Cardinality Constrained Portfolio Optimization via Alternating Direction Method of Multipliers

Shi, Zhang-Lei; Li, Xiao Peng; Leung, Chi-Sing; So, Hing Cheung

doi:10.1109/tnnls.2022.3192065

Cited by 11 publications

(5 citation statements)

References 45 publications

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“…As for the comparison methods, in addition to the aforementioned NNOMP-PGD [8] and LAIT [5], the state-ofthe-art sparse index tracking methods, we also compare our method with ℓ 0 -ADMM (Alternating Direction Method of Multipliers) [40]. Despite how ℓ 0 -ADMM focuses on optimizing between return and risk, making it distinct from typical index tracking approaches, its implementation of an ℓ 0 -norm constraint mirrors that of NNOMP-PGD and our proposed method, warranting its inclusion in our comparison.…”

Section: Experiments a Dataset And Settingsmentioning

confidence: 99%

Sparse Index Tracking: Simultaneous Asset Selection and Capital Allocation via ℓ₀ -Constrained Portfolio

Yamagata,

Ono

2024

IEEE Open J. Signal Process.

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Sparse index tracking is a prominent passive portfolio management strategy that constructs a sparse portfolio to track a financial index. A sparse portfolio is preferable to a full portfolio in terms of reducing transaction costs and avoiding illiquid assets. To achieve portfolio sparsity, conventional studies have utilized ℓ p -norm regularizations as a continuous surrogate of the ℓ 0 -norm regularization. Although these formulations can construct sparse portfolios, their practical application is challenging due to the intricate and time-consuming process of tuning parameters to define the precise upper limit of assets in the portfolio. In this paper, we propose a new problem formulation of sparse index tracking using an ℓ 0 -norm constraint that enables easy control of the upper bound on the number of assets in the portfolio. Moreover, our approach offers a choice between constraints on portfolio and turnover sparsity, further reducing transaction costs by limiting asset updates at each rebalancing interval. Furthermore, we develop an efficient algorithm for solving this problem based on a primal-dual splitting method. Finally, we illustrate the effectiveness of the proposed method through experiments on the S&P500 and Russell3000 index datasets.INDEX TERMS ℓ 0 -norm constraint, Primal-dual splitting, Sparse index tracking.

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Section: Experiments a Dataset And Settingsmentioning

confidence: 99%

Sparse Index Tracking: Simultaneous Asset Selection and Capital Allocation via ℓ₀ -Constrained Portfolio

Yamagata,

Ono

2024

IEEE Open J. Signal Process.

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“…Cardinality: In this work, in order to avoid complicated mathematics, the cardinality constraint was not utilized, but it is suggested to use cardinality to extend the degree of the investor's control of the portfolio [62][63][64][65][66][67].…”

Section: Conclusion and Research Prospectsmentioning

confidence: 99%

Credibilistic Multi-Period Mean-Entropy Rolling Portfolio Optimization Problem Based on Multi-Stage Scenario Tree

Peykani,

Nouri,

Pishvaee

et al. 2023

Mathematics

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This study considers a time-consistent multi-period rolling portfolio optimization issue in the context of a fuzzy situation. Rolling optimization with a risk aversion component attempts to separate the time periods and psychological effects of one’s investment in a mathematical model. Furthermore, a resilient portfolio selection may be attained by taking into account fuzzy scenarios. Credibilistic entropy of fuzzy returns is used to measure portfolio risk because entropy, as a measure of risk, is not dependent on any certain sort of symmetric membership function of stock returns and may be estimated using nonmetric data. Mathematical modeling is performed to compare the Rolling Model (RM) and the Unified Model (UM). Two empirical studies from the Tehran stock market (10 stocks from April 2017 to April 2019) and the global stock market (20 stocks from April 2021 to April 2023) are utilized to illustrate the applicability of the suggested strategy. The findings reveal that RM can limit the risk of the portfolio at each time, but the portfolio’s return is smaller than that of UM. Furthermore, the suggested models outperform the standard deterministic model.

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“…6: Train this model based on the gradient descent method (13) until it converges. 7: By (15), calculate the thresholds τ. Use the Cond.RS (14) to select the important rules.…”

Section: First-order Sparse Tsk Nonstationary Fuzzy Neural Network (S...mentioning

confidence: 99%

“…The training of FNNs is a necessary work. There are many existing training algorithms, such as backpropagation [5], particle swarm algorithm [13], hybrid algorithm [14] and so on [15]. Although evolutionary algorithms and hybrid-type algorithms work well, they require considerable running time.…”

Section: Introductionmentioning

confidence: 99%

First-Order Sparse TSK Nonstationary Fuzzy Neural Network Based on the Mean Shift Algorithm and the Group Lasso Regularization

Zhang,

Wang,

Gong

et al. 2023

Mathematics

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Nonstationary fuzzy inference systems (NFIS) are able to tackle uncertainties and avoid the difficulty of type-reduction operation. Combining NFIS and neural network, a first-order sparse TSK nonstationary fuzzy neural network (SNFNN-1) is proposed in this paper to improve the interpretability/translatability of neural networks and the self-learning ability of fuzzy rules/sets. The whole architecture of SNFNN-1 can be considered as an integrated model of multiple sub-networks with a variation in center, variation in width or variation in noise. Thus, it is able to model both “intraexpert” and “interexpert” variability. There are two techniques adopted in this network: the Mean Shift-based fuzzy partition and the Group Lasso-based rule selection, which can adaptively generate a suitable number of clusters and select important fuzzy rules, respectively. Quantitative experiments on six UCI datasets demonstrate the effectiveness and robustness of the proposed model.

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Cardinality Constrained Portfolio Optimization via Alternating Direction Method of Multipliers

Cited by 11 publications

References 45 publications

Sparse Index Tracking: Simultaneous Asset Selection and Capital Allocation via ℓ₀ -Constrained Portfolio

Sparse Index Tracking: Simultaneous Asset Selection and Capital Allocation via ℓ₀ -Constrained Portfolio

Credibilistic Multi-Period Mean-Entropy Rolling Portfolio Optimization Problem Based on Multi-Stage Scenario Tree

First-Order Sparse TSK Nonstationary Fuzzy Neural Network Based on the Mean Shift Algorithm and the Group Lasso Regularization

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Cardinality Constrained Portfolio Optimization via Alternating Direction Method of Multipliers

Cited by 11 publications

References 45 publications

Sparse Index Tracking: Simultaneous Asset Selection and Capital Allocation via ℓ0 -Constrained Portfolio

Sparse Index Tracking: Simultaneous Asset Selection and Capital Allocation via ℓ0 -Constrained Portfolio

Credibilistic Multi-Period Mean-Entropy Rolling Portfolio Optimization Problem Based on Multi-Stage Scenario Tree

First-Order Sparse TSK Nonstationary Fuzzy Neural Network Based on the Mean Shift Algorithm and the Group Lasso Regularization

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Product

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Sparse Index Tracking: Simultaneous Asset Selection and Capital Allocation via ℓ₀ -Constrained Portfolio

Sparse Index Tracking: Simultaneous Asset Selection and Capital Allocation via ℓ₀ -Constrained Portfolio