Sparse Index Tracking With K-Sparsity or ϵ-Deviation Constraint via ℓ0-Norm Minimization

Sparse index tracking, as one of the passive investment strategies, is to track a benchmark financial index via constructing a portfolio with a few assets in a market index. It can be considered as parameter learning in an adaptive system, in which we periodically update the selected assets and thei...

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Vydáno v:IEEE transaction on neural networks and learning systems Ročník 34; číslo 12; s. 10930 - 10943
Hlavní autoři: Li, Xiao Peng, Shi, Zhang-Lei, Leung, Chi-Sing, So, Hing Cheung
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States IEEE 01.12.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Adaptive systems
Algorithms
Alternating direction method of multipliers (ADMM)
Constraints
Gradient methods
index tracking
Indexes
Investment
Investment strategy
Matched pursuit
Matching pursuit algorithms
nonnegative orthogonal matching pursuit (NNOMP)
Optimization
Portfolios
projected gradient descent (PGD)
Signal processing algorithms
sparse recovery
Target tracking
Tracking control
Tracking errors
ISSN:2162-237X, 2162-2388, 2162-2388
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Popis
Shrnutí:Sparse index tracking, as one of the passive investment strategies, is to track a benchmark financial index via constructing a portfolio with a few assets in a market index. It can be considered as parameter learning in an adaptive system, in which we periodically update the selected assets and their investment percentages based on the sliding window approach. However, many existing algorithms for sparse index tracking cannot explicitly and directly control the number of assets or the tracking error. This article formulates sparse index tracking as two constrained optimization problems and then proposes two algorithms, namely, nonnegative orthogonal matching pursuit with projected gradient descent (NNOMP-PGD) and alternating direction method of multipliers for <inline-formula> <tex-math notation="LaTeX">\ell _{0} </tex-math></inline-formula>-norm (ADMM-<inline-formula> <tex-math notation="LaTeX">\ell _{0} </tex-math></inline-formula>). The NNOMP-PGD aims at minimizing the tracking error subject to the number of selected assets less than or equal to a predefined number. With the NNOMP-PGD, investors can directly and explicitly control the number of selected assets. The ADMM-<inline-formula> <tex-math notation="LaTeX">\ell _{0} </tex-math></inline-formula> aims at minimizing the number of selected assets subject to the tracking error that is upper bounded by a preset threshold. It can directly and explicitly control the tracking error. The convergence of the two proposed algorithms is also presented. With our algorithms, investors can explicitly and directly control the number of selected assets or the tracking error of the resultant portfolio. In addition, numerical experiments demonstrate that the proposed algorithms outperform the existing approaches.
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ISSN:2162-237X
2162-2388
2162-2388
DOI:10.1109/TNNLS.2022.3171819