Two nonparametric approaches to mean absolute deviation portfolio selection model

Zhifeng Dai; Huan Zhu; Fenghua Wen

doi:10.3934/jimo.2019054

Article Contents

2020, Volume 16, Issue 5: 2283-2303. Doi: 10.3934/jimo.2019054

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Two nonparametric approaches to mean absolute deviation portfolio selection model

1.
College of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, China
2.
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha 410114, China
3.
Department of finance, College of business, Central South University, Hunan, 410083, China

^* Corresponding author: wfh@amss.ac.cn
^* Corresponding author: wfh@amss.ac.cn

Received: June 2018

Revised: December 2018

Early access: May 2019

Published: August 2020

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Abstract

In this paper, we apply two nonparametric approaches to mean absolute deviation (MAD) portfolio selection model. The first one is to use the nonparametric kernel mean estimation to replace the returns of assets with five different kernel functions. Then, we construct the nonparametric kernel mean estimation-based MAD portfolio model. The second one is to utilize the nonparametric kernel median estimation to replace the returns of assets with five different kernel functions. Then, we construct the nonparametric kernel median estimation-based MAD portfolio model. We also extend the two kinds of nonparametric approach to mean-Conditional Value-at-Risk portfolio model. Finally, we give the in-sample and out-of-sample analysis of the proposed strategies and compare the performance of the proposed models by using actual stock returns in Shanghai stock exchange of China. The experimental results show the nonparametric estimation-based portfolio models are more efficient than the original portfolio model.

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Mathematics Subject Classification: Primary: 90C30, 90C90; Secondary: 65k05.

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Figure 1. Comparision of efficient frontier of MAD portfolio models

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Figure 2. Efficient frontier of the MAD model based on the kernel median estimation

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Figure 3. Efficient frontier of the mean-CVaR portfolio models

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Figure 4. Efficient frontier of MAD models of kernel mean estimation under different kernel functions

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Figure 5. Efficient frontier of the mean-CVaR portfolio models of kernel mean estimation under different kernel functions

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Figure 6. Efficient frontier of MAD models of kernel median estimation under different kernel functions

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Figure 7. Efficient frontier of mean-CVaR models of kernel median estimation under different kernel functions

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Figure 8. Comparison betwen the daily return of Shanghai Composite Index and portfolio return of the MAD model

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Figure 9. Comparison betwen the daily return of Shanghai Composite Index and portfolio return of MAD model of kernel mean estimation

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Figure 10. Comparison betwen the daily return of Shanghai Composite Index and portfolio return of MAD of kernel median estimation

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Figure 11. Comparison betwen the daily return of Shanghai Composite Index and portfolio return of the mean-CVaR model

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Figure 12. Comparison betwen the daily return of Shanghai Composite Index and portfolio return of mean-CVaR model of kernel mean estimation

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Figure 13. Comparison betwen the daily return of Shanghai Composite Index and portfolio return of mean-CVaR of kernel median estimation

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Table 1. Descriptive Statistics of daily return of 20 stocks from Shanghai A shares

Stock nam	Number	Max	Min	Mean	Sd.	Skewness	Kurtosis
P.R.E.	600048	0.10038	-0.35544	0.00049	0.03308	-1.47313	22.2281
T.J.H.	600717	0.10025	-0.10029	0.00074	0.03040	-0.08191	5.4232
H.E.	600060	0.10035	-0.11024	0.00109	0.03355	-0.00870	5.15926
H.N.I.	600011	0.10050	-0.10036	0.00064	0.02654	-0.28255	7.6319
N.J.H.T.	600064	0.10028	-0.32864	0.00112	0.03146	-1.69324	20.8171
S.H.I.	600031	0.10066	-0.10042	0.00015	0.02843	-0.14598	6.8630
S.H.A.	600009	0.09996	-0.10007	0.00112	0.02464	-0.09756	7.3309
T.R.T.	600085	0.10022	-0.10016	0.00109	0.02834	-0.04908	6.7348
Ch.M.B.	600036	0.09571	-0.09914	0.00087	0.01999	0.44853	8.3975
Ch.S.	600150	0.10016	-0.10011	0.00101	0.03593	-0.04488	4.6552
Ch.U.	600050	0.10103	-0.10056	0.00096	0.02846	0.21470	6.7539
Sino.	600028	0.10035	-0.10040	0.00037	0.02138	-0.15015	8.9252
Ch.S.	600118	0.10027	-0.10009	0.00170	0.03683	-0.03555	4.7026
C.S.	600030	0.10043	-0.10012	0.00091	0.03038	0.23151	5.9787
C.S.M.	601098	0.10027	-0.10017	0.00120	0.02910	-0.14500	5.4879
Ch.L.I.	601628	0.10036	-0.10007	0.00095	0.02689	0.62490	6.7596
O.F.X.	600612	0.10010	-0.10006	0.00109	0.02811	0.29691	5.8163
C.Q.B.	600132	0.10027	-0.10699	0.00042	0.02841	-0.37571	6.9771
J.J.I.	600650	0.10037	-0.10018	0.00202	0.03929	0.20423	4.3077
Q.J.B.	600706	0.10028	-0.10024	0.00125	0.03459	-0.26875	4.7732

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Table 2. Descriptive statistics of daily return of Shanghai Composite Index

	Max	Min	average	sd	Skewness	Kurtosis
Shanghai S-I-R	0.04310	-0.07045	-0.00016	0.01566	-1.37612	8.38382

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