grauer, R. (1991). Sensitivity analysis for mean-variance portfolio problems. Management Science, 37(8), 980-989. https://doi.org/10.1287/mnsc.37.8.980
Black, F. y Litterman, R. (1992). Global portfolio optimization. Financial Analysts Journal, 48(5), 28-43. https://doi.org/10.2469/faj.v48.n5.28
Fabozzi, F., Focardi, S., Kolm, P. y Pachamanova, D. (2007). Robust portfolio optimi¬zation and management. John Wiley & Sons.
Fama, E. y French, K. (1993). Common risk factors in the returns on stocks and bonds. Journal of financial economics, 33(1), 3-56. https://doi.org/10.1016/0304- 405X(93)90023-5
Garlappi, L., Uppal, R. y Wang, T. (2007). Portfolio selection with parameter and mo¬del uncertainty: A multi-prior approach. The Review of Financial Studies, 20(1), 41-81. https://doi.org/10.1093/rfs/hhl003
Georgantas, A. (2020). Robust Optimization Approaches for Portfolio Selection: A Computational and Comparative Analysis. Working paper. https://arxiv.org/ abs/2010.13397
Goldfarb, D. e Iyengar, G. (2003). Robust portfolio selection problems. Mathematics of Operations Research, 28(1), 1-38. https://doi.org/10.1287/moor.28.1.1.14260
Halldórsson, B. y Tütüncü, R. H. (2003). An interior-point method for a class of saddle-point problems. Journal of Optimization Theory and Applications, 116(3), 559-590. https://doi.org/10.1023/A:1023065319772
Hoffman, M., Brochu, E. y De Freitas, N. (2011). Portfolio allocation for ayesian optimi-zation. En Proceedings of the Twenty-Seventh Conference on Uncertainty in Ar¬tificial Intelligence, 327-336. https://dl.acm.org/doi/abs/10.5555/3020548.3020587
Kim, W. C., Kim, J. H., Ahn, S. H. y Fabozzi, F. J. (2013). What do robust equity port¬folio models really do? Annals of Operations Research, 205(1), 141-168. https:// doi.org/10.1007/s10479-012-1247-6
Kim, W. C., Kim, J. H. y Fabozzi, F. J. (2015). Robust Equity Portfolio Management: Formulations, Implementations, and Properties Using MATLAB. John Wiley & Sons.
Kim, J. H., Kim, W. C., Kwon, D. G. y Fabozzi, F. J. (2018). Robust equity portfo¬lio performance. Annals of Operations Research, 266(1), 293-312. https://doi. org/10.1007/s10479-017-2739-1
Lobo, M. S., Vandenberghe, L., Boyd, S. y Lebret, H. (1998). Applications of second-order cone programming. Linear Algebra and its Applications, 284(1-3), 193-228. https://doi.org/10.1016/S0024-3795(98)10032-0
Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91.
Markowitz, H. (1959). Portfolio selection: Efficient diversification of investments. New Heaven: Yale university Press.
Meucci, A. (2005). Risk and asset allocation (vol. 1). Springer.
Meucci, A. (2011). Robust Bayesian Allocation. ssrn Working paper 681553. https:// papers.ssrn.com/sol3/papers.cfm?abstract_id=681553
Michaud, R. (1998). Efficient asset management: A practical guide to stock portfolio optimization and asset allocation. Oxford University Press.
Michaud, R. y Michaud, R. (2008). Estimation error and portfolio optimization: A resampling solution. Journal of Investment Management, 6(1), 8-28.
Nesterov, Y. y Nemirovsky, A. (1993). Interior Point Polynomial Methods in Convex Programming: Theory and Algorithms. SIAM.
Pachamanova, D. y Fabozzi, F. (2012). Equity portfolio selection models in practice. En-cyclopedia of Financial Models, 1(1), 61-87. https://doi.org/10.1002/9781118182635. efm0046
Tütüncü, R. y Koenig, M. (2004). Robust asset allocation. Annals of Operations Research, 132(1), 157-187. https://doi.org/10.1023/b:anor.0000045281.41041.ed
Williams, J. (1938). The Theory of Investment Value. Harvard University Press.
Zapata, C. (2021). Optimización robusta de portafolios: conjuntos de incertidumbre y contrapartes robustas. odeon, 20, 93-121. https://doi.org/10.18601/17941113.n20.04
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