基于蒙特卡洛小波去噪的股票投资组合风险优化研究
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摘要
股票投资是我国重要的投资形式之一,但是从股票市场到投资者的个人投资决策都充斥着干扰和噪声。传统的随机矩阵理论(RMT)对证券投资组合风险优化产生了显著效果,然而RMT的去噪效果会随着组合证券数量的减少而下降,同时RMT仅仅是对证券收益协方差矩阵进行去噪,所以存在着一定局限性。从马科维茨(Markowitz)投资组合风险优化模型出发,基于小波分析视角讨论了蒙特卡洛模拟与小波去噪应用在投资组合风险优化上的可行性,并构造了蒙特卡洛小波去噪算法(MWF)。运用上海证券交易所A股股票交易数据进行实证分析,对比了传统的蒙特卡洛RMT(MKR)去噪方法、传统的RMT去噪法(LCPB、PG+和KR)以及单纯的Markowitz模型在股票投资组合上的风险优化效果。实证结果表明,蒙特卡洛小波去噪法在股票投资组合风险优化方面表现更好,并提供了一种新的股票投资组合配置方式。
Stock investment is one of the most important investment forms in China. Nevertheless,it is filled with interference and noise in the procedure from stock's market to individual investment decision. The traditional method,random matrix theory(RMT),plays a critical role in risk optimization of stock portfolio,but the de-noising effect of RMT is deteriorating as the number of portfolio reducing. At the same time,RMT only can filter on securities revenue covariance matrix. Consequently,to some extent,there are many limitations. This paper discussed the feasibility of Monte Carlo simulation and wavelet filtering that applied in investment risk optimization from the Markowitz portfolio risk optimization model,based on wavelet analysis perspective. Then it designed the filtering method of wavelet using Monte Carlo simulation(MWF). By using the A shares stock exchange data of Shanghai stock exchange,it conducted the empirical analysis to compared with the risk optimization effect of traditional Monte Carlo RMT(MKR) filtering method,traditional RMT filtering method(LCPB,PG + and KR) and simple Markowitz model in the stock investment. The empirical result shows that the filtering method of wavelet using Monte Carlo simulation performs better and provides a new configuration method in terms of stock portfolio risk optimization.
Stock investment is one of the most important investment forms in China. Nevertheless,it is filled with interference and noise in the procedure from stock's market to individual investment decision. The traditional method,random matrix theory(RMT),plays a critical role in risk optimization of stock portfolio,but the de-noising effect of RMT is deteriorating as the number of portfolio reducing. At the same time,RMT only can filter on securities revenue covariance matrix. Consequently,to some extent,there are many limitations. This paper discussed the feasibility of Monte Carlo simulation and wavelet filtering that applied in investment risk optimization from the Markowitz portfolio risk optimization model,based on wavelet analysis perspective. Then it designed the filtering method of wavelet using Monte Carlo simulation(MWF). By using the A shares stock exchange data of Shanghai stock exchange,it conducted the empirical analysis to compared with the risk optimization effect of traditional Monte Carlo RMT(MKR) filtering method,traditional RMT filtering method(LCPB,PG + and KR) and simple Markowitz model in the stock investment. The empirical result shows that the filtering method of wavelet using Monte Carlo simulation performs better and provides a new configuration method in terms of stock portfolio risk optimization.
引文
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[14]唐晓清,白延琴,刘念祖.基于随机矩阵理论的Markowitz组合投资模型[J].上海大学学报:自然科学版,2013,19(3):293-297.
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[17]刘柏年,皇群博,张卫民,等.集合背景误差方差中小波阈值去噪方法研究及试验[J].物理学报,2017,66(2):89-97.
[18]吴光文,王昌明,包建东,等.基于自适应阈值函数的小波阈值去噪方法[J].电子与信息学报,2014,36(6):1340-1347.
[19]王向红,尹东,胡宏伟,等.基于小波包和独立分量分析的微弱多源故障声发射信号分离[J].上海交通大学学报,2016,50(5):757-763.
[20]李力,倪松松.基于改进小波去噪预处理和EEMD的采煤机齿轮箱故障诊断[J].中南大学学报:自然科学版,2016,47(10):3394-3400.
[21]钟建军,宋健,由长喜,等.基于信噪比评价的阈值优选小波去噪法[J].清华大学学报:自然科学版,2014,54(2):259-263.
[22]刘向丽,王旭朋.基于小波分析的股指期货高频预测研究[J].系统工程理论与实践,2015,35(6):1425-1432.
[23]王帅,谢赤.基于小波CCC-GARCH模型的融资融券交易与证券市场波动率关系研究[J].财经理论与实践,2016,37(6):47-52.
[24]姚卫东,王瑞君.结构分解视角下股市波动与政策事件关系的实证研究——基于EEMD算法[J].上海经济研究,2016(1):71-80.
[25]张东祥,刘英顺.盈余、资产质量与银行股价预测力——基于中国16家上市银行的实证检验[J].金融论坛,2017(1):56-66,80.
[2]Kalayci C B,Ertenlice O,Akyer H,et al.An artificial bee colony algorithm with feasibility enforcement and infeasibility toleration procedures for cardinality constrained portfolio optimization[J].Expert Systems with Applications,2017,85(11):61-75.
[3]Nalpas N,Simar L,Vanhems A.Portfolio selection in a multi-moment setting:a simple Monte-Carlo-FDH algorithm[J].European Journal of Operational Research,2017,263(1):308-320.
[4]杨建辉,江文婷.基于PSO的考虑完整费用的证券组合优化研究[J].计算机应用研究,2010,27(9):3364-3367.
[5]李国成,肖庆宪.基数约束投资组合问题的一种混合元启发式算法求解[J].计算机应用研究,2013,30(8):2292-2297.
[6]刘晓勇.基于引力搜索算法的证券投资组合问题研究[J].计算机应用研究,2014,31(11):3243-3246.
[7]Daly J,Crane M,Ruskin H J.Random matrix theory filters in portfolio optimization:a stability and risk assessment[J].Physical A:Statistical Mechanics and Its Applications,2008,387(16/17):4248-4260.
[8]Daly J,Crane M,Ruskin H J.Random matrix theory filters and currency portfolio optimization[J].Journal of Physics:Conference Series,2010,221(1):1-14.
[9]Laloux L,Cizeau P,Potters M,et al.Random matrix theory and financial correlations[J].International Journal of Theoretical and Applied Finance,2000,3(3):391-397.
[10]Plerou V,Gopikrishnan P,Rosenow B,et al.Random matrix approach to cross correlations in financial data[J].Physical Review E:Statistical Nonlinear&Soft Matter Physics,2002,65(6):1-6.
[11]Sharifi S,Crane M,Shamaie A,et al.Random matrix theory for portfolio optimization:a stability approach[J].Physica A:Statistical Mechanics and Its Applications,2004,335(3):629-643.
[12]Tang Lichun,Chen Yanan.Noise dressing of ECM and investment portfolio selection based on RMT in China financial market[C]//Proc of International Conference on Management&Service Science.Piscataway,NJ:IEEE Press,2010:1-4.
[13]惠晓峰,李冰娜.基于随机矩阵理论决定多元GARCH模型最佳维度研究[J].运筹与管理,2011,20(4):141-148.
[14]唐晓清,白延琴,刘念祖.基于随机矩阵理论的Markowitz组合投资模型[J].上海大学学报:自然科学版,2013,19(3):293-297.
[15]韩华,吴翎燕,宋宁宁.基于随机矩阵的金融网络模型[J].物理学报,2014,63(13):1-10.
[16]李冰娜,惠晓峰,李连江.基于蒙特卡洛RMT去噪法小股票组合风险优化研究[J].管理科学,2016,29(2):134-136.
[17]刘柏年,皇群博,张卫民,等.集合背景误差方差中小波阈值去噪方法研究及试验[J].物理学报,2017,66(2):89-97.
[18]吴光文,王昌明,包建东,等.基于自适应阈值函数的小波阈值去噪方法[J].电子与信息学报,2014,36(6):1340-1347.
[19]王向红,尹东,胡宏伟,等.基于小波包和独立分量分析的微弱多源故障声发射信号分离[J].上海交通大学学报,2016,50(5):757-763.
[20]李力,倪松松.基于改进小波去噪预处理和EEMD的采煤机齿轮箱故障诊断[J].中南大学学报:自然科学版,2016,47(10):3394-3400.
[21]钟建军,宋健,由长喜,等.基于信噪比评价的阈值优选小波去噪法[J].清华大学学报:自然科学版,2014,54(2):259-263.
[22]刘向丽,王旭朋.基于小波分析的股指期货高频预测研究[J].系统工程理论与实践,2015,35(6):1425-1432.
[23]王帅,谢赤.基于小波CCC-GARCH模型的融资融券交易与证券市场波动率关系研究[J].财经理论与实践,2016,37(6):47-52.
[24]姚卫东,王瑞君.结构分解视角下股市波动与政策事件关系的实证研究——基于EEMD算法[J].上海经济研究,2016(1):71-80.
[25]张东祥,刘英顺.盈余、资产质量与银行股价预测力——基于中国16家上市银行的实证检验[J].金融论坛,2017(1):56-66,80.