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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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2023
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| Online Access: | https://hdl.handle.net/10356/169279 |
| _version_ | 1826128407521394688 |
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| author | Marisu, Godeliva Petrina Pun, Chi Seng |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Marisu, Godeliva Petrina Pun, Chi Seng |
| author_sort | Marisu, Godeliva Petrina |
| collection | NTU |
| 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. |
| first_indexed | 2024-10-01T07:24:08Z |
| format | Journal Article |
| id | ntu-10356/169279 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:24:08Z |
| publishDate | 2023 |
| record_format | dspace |
| spelling | ntu-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. |
| spellingShingle | Science::Mathematics High Dimensionality sequential regularization Marisu, Godeliva Petrina Pun, Chi Seng Bayesian estimation and optimization for learning sequential regularized portfolios |
| title | 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_short | Bayesian estimation and optimization for learning sequential regularized portfolios |
| title_sort | bayesian estimation and optimization for learning sequential regularized portfolios |
| topic | Science::Mathematics High Dimensionality sequential regularization |
| url | https://hdl.handle.net/10356/169279 |
| work_keys_str_mv | AT marisugodelivapetrina bayesianestimationandoptimizationforlearningsequentialregularizedportfolios AT punchiseng bayesianestimationandoptimizationforlearningsequentialregularizedportfolios |