图网络风险感知与稀疏低秩的组合管理策略

doi:10.16381/j.cnki.issn1003-207x.2021.0579

摘要/Abstract

摘要：

资产的联动性具有很强的网络特性，其风险的传染、蔓延由简单的单向驱动关系逐步演化为网络式的循环互动关系。将风险的传染和溢出纳入投资组合优化配置的框架，深入研究资产的波动集聚效应、风险的网络传播效应以及非线性叠加效应，可为规避投资风险和全面风险管理提供新的视角和思路。本文通过高维稀疏低秩算法和基于图网络结构的熵不确定性网络风险模型，深入挖掘资产特征和捕捉其间的相依关系，运用核范数多目标矩阵回归的动态跟踪策略和自适应权重学习方法对不确定性环境下的投资组合进行优化配置，最终获得非线性风险叠加和高维稀疏低秩优化下资产组合的最优投资策略。研究发现，基于图网络结构的熵不确定性风险链路预测模型可以有效捕捉资产之间的非线性叠加效应和发现潜在风险点，稀疏、低秩优化组合能够高效地对高维资产进行选择，更好地集中配置优质资产，风险收益的均衡性更合理，组合性能更具优势，鲁棒性更强。实证结论对全面风险管理、量化组合分析、指数基金投资和风险资产定价具有重要指导意义。

关键词: 高维稀疏网络, 全面风险管理, 低秩矩阵回归, 非负矩阵分解, 链路预测

Abstract:

The linkage of assets has strong network characteristics， and the contagion and spread of risks has gradually evolved from a simple one-way driving relationship to a network-like cyclical interaction relationship. Incorporating the contagion and spillover of risks into the framework of optimal allocation of investment portfolios， and studying the effects of asset volatility clustering and network spreading effects of risks， can provide a new perspective and thinking for avoiding investment risks and comprehensive risk management.Sparse low-rank algorithms and graph network structure-based entropy uncertainty risk models are used to dig deeper into asset characteristics and capture the dependencies between them. Then， using the dynamic tracking strategy of kernel-norm multi-objective matrix regression and adaptive weight learning method to optimize the allocation of portfolios in uncertain environments， the portfolios under nonlinear risk superposition and sparse low-rank optimization Strategy are obtained. It is found that the uncertainty risk model based on network structure entropy can effectively capture the non-linear superposition effect between assets， and the sparse， low-rank optimized portfolio can effectively select high-dimensional assets， and better focus on the allocation of high-quality assets. The income balance is more reasonable， the portfolio performance is more advantageous， and the robustness is stronger. The empirical conclusions have important guiding significance for comprehensive risk management， quantitative portfolio analysis， index fund investment， and risk asset pricing.

Key words: high-dimensional sparse network, comprehensive risk management, low-rank matrix regression, non-negative matrix factorization, link prediction

中图分类号:

F830

李爱忠,任若恩,董纪昌. 图网络风险感知与稀疏低秩的组合管理策略[J]. 中国管理科学, 2024, 32(4): 58-65.

Aizhong Li,Ruoen Ren,Jichang Dong. Graph Network Risk Perception and Sparse Low-rank Portfolio Management Strategy[J]. Chinese Journal of Management Science, 2024, 32(4): 58-65.

图/表 4

表1

核范数多目标回归算法"

核范数回归优化算法

输入：数据矩阵Y、X,最大迭代次数

k m a x

,初始化

? P 0 = E 0 = A 0 = B 0 = C 1, ? 0 = C 2, ? 0 = C 3, ? 0 = 0, ? μ 0 = 0.1, ? μ m a x = 107, ? ρ 0 = 1.01, ? = 10 - 4

for k=1 to $k m a x$ do

分别根据式(9)、式(12)、式(13)、式(16)，

更新 $A k + 1 、 B k + 1 、 E k + 1 、 P k + 1$ ;

更新 $C 1, k + 1 = C 1, k - μ k (Y - X B k + 1 - E k + 1)$ ;

$C 2, k + 1 = C 2, k - μ k B k + 1 - A k + 1$ ;

$C 3, k + 1 = C 3, k - μ k B k + 1 - P k + 1$ ;

更新 $μ k + 1 = m i n ? (ρ μ k, ? μ m a x)$ ;

if $Y - X B k + 1 - E k + 1 ∝ ≤ ?, B k + 1 - A k + 1 ∝ ≤ ?, B k + 1 - P k + 1 ∝ ≤ ?, E k + 1 - E k ∝ ≤ ?$

则返回 $B$ , 结束循环;否则, 返回进入下一循环；

end

输出：

? B

表1

表2

表3

不同组合性能的对比分析"

变量

图网络链路预测组合

均值-方差组合

等权组合

市值加权组合

γ

0.0183

(0.0477)

0.0132

(0.0701)

0.01122

(0.0511)

0.01104

(0.0556)

φ

1.6915^**

(0.1412)

1.1301^**

(0.2643)

1.2243^**

(0.3102)

0.9937^**

(0.2878)

α 0

0.0024^**

(0.2378)

0.0332

(0.2874)

0.0031^*

(0.2667)

0.0337

(0.2663)

α 1

0.1988^**

(0.2713)

0.0289

(0.3141)

0.2283^**

(0.3342)

0.0411

(0.2934)

β 1

0.6645^**

(0.6177)

0.7349

(0.6654)

0.7244^**

(0.6887)

0.8542

(0.7001)

表3

表4

组合归因分析"

因子组	$α$	$β$	$β 1$	$β 2$	$β 3$	$β 2 + β 3$	$R 2$
1	0.633^**	0.334^**	0.184^**				0.7033
1	(0.0011)	(0.0027)	(0.0058)				0.7033
2	0.588^**	0.359^**		-0.137^** (0.0050)			0.6738
2	(0.0049)	(0.0031)		-0.137^** (0.0050)			0.6738
3	0.588^**	0.376^**		-0.082^** (0.0055)	-0.211^** (0.0044)	-0.371	0.6195
3	(0.0041)	(0.0049)		-0.082^** (0.0055)	-0.211^** (0.0044)	-0.371	0.6195

表4

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样本选取	多目标	图网络链路预测组合	非链路预测组合
样本选取	多目标	单位风险收益	单位风险收益
	上证50、上证指数	1.7248 (0.0371)	1.1196 (0.0533)
	上证50、深圳成指	1.6112 (0.0483)	1.0327 (0.0615)
样本内	上证指数、深圳成指	1.5653 (0.0338)	1.2001 (0.0677)
	上证50、上证指数、深圳成指	1.4589 (0.0336)	1.0994 (0.0534)
	上证50、上证指数、深圳成指和沪深300	1.4123 (0.0378)	1.0088 (0.0441)
	上证50、上证指数	1.5995 (0.0303)	0.9445 (0.0437)
	上证50、深圳成指	1.5256 (0.0258)	0.9012 (0.0524)
样本外	上证指数、深圳成指	1.4887 (0.0288)	0.8791 (0.0503)
	上证50、上证指数、深圳成指	1.4015 (0.0255)	0.8325 (0.0423)
	上证50、上证指数、深圳成指和沪深300	1.3916 (0.0232)	0.7012 (0.0339)

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