No. | Dataset | Number of asset | Time Period | Sourse |
1 | FF-100 | 100 | 12/1992-12/2014 | K. French |
2 | FF-48 | 48 | 12/1992-12/2014 | K. French |
3 | 500 CRSP | 500 | 04/1992-04/2014 | CRSP |
4 | 100 CRSP | 100 | 04/1992-04/2014 | CRSP |
5 | S&P 500 | 461 | 12/2007-12/2014 | Datastream |
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.
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Table 1. List of Datasets
No. | Dataset | Number of asset | Time Period | Sourse |
1 | FF-100 | 100 | 12/1992-12/2014 | K. French |
2 | FF-48 | 48 | 12/1992-12/2014 | K. French |
3 | 500 CRSP | 500 | 04/1992-04/2014 | CRSP |
4 | 100 CRSP | 100 | 04/1992-04/2014 | CRSP |
5 | S&P 500 | 461 | 12/2007-12/2014 | Datastream |
Table 2. Portfolio variances of all considered portfolio strategies.
Dataset | 500 CRSP | 100 CRSP | S&P 500 | FF-100 | FF48 |
Model 1 | 0.00049 | 0.00109 | 0.00060 | 0.00098 | 0.00119 |
Model 2 | 0.00042 | 0.00102 | 0.00052 | 0.00091 | 0.00111 |
1/N | 0.00172 | 0.00168 | 0.00179 | 0.00208 | 0.00232 |
MINC | 0.00094 | 0.00139 | 0.00108 | 0.00142 | 0.00141 |
NC1V | 0.00081 | 0.00119 | 0.00078 | 0.00121 | 0.00129 |
NC2V | 0.00073 | 0.00121 | 0.00084 | 0.00125 | 0.00132 |
NCFV | 0.00070 | 0.00123 | 0.00087 | 0.00120 | 0.00125 |
CC-Minvar | 0.00072 | 0.00113 | 0.00082 | 0.00102 | 0.00120 |
Table 3. Out-of-sample Sharpe ratio of the portfolio strategies.
Dataset | 500 CRSP | 100 CRSP | S&P 500 | FF-100 | FF48 |
Model 1 | 0.4278 | 0.4460 | 0.4314 | 0.3998 | 0.3146 |
Model 2 | 0.4636 | 0.4548 | 0.4568 | 0.4024 | 0.3220 |
1/N | 0.3102 | 0.3358 | 0.3586 | 0.2808 | 0.2524 |
MINC | 0.3882 | 0.3649 | 0.3723 | 0.3142 | 0.2712 |
NC1V | 0.4001 | 0.4122 | 0.4055 | 0.3224 | 0.2922 |
NC2V | 0.4151 | 0.4212 | 0.4186 | 0.3522 | 0.2916 |
NCFV | 0.4063 | 0.4136 | 0.4028 | 0.3458 | 0.2806 |
CC-Minvar | 0.4042 | 0.4326 | 0.4101 | 0.3875 | 0.3206 |
Table 4. Turnover of the portfolio strategies.
Dataset | 500 CRSP | 100 CRSP | S&P 500 | FF-100 | FF48 |
Model 1 | 0.4028 | 0.3124 | 0.4120 | 0.3068 | 0.2580 |
Model 2 | 0.4145 | 0.3182 | 0.4166 | 0.3022 | 0.2528 |
1/N | 0.0625 | 0.0445 | 0.0586 | 0.0508 | 0.0324 |
MINC | 0.3125 | 0.2025 | 0.4030 | 0.2221 | 0.1822 |
NC1V | 0.6654 | 0.4670 | 0.6208 | 0.5308 | 0.2822 |
NC2V | 0.6022 | 0.4249 | 0.6030 | 0.5421 | 0.3168 |
NCFV | 0.5948 | 0.4132 | 0.5870 | 0.5134 | 0.2762 |
CC-Minvar | 0.3542 | 0.2802 | 0.3980 | 0.2632 | 0.2356 |
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