IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

A Note on Sparse Minimum Variance Portfolios and Coordinate-Wise Descent Algorithms

  • Yu-Min Yen
Registered author(s):

    In this short report, we discuss how coordinate-wise descent algorithms can be used to solve minimum variance portfolio (MVP) problems in which the portfolio weights are constrained by $l_{q}$ norms, where $1\leq q \leq 2$. A portfolio which weights are regularised by such norms is called a sparse portfolio (Brodie et al.), since these constraints facilitate sparsity (zero components) of the weight vector. We first consider a case when the portfolio weights are regularised by a weighted $l_{1}$ and squared $l_{2}$ norm. Then two benchmark data sets (Fama and French 48 industries and 100 size and BM ratio portfolios) are used to examine performances of the sparse portfolios. When the sample size is not relatively large to the number of assets, sparse portfolios tend to have lower out-of-sample portfolio variances, turnover rates, active assets, short-sale positions, but higher Sharpe ratios than the unregularised MVP. We then show some possible extensions; particularly we derive an efficient algorithm for solving an MVP problem in which assets are allowed to be chosen grouply.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: http://arxiv.org/pdf/1005.5082
    File Function: Latest version
    Download Restriction: no

    Paper provided by arXiv.org in its series Papers with number 1005.5082.

    as
    in new window

    Length:
    Date of creation: May 2010
    Date of revision: Sep 2013
    Handle: RePEc:arx:papers:1005.5082
    Contact details of provider: Web page: http://arxiv.org/

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    as in new window
    1. Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
    2. Brodie, Joshua & Daubechies, Ingrid & De Mol, Christine & Giannone, Domenico & Loris, Ignace, 2008. "Sparse and stable Markowitz portfolios," Working Paper Series 0936, European Central Bank.
    3. Jianqing Fan & Jingjin Zhang & Ke Yu, 2008. "Asset Allocation and Risk Assessment with Gross Exposure Constraints for Vast Portfolios," Papers 0812.2604, arXiv.org.
    4. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67.
    5. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1684, 08.
    6. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320.
    7. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:arx:papers:1005.5082. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.