A Sparse Learning Approach to Relative-Volatility-Managed Portfolio Selection
23 Mar 2021-Siam Journal on Financial Mathematics (Society for Industrial & Applied Mathematics (SIAM))-Vol. 12, Iss: 1, pp 410-445
TL;DR: In this paper, a self-calibrated sparse learning approach for estimating a sparse target vector, which is a product of a precision matrix and a vector, is proposed, and investigated its application to fina...
Abstract: This paper proposes a self-calibrated sparse learning approach for estimating a sparse target vector, which is a product of a precision matrix and a vector, and investigates its application to fina...
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22Ā citations
TL;DR: With the theoretical and empirical evidence, it is shown that the proposed estimator is better than its competitors in statistical accuracy and has clear computational advantages.
8Ā citations
TL;DR: Bayesian optimization (BO) is introduced to replace traditional grid-search cross-validation (CV) in tuning hyperparameters of the LPO strategy and outperform original proposal of LPO, as well as the benchmark equally weighted and plug-in strategies.
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 š1 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.
2Ā citations
TL;DR: In this article , a constrained minimization approach, called the linear programming optimal (LPO) portfolio, is proposed to directly estimate effective parameters appearing in the optimal portfolio, and a Bayesian optimization (BO) is introduced to replace traditional grid-search cross-validation (CV) in tuning hyperparameters of the LPO strategy.
Abstract: 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 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 improvementās 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.
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TL;DR: It is shown that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation, and an algorithm called LARSāEN is proposed for computing elastic net regularization paths efficiently, much like algorithm LARS does for the lamba.
Abstract: Summary. We propose the elastic net, a new regularization and variable selection method. Real world data and a simulation study show that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation. In addition, the elastic net encourages a grouping effect, where strongly correlated predictors tend to be in or out of the model together.The elastic net is particularly useful when the number of predictors (p) is much bigger than the number of observations (n). By contrast, the lasso is not a very satisfactory variable selection method in the
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TL;DR: In this paper, the authors considered the continuous-time consumption-portfolio problem for an individual whose income is generated by capital gains on investments in assets with prices assumed to satisfy the geometric Brownian motion hypothesis, which implies that asset prices are stationary and lognormally distributed.
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TL;DR: In this paper, the authors present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets, including distributional properties, tail properties and extreme fluctuations, pathwise regularity, linear and nonlinear dependence of returns in time and across stocks.
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TL;DR: In this article, the authors evaluate the out-of-sample performance of the sample-based mean-variance model, and its extensions designed to reduce estimation error, relative to the naive 1-N portfolio.
Abstract: We evaluate the out-of-sample performance of the sample-based mean-variance model, and its extensions designed to reduce estimation error, relative to the naive 1-N portfolio. Of the 14 models we evaluate across seven empirical datasets, none is consistently better than the 1-N rule in terms of Sharpe ratio, certainty-equivalent return, or turnover, which indicates that, out of sample, the gain from optimal diversification is more than offset by estimation error. Based on parameters calibrated to the US equity market, our analytical results and simulations show that the estimation window needed for the sample-based mean-variance strategy and its extensions to outperform the 1-N benchmark is around 3000 months for a portfolio with 25 assets and about 6000 months for a portfolio with 50 assets. This suggests that there are still many "miles to go" before the gains promised by optimal portfolio choice can actually be realized out of sample. The Author 2007. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org, Oxford University Press.
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