Estimating Market Expectations for Portfolio Selection Using Penalized Statistical Models

Estimación de expectativas del mercado para la selección de portafolios usando modelos estadísticos penalizados

Palabras clave: Penalized models, regularization, state price density estimation, financial options, portfolio optimization (en_US)
Palabras clave: Optimización de portafolios, regularización, modelos penalizados, estimación de la densidad del precio implícita, opciones financieras (es_ES)

Resumen (en_US)

The portfolio selection problem can be viewed as an optimization problem that maximizes the risk–return relationship. It consists of a number of elements, such as an objective function, decision variables and input parameters, which are used to predict expected returns and the covariance between the said returns. However, the real values of these parameters cannot be directly observed; thus, estimations based on historical data are required. Historical data, however, can often result in modelling errors when the parameters are replaced by their estimations. We propose to address this by using some regularization mechanisms in the optimization.  In addition, we explore the use of implicit information to improve the portfolio performance, such as options market prices, which are a rich source of investor expectations. Accordingly, we propose a new estimator for risk and return that combines historical and implicit information in the portfolio selection problem. We implement the new estimators for the mean-VAR and mean-VaR2 problems using an elastic-net model that reduces the risk of all estimations performed. The results suggest that the model has a good out-of-sample performance that is superior to models with pure historical estimations.

Resumen (es_ES)

El problema de selección de portafolios puede ser visto como un problema de optimización que maximiza una relación riesgo-retorno cuyos parámetros son los retornos esperados y las covarianzas entre ellos. Sin embargo, los valores reales de dichos parámetros no son observables, por lo cual es necesario realizar estimaciones que comúnmente están basadas en datos históricos. Estas estimaciones pueden introducir errores en el modelo, haciendo necesario usar diferentes mecanismos de regularización, como los propuestos en el presente estudio. Además, proponemos el uso de información adicional para mejorar el desempeño de los portafolios, como los son los precios de las opciones que contienen una rica fuente de información que muestra las expectativas de los inversionistas con base en sus conocimientos acerca de cada uno de los subyacentes. De esta manera, proponemos el uso de un nuevo estimador de riesgo-retorno que mezcla la información histórica con la implícita para el problema de selección de portafolios. Implementamos los nuevos estimadores para el problema de Media-Varianza y Media-VaR2 a través de un modelo de red-elástica que permite reducir el impacto del riesgo de las estimaciones realizadas. Los resultados sugieren rendimientos de portafolio superiores a los modelos con estimadores basados en datos históricos.

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Cómo citar
Valencia-Arboleda, C. F., & Segura-Acosta, D. H. (2020). Estimación de expectativas del mercado para la selección de portafolios usando modelos estadísticos penalizados. Revista Científica, 2(38). Recuperado a partir de https://revistas.udistrital.edu.co/index.php/revcie/article/view/15797
Publicado: 2020-05-01
Sección
Ciencia e ingeniería