Bayesian estimation and optimization for learning sequential regularized portfolios

This paper incorporates Bayesian estimation and optimization into a portfolio selection framework, particularly for high-dimensional portfolios in which the number of assets is larger than the number of observations. We leverage a constrained \ell 1 minimization approach, called the linear programmi...

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Main Authors: Marisu, Godeliva Petrina, Pun, Chi Seng
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2023
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Online Access:https://hdl.handle.net/10356/169279
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1692792023-07-11T02:47:45Z Bayesian estimation and optimization for learning sequential regularized portfolios Marisu, Godeliva Petrina Pun, Chi Seng School of Physical and Mathematical Sciences Science::Mathematics High Dimensionality sequential regularization This paper incorporates Bayesian estimation and optimization into a portfolio selection framework, particularly for high-dimensional portfolios in which the number of assets is larger than the number of observations. We leverage a constrained \ell 1 minimization approach, called the linear programming optimal (LPO) portfolio, to directly estimate effective parameters appearing in the optimal portfolio. We propose two refinements for the LPO strategy. First, we explore improved Bayesian estimates, instead of sample estimates, of the covariance matrix of asset returns. Second, we introduce Bayesian optimization (BO) to replace traditional grid-search cross-validation (CV) in tuning hyperparameters of the LPO strategy. We further propose modifications in the BO algorithm by (1) taking into account the time-dependent nature of financial problems and (2) extending the commonly used expected improvement acquisition function to include a tunable trade-off with the improvement's variance. Allowing a general case of noisy observations, we theoretically derive the sublinear convergence rate of BO under the newly proposed EIVar and thus our algorithm has no regret. Our empirical studies confirm that the adjusted BO results in portfolios with higher out-of-sample Sharpe ratio, certainty equivalent, and lower turnover compared to those tuned with CV. This superior performance is achieved with a significant reduction in time elapsed, thus also addressing time-consuming issues of CV. Furthermore, LPO with Bayesian estimates outperforms the original proposal of LPO, as well as the benchmark equally weighted and plugin strategies. Ministry of Education (MOE) This work was funded by the Ministry of Education, Singapore (MOE2017-T2-1-044). 2023-07-11T02:47:45Z 2023-07-11T02:47:45Z 2023 Journal Article Marisu, G. P. & Pun, C. S. (2023). Bayesian estimation and optimization for learning sequential regularized portfolios. SIAM Journal On Financial Mathematics, 14(1), 127-157. https://dx.doi.org/10.1137/21M1427176 1945-497X https://hdl.handle.net/10356/169279 10.1137/21M1427176 2-s2.0-85152208477 1 14 127 157 en SIAM Journal on Financial Mathematics © 2023 Society for Industrial and Applied Mathematics Publications. All rights reserved.
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Mathematics
High Dimensionality
sequential regularization
spellingShingle Science::Mathematics
High Dimensionality
sequential regularization
Marisu, Godeliva Petrina
Pun, Chi Seng
Bayesian estimation and optimization for learning sequential regularized portfolios
description This paper incorporates Bayesian estimation and optimization into a portfolio selection framework, particularly for high-dimensional portfolios in which the number of assets is larger than the number of observations. We leverage a constrained \ell 1 minimization approach, called the linear programming optimal (LPO) portfolio, to directly estimate effective parameters appearing in the optimal portfolio. We propose two refinements for the LPO strategy. First, we explore improved Bayesian estimates, instead of sample estimates, of the covariance matrix of asset returns. Second, we introduce Bayesian optimization (BO) to replace traditional grid-search cross-validation (CV) in tuning hyperparameters of the LPO strategy. We further propose modifications in the BO algorithm by (1) taking into account the time-dependent nature of financial problems and (2) extending the commonly used expected improvement acquisition function to include a tunable trade-off with the improvement's variance. Allowing a general case of noisy observations, we theoretically derive the sublinear convergence rate of BO under the newly proposed EIVar and thus our algorithm has no regret. Our empirical studies confirm that the adjusted BO results in portfolios with higher out-of-sample Sharpe ratio, certainty equivalent, and lower turnover compared to those tuned with CV. This superior performance is achieved with a significant reduction in time elapsed, thus also addressing time-consuming issues of CV. Furthermore, LPO with Bayesian estimates outperforms the original proposal of LPO, as well as the benchmark equally weighted and plugin strategies.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Marisu, Godeliva Petrina
Pun, Chi Seng
format Article
author Marisu, Godeliva Petrina
Pun, Chi Seng
author_sort Marisu, Godeliva Petrina
title Bayesian estimation and optimization for learning sequential regularized portfolios
title_short Bayesian estimation and optimization for learning sequential regularized portfolios
title_full Bayesian estimation and optimization for learning sequential regularized portfolios
title_fullStr Bayesian estimation and optimization for learning sequential regularized portfolios
title_full_unstemmed Bayesian estimation and optimization for learning sequential regularized portfolios
title_sort bayesian estimation and optimization for learning sequential regularized portfolios
publishDate 2023
url https://hdl.handle.net/10356/169279
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