Sparse and Stable Markowitz Portfolios

Brodie, Joshua; Daubechies, Ingrid; Mol, Christine De; Giannone, Domenico; Loris, Ignace

doi:10.2139/ssrn.1258442

Cited by 82 publications

(162 citation statements)

References 8 publications

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“…While the literature offers a significative number of methods for Tikhonov regularization [19], l 1 regularization parameter selection is often based on problem-dependent criteria and related to iterative empirical estimates, that require a high computational cost. In [7] least-angle regression (LARS) algorithm proceeds by decreasing the value of τ progressively from very large values, exploiting the fact that the dependence of the optimal weights on τ is piecewise linear.…”

Section: Modified Bregman Iterationmentioning

confidence: 99%

“…In this section, we present a numerical algorithm, based on a modified Bregman iteration with adaptive updating rule for τ . Our basic idea for defining the rule for τ comes from the well-known properties of the l 1 norm and the following proposition [7]:…”

Section: Modified Bregman Iterationmentioning

confidence: 99%

“…In [6] authors regularize the meanvariance objective function with a weighted elastic net penalty. In this paper, we consider the l 1 mean-variance regularized model introduced in [7], where a l 1 -penalty term is added to promote sparsity in the solution. Since solutions establish the amount of capital to be invested in each available security, sparsity means that money are invested in a few securities, the active positions.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive l1-regularization for short-selling control in portfolio selection

Corsaro¹,

Simone²

2018

Preprint

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We consider the l1-regularized Markowitz model, where a l1-penalty term is added to the objective function of the classical mean-variance one to stabilize the solution process, promoting sparsity in the solution. The l1-penalty term can also be interpreted in terms of short sales, on which several financial markets have posed restrictions. The choice of the regularization parameter plays a key role to obtain optimal portfolios that meet the financial requirements. We propose an updating rule for the regularization parameter in Bregman iteration to control both the sparsity and the number of short positions. We show that the modified scheme preserves the properties of the original one. Numerical tests are reported, which show the effectiveness of the approach.

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Section: Modified Bregman Iterationmentioning

confidence: 99%

Section: Modified Bregman Iterationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Adaptive l1-regularization for short-selling control in portfolio selection

Corsaro¹,

Simone²

2018

Preprint

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show abstract

“…To control these weights and avoid calculating the extreme weights in portfolio optimization, first, Jagannathan and Ma (2003) sought to control this issue by modifying the proposed approach by Green and Hollifield (1992) and adding a constraint on the extreme values of stock weights in the portfolio. In this way, a SCAD penalty function was added to the portfolio constraint, for instance, studies by Fan & Li (2001) and Brodie et al (2009) who tried to reduce this problem by considering the penalty function and adding it to the budget constraint of portfolio optimization for certain extreme weights. To improve this issue in the existing literature, Rockafellar et al (2014) proposed the generalized least squares regression in the conditional value at risk minimization approach in portfolio optimization problems to reduce problems in extreme weights.…”

Section: Introductionmentioning

confidence: 99%

Portfolio Optimization based on the Risk Minimization by the Weight-Modified CVaR vs. CVaR Method

Fadaeinejad

Vaziri

Asadi

et al. 2022

IJFIFSA

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Given the lack of a specific approach to the explanation of values of optimal portfolio weights in the portfolio optimization, the present study aimed to examine large-scale portfolio optimization according to both stock weighting and utilization of SCAD function to minimize the portfolio risk based on the "weight-modified conditional value at risk (CVaR)" and its comparison with Portfolio Optimization based on the Risk Minimization by… the "conditional value at risk (CVaR)" method in the Tehran Stock Exchange. Therefore, the price information of companies listed in the Tehran Stock Exchange and Over-the-counter (OTC) from 2012 to the end of September 2020 was collected, screened, and analyzed daily, and then the risk and return of the portfolios were examined by forming optimal portfolios. The results indicated that the efficiency limit of the stock portfolio and also the ranks of different companies were different according to the types of the optimization method. Based on the behavior of the TEDPIX, the investors' degrees of risktaking, and the risk management, diversification, and computational complexity of each method, the weight-modified CVaR had a better performance due to better diversification and risk management. Furthermore, the SCAD function added computational complexity to this method.

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“…3 Technically, including too many stocks increases both the odds of overfitting and the difficulty in computing efficient allocation strategies. One way to address this issue is to add a regularization term in the Markowitz mean-variance optimization model (Brodie et al, 2009;Ho et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

Asset Selection via Correlation Blockmodel Clustering

Tang¹,

Xu²

2021

Preprint

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We aim to cluster financial assets in order to identify a small set of stocks to approximate the level of diversification of the whole universe of stocks. We develop a datadriven approach to clustering based on a correlation blockmodel in which assets in the same cluster have the same correlations with all other assets. We devise an algorithm to detect the clusters, with a theoretical analysis and a practical guidance. Finally, we conduct an empirical analysis to attest the performance of the algorithm.

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Sparse and Stable Markowitz Portfolios

Cited by 82 publications

References 8 publications

Adaptive l1-regularization for short-selling control in portfolio selection

Adaptive l1-regularization for short-selling control in portfolio selection

Portfolio Optimization based on the Risk Minimization by the Weight-Modified CVaR vs. CVaR Method

Asset Selection via Correlation Blockmodel Clustering

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