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Sparse Weighted-Norm Minimum Variance Portfolios

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  • Yu-Min Yen

Abstract

We propose to impose a weighted l1 and squared l2 norm penalty on the portfolio weights to improve out-of-sample (OOS) performances of portfolio optimization when the number of assets becomes large. We show that under certain conditions, the realized risk of the optimal minimum variance portfolio (MVP) obtained from the strategy can asymptotically be lower than those of benchmark portfolios with a high probability. Our theoretical results imply that penalty parameters for the weighted-norm penalty can be specified as a simple function of the number of assets and sample size. With the theoretical results, we also develop an automatic calibration procedure for choosing the penalty parameters. We demonstrate superior OOS performances of the weighted-norm MVP with two real data sets. Finally, we propose several alternative norm penalties and show that their OOS performances are comparable to the weighted-norm strategy.

Suggested Citation

  • Yu-Min Yen, 2016. "Sparse Weighted-Norm Minimum Variance Portfolios," Review of Finance, European Finance Association, vol. 20(3), pages 1259-1287.
    • Handle: RePEc:oup:revfin:v:20:y:2016:i:3:p:1259-1287.
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    File URL: http://hdl.handle.net/10.1093/rof/rfv024
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    References listed on IDEAS

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    1. B. Fastrich & S. Paterlini & P. Winker, 2015. "Constructing optimal sparse portfolios using regularization methods," Computational Management Science, Springer, vol. 12(3), pages 417-434, July.
    2. Fan, Jianqing & Liao, Yuan & Shi, Xiaofeng, 2015. "Risks of large portfolios," Journal of Econometrics, Elsevier, vol. 186(2), pages 367-387.
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    Cited by:

    1. Dai, Zhifeng & Wen, Fenghua, 2018. "Some improved sparse and stable portfolio optimization problems," Finance Research Letters, Elsevier, vol. 27(C), pages 46-52.
    2. Zhifeng Dai & Jie Kang, 2022. "Some new efficient mean–variance portfolio selection models," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(4), pages 4784-4796, October.
    3. Tu, Xueyong & Li, Bin, 2024. "Robust portfolio selection with smart return prediction," Economic Modelling, Elsevier, vol. 135(C).
    4. Lassance, Nathan & Vanderveken, Rodolphe & Vrins, Frédéric, 2022. "On the optimal combination of naive and mean-variance portfolio strategies," LIDAM Discussion Papers LFIN 2022006, Université catholique de Louvain, Louvain Finance (LFIN).
    5. Chou, Ray Yeutien & Yen, Tso-Jung & Yen, Yu-Min, 2017. "Risk evaluations with robust approximate factor models," Journal of Banking & Finance, Elsevier, vol. 82(C), pages 244-264.

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