Between Nonlinearities, Complexity, and Noises: An Application on Portfolio Selection Using Kernel Principal Component Analysis

Peng, Yaohao; Albuquerque, Pedro Henrique Melo; do Nascimento, Igor Ferreira; Machado, João Victor Freitas

doi:10.3390/e21040376

Open AccessArticle

Between Nonlinearities, Complexity, and Noises: An Application on Portfolio Selection Using Kernel Principal Component Analysis

by

Yaohao Peng

^1,*

,

Pedro Henrique Melo Albuquerque

¹,

Igor Ferreira do Nascimento

^1,2

and

João Victor Freitas Machado

¹

Campus Universitário Darcy Ribeiro-Brasília, University of Brasilia, Brasilia 70910-900, Brazil

²

Federal Institute of Piauí, Rua Álvaro Mendes, 94-Centro (Sul), Teresina-PI 64001-270, Brazil

^*

Author to whom correspondence should be addressed.

Entropy 2019, 21(4), 376; https://doi.org/10.3390/e21040376

Submission received: 22 February 2019 / Revised: 29 March 2019 / Accepted: 4 April 2019 / Published: 7 April 2019

(This article belongs to the Section Multidisciplinary Applications)

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Abstract

This paper discusses the effects of introducing nonlinear interactions and noise-filtering to the covariance matrix used in Markowitz’s portfolio allocation model, evaluating the technique’s performances for daily data from seven financial markets between January 2000 and August 2018. We estimated the covariance matrix by applying Kernel functions, and applied filtering following the theoretical distribution of the eigenvalues based on the Random Matrix Theory. The results were compared with the traditional linear Pearson estimator and robust estimation methods for covariance matrices. The results showed that noise-filtering yielded portfolios with significantly larger risk-adjusted profitability than its non-filtered counterpart for almost half of the tested cases. Moreover, we analyzed the improvements and setbacks of the nonlinear approaches over linear ones, discussing in which circumstances the additional complexity of nonlinear features seemed to predominantly add more noise or predictive performance.

Keywords: nonlinearity; regularization; high dimensionality; portfolio allocation; machine learning; covariance estimation; random matrix theory; kernel methods

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MDPI and ACS Style

Peng, Y.; Albuquerque, P.H.M.; do Nascimento, I.F.; Machado, J.V.F. Between Nonlinearities, Complexity, and Noises: An Application on Portfolio Selection Using Kernel Principal Component Analysis. Entropy 2019, 21, 376. https://doi.org/10.3390/e21040376

AMA Style

Peng Y, Albuquerque PHM, do Nascimento IF, Machado JVF. Between Nonlinearities, Complexity, and Noises: An Application on Portfolio Selection Using Kernel Principal Component Analysis. Entropy. 2019; 21(4):376. https://doi.org/10.3390/e21040376

Chicago/Turabian Style

Peng, Yaohao, Pedro Henrique Melo Albuquerque, Igor Ferreira do Nascimento, and João Victor Freitas Machado. 2019. "Between Nonlinearities, Complexity, and Noises: An Application on Portfolio Selection Using Kernel Principal Component Analysis" Entropy 21, no. 4: 376. https://doi.org/10.3390/e21040376

APA Style

Peng, Y., Albuquerque, P. H. M., do Nascimento, I. F., & Machado, J. V. F. (2019). Between Nonlinearities, Complexity, and Noises: An Application on Portfolio Selection Using Kernel Principal Component Analysis. Entropy, 21(4), 376. https://doi.org/10.3390/e21040376

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Between Nonlinearities, Complexity, and Noises: An Application on Portfolio Selection Using Kernel Principal Component Analysis

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