一个基于BL模型和复杂网络的行业配置模型

doi:10.16381/j.cnki.issn1003-207x.2021.0382

Abstract

Abstract:

Industrial allocation is one of the indispensable steps in portfolio investment process. The traditional allocation models of industry ignores the overall correlation of the industry network. Based on the Black-Litterman （BL） model （the predictive values of machine learning and time series models are subjective points of view） in industrial allocation together with complex network theory， a graphical presentation of the BL model is proposed， the mathematical relation between the optimal portfolio of the BL model and the graphical presentation is proved and the corresponding empirical analysis is done. Then an industry allocation model is proposed， named BL+Network model. The model perfects the application framework of complex network method in “top-down” portfolio management. Empirical comparison with some traditional models finds that BL+Network model improves evidently Sharpe ratio and gain-loss ratio， industries whose eigenvector centrality degree are in near of the median sequence number should be allocated more， but fewer industries is not always better. This research provides a new perspective for asset allocation study， and extends the cross application of BL model and complex network method to portfolio management.

Key words: complex network, BL+Network model, eigenvector centrality degree

CLC Number:

F830

Zhongfei Li,Qi Zhou. An Industry Allocation Model Based on BL Model and Complex Network[J]. Chinese Journal of Management Science, 2024, 32(4): 1-13.

Figures/Tables 15

变量	含义	矩阵维度	变量	含义	矩阵维度
$E (r) B L$	期望收益率向量	$n × 1$	$Ω$	主观观点的信心误差矩阵	$k × k$
$τ$	调整系数	$1 × 1$	$Π$	市场均衡收益率	$n × 1$
$ω e q$	资产的市值权重	$n × 1$	$Q$	主观观点收益矩阵	$k × 1$
$P$	投资者主观观点矩阵	$k × n$	$Σ$	历史收益率的协方差矩阵	$n × n$

变量	$ω B L (G A R C H)$	$ω B L (M A)$	$ω B L (S V M)$
$v i$	-0.0152 (-2.41)^**	-0.0143 (-3.85)^***	-0.0152 (-2.96)^***
$S R i$	0.4728 (3.29)^***	0.3679 (4.25)^***	0.3622 (3.47)^***
N	336	336	336
$R 2$	0.169	0.226	0.184

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时间	1/N模型	MV模型	Min-V模型	BL(GARCH)模型	BL(MA)模型	BL(SVM)模型
2017-04	-0.0351	-0.09004	-0.05681	-0.0316	-0.02336	-0.02674
2017-05	-0.0469	-0.0509	0.068128	-0.0428	-0.01639	-0.04011
2017-06	0.0432	0.050526	0.217576	0.0490	0.039031	0.047659
2017-07	0.0113	0.155548	0.076737	0.0276	0.028705	0.031279
2017-08	0.029	0.004552	-0.04298	0.0313	0.038751	0.03283
2017-09	0.0142	-0.1745	0.012375	0.0176	0.015803	0.01811
2017-10	0.004	0.083156	0.074148	0.0134	0.009781	0.008235
2017-11	-0.0355	-0.47025	0.083917	-0.0340	-0.03495	-0.03299
2017-12	-0.005	-0.03433	-0.04684	-0.0023	0.000196	-0.00133
2018-01	0.0105	0.100866	0.150276	0.0144	0.012852	0.012724
2018-02	-0.0431	-0.04685	-0.04539	-0.0436	-0.0155	-0.04014
2018-03	-0.0307	0.04185	-0.46597	0.0165	0.020901	0.0161
平均收益率	-0.0070	-0.03586	0.002098	0.0013	0.0063	0.0021
夏普比率	-0.2314	-0.2187	0.0123	0.0408	0.2581	0.0704
方差	0.000917	0.026894	0.02905	0.000998	0.000599	0.00092

Strategy	Average Returns	Sharpe Ratio	Omega	Variance
Tradition
1/N	-0.00701	-0.2314	0.5716	0.000917
BL(GARCH)	0.001289629	0.0408	0.5239	0.000997594
BL(MA)	0.006319	0.2581	1.8407	0.000599
BL(SVM)	0.0021342	0.0704	0.5415	0.000919635
1/N+Network
1/N- MidC	0.001721157	0.0564	1.1388	0.000930666
1/N- LowC	-0.008525509	-0.3277	0.4288	0.000676746
1/N- HighC	-0.003056117	-0.098	0.7768	0.000972405
1/N-HSR	-0.004946272	-0.1792	0.5874	0.000802374
BL+Network
BL(GARCH )-MidC	0.00518347	0.15	0.5925	0.001193866
BL(GARCH)- LowC	0.004308787	0.0856	0.551	0.002531251
BL(GARCH) -HighC	-0.004333741	-0.0723	0.4557	0.003595042
BL(GARCH)-HSR	0.001305736	0.03056	0.4938	0.003078329
BL(MA)-MidC	0.024765016	0.5466	4.2366	0.002052442
BL(MA)-LowC	0.013375332	0.3654	0.7218	0.001340048
BL(MA)-HighC	0.004961713	0.0978	0.5625	0.002572639
BL(MA)-HSR	0.00812953	0.1972	0.6146	0.001973671
BL(SVM) -MidC	0.004373806	0.1311	0.5818	0.001113676
BL(SVM)-LowC	0.004095918	0.0871	0.5535	0.002212517
BL(SVM)-HighC	6.70765E-05	0.001	0.5007	0.004228955
BL(SVM)-HSR	0.001539855	0.0274	0.0516	0.002965301

Strategy	Average Returns	Sharpe Ratio	Omega	Variance
Strategy of 1/N in Network
1/N-MidC-9	0.001721	0.0564	1.13884	0.000930666
1/N-MidC-7	0.005087	0.148	1.417339	0.001180472
1/N-MidC-5	0.00835	0.2065	1.656672	0.00163459
Strategy of BL in Network
BL(MA)-MidC-9	0.024765	0.5466	4.236592	0.002052442
BL(MA)-MidC-7	0.027959	0.64	6.103315	0.001908212
BL(MA)-MidC-5	0.020599	0.5177	4.726464	0.001584634

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An Industry Allocation Model Based on BL Model and Complex Network

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