A generalized approach to sparse and stable portfolio optimization problem

Zhifeng Dai; Fenghua Wen

doi:10.3934/jimo.2018025

Article Contents

2018, Volume 14, Issue 4: 1651-1666. Doi: 10.3934/jimo.2018025

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A generalized approach to sparse and stable portfolio optimization problem

Zhifeng Dai^1, and
Fenghua Wen^2,3, ,

1.
College of Mathematics and Statistics, Changsha University of Science and Technology, Hunan 410114, China
2.
College of business, Central South University, Hunan 410083, China
3.
Supply Chain and Logistics Optimization Research Centre, Faculty of Engineering, University of Windsor, Windsor, ON, Canada

* Corresponding author: Fenghua Wen
* Corresponding author: Fenghua Wen

Received: July 31, 2017

Early access: January 2018

Published: October 2018

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Abstract

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.

Keywords:

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

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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

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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

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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

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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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