Abstract：CVaR is an important risk measurement for portfolio investment. It is of great significance to select robust asset portfolio in a CVaR based model so as to reduce both the time cost on management and economic expenditure. Some studies have shown that the decision of asset portfolio under CVaR criterion can be transformed to a classical quantile regression. Motivated by this transformation, an adaptive Lasso quantile regression with a network structure is developed to select high-dimensional assets. Adaptive Lasso can impose a weighted constraint on the regression coefficients, theoretically presenting selection consistency. Network structure, which is constructed based on the complicated network theory, can reflect the complex dynamic relations among all the assets. It can also benefit to the model's variable selection performance. Computation is achieved by a linear programming method, and a two-step iterative approach is proposed to deal with some special computational problems for the CVaR portfolio investment decision. Simulation study under various scenarios shows that the proposed model performs best in terms of variable selection and prediction, and the advantage of network structure becomes more and more obvious with an increasing correlation between variables. An empirical study with 249 stocks is conducted. With a rolling regression technique, the proposed model presents great robustness and applicable significance.
王小燕, 姚佳含, 袁欣. 带网络结构的自适应Lasso分位数回归及其应用[J]. 系统工程理论与实践, 2019, 39(8): 1954-1965.
WANG Xiaoyan, YAO Jiahan, YUAN Xin. Adaptive Lasso quantile regression with network structure and its application. Systems Engineering - Theory & Practice, 2019, 39(8): 1954-1965.
[1] Artzner P, Delbaen F, Eber J M, et al. Thinking coherently[J]. Risk, 1997, 10(11):68-71. [2] Embrechts P, Kluppelberg S, Mikosch T. Extremal events in finance and insurance[M]. Berling:Springer Verlag, 1997. [3] Pflug G C. Some remarks on the value-at-risk and the conditional value-at-risk[M]. Boston:Springer, 2000. [4] Bassett Jr G W, Koenker R, Kordas G. Pessimistic portfolio allocation and Choquet expected utility[J]. Journal of Financial Econometrics, 2004, 2(4):477-492. [5] 许启发,周莹莹,蒋翠侠. 带有范数约束的CVaR高维组合投资决策[J]. 中国管理科学, 2017, 25(2):40-49. Xu Q F, Zhou Y Y, Jiang C X. CVaR based high dimensional portfolio selection under norm constraints[J]. Chinese Journal of Management Science, 2017, 25(2):40-49. [6] Fan J, Zhang J, Yu K. Vast Portfolio selection with gross-exposure constraints[J]. Journal of the American Statistical Association, 2012, 107(498):592-606. [7] 陈艺萍, 张信东, 史金凤. 零杠杆公司业绩研究[J]. 中国管理科学, 2016, 24(6):171-176. Chen Y P, Zhang X D, Shi J F. A research of debt-free firms' performance[J]. Chinese Journal of Management Science, 2016, 24(6):171-176. [8] Brodie J, Daubechies I, De Mol C, et al. Sparse and stable Markowitz portfolios[J]. Proceedings of the National Academy of Sciences, 2009, 106(30):12267-12272. [9] Fastrich B, Paterlini S, Winker P. Constructing optimal sparse portfolios using regularization methods[J]. Computational Management Science, 2015, 12(3):417-434. [10] 蒋翠侠,刘玉叶,许启发. 基于LASSO分位数回归的对冲基金投资策略研究[J]. 管理科学学报, 2016, 19(3):107-126. Jiang C X, Liu Y Y, Xu Q F. Hedge fund investment strategies based on LASSO quantile regression[J]. Journal of Management Sciences in China, 2016, 19(3):107-126. [11] 张金清, 李徐. 资产组合的集成风险度量及其应用——基于最优拟合Copula函数的VaR方法[J]. 系统工程理论与实践, 2008, 28(6):14-21. Zhang J Q, Li X. Portfolio integrated risk measurement and its application-VaR method based on goodness-of-fit copula functions[J]. Systems Engineering-Theory & Practice, 2008, 28(6):14-21. [12] 潘志远, 毛金龙, 周彬蕊. 高维的相关性建模及其在资产组合中的应用[J]. 金融研究, 2018(2):190-206. Pan Z Y, Mao J L, Zhou B R. Modeling high-dimensional correlation and its application to asset allocation[J]. Journal of Financial Research, 2018(2):190-206. [13] 王明哲. 基于Copula-VaR模型的资产组合风险研究[J]. 金融理论与实践, 2017(6):7-11. Wang M Z. Analysis of portfolio's value at risk based on Copula-VaR model[J]. Financial Theory & Practice, 2017(6):7-11. [14] 范国斌, 曾勇, 黄文光. 一种多资产组合风险度量解决之道:正则藤Copula[J]. 数量经济技术经济研究, 2013, 30(1):88-102. Fan G B, Zeng Y, Huang W G. A new approach for measuring the risk of portfolios with multiple assets[J]. The Journal of Quantitative & Technical Economics, 2013, 30(1):88-102. [15] Li C, Li H. Variable selection and regression analysis for graph-structured covariates with an application to genomics[J]. Annals of Applied Statistics, 2010, 4(3):1498-1516. [16] Huang J, Ma S, Li H, et al. The sparse Laplacian shrinkage estimator for high-dimensional regression[J]. Annals of Statistics, 2011, 39(4):2021-2046. [17] Wang X, Fang K, Zhang Q, et al. Network-incorporated integrative sparse linear discriminant analysis[J]. Statistics and Its Interface, 2019, 12(1):149-166. [18] 苏治,秦磊,方彤. 含有图结构约束的稀疏最小方差资产组合模型[J]. 中国管理科学, 2015, 23(9):65-70. Su Z, Qin L, Fang T. Spare minimum variance portfolio with graph structure penalty[J]. Chinese Journal of Management Science, 2015, 23(9):65-70. [19] 苏治,方彤,秦磊. 一种基于规则化方法的最优稀疏指数追踪模型设计[J]. 数量经济技术经济研究, 2016, 33(4):145-160. Su Z, Fang T, Qin L. A design of optimal index tracking models based on regularized methods[J]. The Journal of Quantitative & Technical Economics, 2016, 33(4):145-160. [20] 方匡南,范新妍,马双鸽. 基于网络结构Logistic模型的企业信用风险预警[J]. 统计研究, 2016, 33(4):50-55. Fang K N, Fan X Y, Ma S G. Forecasting of enterprise's credit risk based on network-logistic model[J]. Statistical Research, 2016, 33(4):50-55. [21] 肖琴. 复杂网络在股票市场相关分析中的应用[J]. 中国管理科学, 2016(S1):470-474. Xiao Q. Application of the complex network in stock market board analysis[J]. Chinese Journal of Management Science, 2016(S1):470-474. [22] 梁洪振, 姚洪兴, 姚晶晶. 基于双重度量的负相关股票复杂网络特性[J]. 系统工程, 2017(3):12-20. Liang H Z, Yao H X, Yao J J. Complex network characteristics of negative related stocks based on the dual measure[J]. Systems Engineering, 2017(3):12-20. [23] Belloni A, Chernozhukov V. L1-Penalized quantile regression in high-dimensional sparse models[J]. Annals of Statistics, 2009, 39(1):82-130. [24] Wu Y, Liu Y. Variable selection in quantile regression[J]. Statistica Sinica, 2009, 19(19):801-817. [25] Alhamzawi R, Yu K, Benoit D F. Bayesian adaptive Lasso quantile regression[J]. Statistical Modelling, 2011, 12(3):279-297. [26] Ciuperca G. Adaptive LASSO model selection in a multiphase quantile regression[J]. Statistics A:Journal of Theoretical & Applied Statistics, 2016(5):1100-1131. [27] Jiang Y. Double-Penalized quantile regression in partially linear models[J]. Open Journal of Statistics, 2015, 5(2):158-164. [28] Fan J, Li R. Variable selection via nonconcave penalized likelihood and its oracle properties[J]. Journal of the American Statistical Association, 2001, 96(456):1348-1360. [29] Ferguson T S. Mathematical statistics:A decision theoretic approach[M]. New York:Academic Press, 1967. [30] Steland A, Von Sachs R. Large-Sample approximations for variance-covariance matrices of high-dimensional time series[J]. Bernoulli, 2017, 23(4):2299-2329.
2019, Vol. 39 
