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A generalized approach to sparse and stable portfolio optimization problem

  • * Corresponding author: Fenghua Wen

    * Corresponding author: Fenghua Wen
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  • In this paper, we firstly examine the relation between the portfolio weights norm constraints method and the objective function regularization method in portfolio selection problems. We find that the portfolio weights norm constrained method mainly tries to obtain stable portfolios, however, the objective function regularization method mainly aims at obtaining sparse portfolios. Then, we propose some general sparse and stable portfolio models by imposing both portfolio weights norm constraints and objective function $L_{1}$ regularization term. Finally, three empirical studies show that the proposed strategies have better out-of-sample performance and lower turnover than many other strategies for tested datasets.

    Mathematics Subject Classification: Primary: 90C15, 90C90; Secondary: 91G10.


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  • Table 1.  List of Datasets

    No.DatasetNumber of assetTime PeriodSourse
    1FF-10010012/1992-12/2014K. French
    2FF-484812/1992-12/2014K. French
    3500 CRSP50004/1992-04/2014CRSP
    4100 CRSP10004/1992-04/2014CRSP
    5S&P 50046112/2007-12/2014Datastream
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    Table 2.  Portfolio variances of all considered portfolio strategies.

    Dataset500 CRSP100 CRSPS&P 500FF-100FF48
    Model 10.000490.001090.000600.000980.00119
    Model 20.000420.001020.000520.000910.00111
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    Table 3.  Out-of-sample Sharpe ratio of the portfolio strategies.

    Dataset500 CRSP100 CRSPS&P 500FF-100FF48
    Model 10.42780.44600.43140.39980.3146
    Model 20.46360.45480.45680.40240.3220
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    Table 4.  Turnover of the portfolio strategies.

    Dataset500 CRSP100 CRSPS&P 500FF-100FF48
    Model 10.40280.31240.41200.30680.2580
    Model 20.41450.31820.41660.30220.2528
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