Bayesian Estimation and Optimization for Learning Sequential Regularized Portfolios

29 Pages Posted: 24 Jun 2021

See all articles by Godeliva Petrina Marisu

Godeliva Petrina Marisu

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences

Chi Seng Pun

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences

Date Written: June 15, 2021

Abstract

This paper incorporates Bayesian estimation and optimization into portfolio selection framework, particularly for high-dimensional portfolio in which the number of assets is larger than the number of observations. We leverage a constrained 𝓁1 minimization approach, called 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 time-dependent nature of financial problems and (2) extending commonly used expected improvement (EI) acquisition function to include a tunable trade-off with the improvement's variance (EIVar). Allowing a general case of noisy observations, we theoretically derive the sub-linear convergence rate of BO under the newly proposed EIVar and thus our algorithm has no regret. Our empirical studies confirm that the adjusted BO result 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 significant reduction in time elapsed, thus also addressing time-consuming issues of CV. Furthermore, LPO with Bayesian estimates outperform original proposal of LPO, as well as the benchmark equally weighted and plug-in strategies.

Keywords: sequential portfolio selection, Bayesian estimation, Bayesian optimization, high dimensionality, sequential regularization, sequential hyperparameter tuning

JEL Classification: G11, C13, C16

Suggested Citation

Marisu, Godeliva Petrina and Pun, Chi Seng, Bayesian Estimation and Optimization for Learning Sequential Regularized Portfolios (June 15, 2021). Available at SSRN: https://ssrn.com/abstract=3867297 or http://dx.doi.org/10.2139/ssrn.3867297

Godeliva Petrina Marisu

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences ( email )

S3 B2-A28 Nanyang Avenue
Singapore, 639798
Singapore

Chi Seng Pun (Contact Author)

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences ( email )

SPMS-MAS-05-22
21 Nanyang Link
Singapore, 637371
Singapore
(+65) 6513 7468 (Phone)

HOME PAGE: http://personal.ntu.edu.sg/cspun/

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