序列相关性在资产组合绩效改善中的作用
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摘要
均值-方差理论是资产组合领域的经典理论之一,由于参数估计的不确定性,均值-方差最优风险组合在样本外检验中绩效较差。因此,构建估计误差更小的估计值成为资产组合领域的重点问题,现有方法主要从改善期望收益、协方差和利用边际信息来减少估计误差。研究证券收益间的序列相关性在改善投资组合样本外绩效的作用。首先,将序列相关性引入资产组合构建过程中,以改进均值-方差最优风险组合,利用向量自回归模型挖掘序列相关性,并对证券收益的期望收益估计进行改进,实证检验向量自回归模型是否能够提高资产组合的样本外绩效。其次,针对改进后的均值-方差组合绩效不稳定和换手率较高的缺点,利用收缩估计的思想联合均值改善组合和简单分散化组合,给出最优收缩强度的估计值,从理论和实证两个方面说明新提出的资产组合对资产组合绩效的改进效果。最后,在1997年至2015年中国A股市场的4组数据集上进行实证检验,比较14种投资组合的样本外绩效。研究结果表明,序列相关性有助于改善股票组合的样本外绩效。(1)向量自回归模型预测值的均值-方差组合取得了比样本均值的均值-方差组合更好的样本外绩效,向量自回归模型预测值比历史样本均值更适合作为资产期望收益的估计值。(2)收缩估计组合在样本外框架中取得了更加稳健的结果,在所有的数据集上都取得了高于简单分散化组合的确定性等价收益,最优收缩强度估计值的分布情况也肯定了收缩估计方法在减少资产组合估计误差中的有效性。向量自回归模型和收缩估计方法有助于市场参与主体更好地认识和分析参数不确定性的影响,对于缓解参数不确定性的影响、减少估计误差、提高投资者的效用具有一定的参考意义,更好地利用序列相关性得到显式解是未来可能的研究方向。
Mean-variance theory is one of the classic theories in the portfolio selection field. Due to parameter uncertainty,meanvariance optimal portfolio performs not better than expected in out-of-sample evaluation. Therefore,reducing estimation error in portfolio selection has become a hot topic in the field of portfolio selection. Existing methods mainly reduce the estimation error via improving the estimation of expected return and covariance matrix and utilizing side information in the process of portfolio selection.This paper studies the effect of serial dependence of stock returns on improving portfolio's out-of-sample performance. First,this study introduces serial dependence into portfolio selection so as to improve the mean estimation in mean-variance portfolio selection model. To exploit the serial dependence,we apply vector auto-regression( VAR) model and empirical evaluate whether VAR model could improve portfolio' s out-of-sample performance. Compared with other linear models,VAR could exploit both auto-correlation and cross-sectional correlation among stocks returns,which contributes to the reduction of estimation error in stocks' expected return. Second,to moderate the unstable performance and higher turnover of improved portfolio,this study applies shrinkage method to combine the mean-improved portfolio and equally weighted portfolio,gives an estimator of the optimal shrinkage,and theoretically and empirically analyzes the shrinkage portfolios' improvement on the out-of-sample performance. Finally,to validate the effectiveness of serial dependence on improving portfolios' out-of-sample performance,this study compares the out-of-sample performance of 14 representative portfolios on Chinese A-share stock market from 1997 to 2015.Empirical results show that serial dependence does improve the out-of-sample performance on A-share stock portfolios.First,mean-variance portfolio based on VAR's prediction outperforms sample mean based mean-variance portfolio in an out-ofsample framework,which suggests that VAR prediction is a better estimator of expected return than sample mean. Second,outof-sample results show that portfolio based on shrinkage estimator could achieve more robust performance and yield higher certain equivalent return. Distributions of optimal shrinkage estimators also suggest that shrinkage method could reduce portfolio' s estimation error. All these findings confirm the value of mean-variance portfolio in portfolio selection.To exploit serial dependence,VAR model and shrinkage estimation method have been applied to portfolio selection,which could help market participants understand the influence of parameter uncertainty. This provides a meaningful model to alleviate the parameter uncertainty,reduce the estimation error in portfolio selection and enhance investor's utility in practice. The exploitation of serial dependence with more accurate model and closed form solutions may serve as research directions in future.
Mean-variance theory is one of the classic theories in the portfolio selection field. Due to parameter uncertainty,meanvariance optimal portfolio performs not better than expected in out-of-sample evaluation. Therefore,reducing estimation error in portfolio selection has become a hot topic in the field of portfolio selection. Existing methods mainly reduce the estimation error via improving the estimation of expected return and covariance matrix and utilizing side information in the process of portfolio selection.This paper studies the effect of serial dependence of stock returns on improving portfolio's out-of-sample performance. First,this study introduces serial dependence into portfolio selection so as to improve the mean estimation in mean-variance portfolio selection model. To exploit the serial dependence,we apply vector auto-regression( VAR) model and empirical evaluate whether VAR model could improve portfolio' s out-of-sample performance. Compared with other linear models,VAR could exploit both auto-correlation and cross-sectional correlation among stocks returns,which contributes to the reduction of estimation error in stocks' expected return. Second,to moderate the unstable performance and higher turnover of improved portfolio,this study applies shrinkage method to combine the mean-improved portfolio and equally weighted portfolio,gives an estimator of the optimal shrinkage,and theoretically and empirically analyzes the shrinkage portfolios' improvement on the out-of-sample performance. Finally,to validate the effectiveness of serial dependence on improving portfolios' out-of-sample performance,this study compares the out-of-sample performance of 14 representative portfolios on Chinese A-share stock market from 1997 to 2015.Empirical results show that serial dependence does improve the out-of-sample performance on A-share stock portfolios.First,mean-variance portfolio based on VAR's prediction outperforms sample mean based mean-variance portfolio in an out-ofsample framework,which suggests that VAR prediction is a better estimator of expected return than sample mean. Second,outof-sample results show that portfolio based on shrinkage estimator could achieve more robust performance and yield higher certain equivalent return. Distributions of optimal shrinkage estimators also suggest that shrinkage method could reduce portfolio' s estimation error. All these findings confirm the value of mean-variance portfolio in portfolio selection.To exploit serial dependence,VAR model and shrinkage estimation method have been applied to portfolio selection,which could help market participants understand the influence of parameter uncertainty. This provides a meaningful model to alleviate the parameter uncertainty,reduce the estimation error in portfolio selection and enhance investor's utility in practice. The exploitation of serial dependence with more accurate model and closed form solutions may serve as research directions in future.
引文
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[2]徐佳,谭娅.中国家庭金融资产配置及动态调整.金融研究,2016(12):95-110.XU Jia,TAN Ya. The dynamic adjustment of Chinese households'financial asset allocation. Journal of Financial Research,2016(12):95-110.(in Chinese)
[3]吴卫星,丘艳春,张琳琬.中国居民家庭投资组合有效性:基于夏普率的研究.世界经济,2015,38(1):154-172.WU Weixing,QIU Yanchun,ZHANG Linwan. Efficiency of Chinese households'portfolio:a study based on Sharper ratio. The Journal of World Economy,2015,38(1):154-172.(in Chinese)
[4]陈永伟,史宇鹏,权五燮.住房财富、金融市场参与和家庭资产组合选择:来自中国城市的证据.金融研究,2015(4):1-18.CHEN Yongwei,SHI Yupeng,O Sub Kown. Housing wealth,financial market participation and household portfolio choice:evidence from China's urban districts. Journal of Financial Research,2015(4):1-18.(in Chinese)
[5] MARKOWITZ H. Portfolio selection. Journal of Finance,2012,7(1):77-91.
[6] DEMIGUEL V,GARLAPPI L,UPPAL R. Optimal versus naive diversification:how inefficient is the 1/N portfolio strategy?. Review of Financial Studies,2009,22(5):1915-1953.
[7] MEI X,DEMIGUEL V,NOGALES F J. Multi-period portfolio optimization with multiple risky assets and general transaction costs. Journal of Banking&Finance,2016,69:108-120.
[8]黄琼,朱书尚,姚京.投资组合策略的有效性检验:基于中国市场的实证分析.管理评论,2011,23(7):3-10,33.HUANG Qiong,ZHU Shushang,YAO Jing. Investment efficiency of portfolio strategies:an empirical study in China.Management Review,2011,23(7):3-10,33.(in Chinese)
[9]韩其恒,吴文生,曹志广.资产配置模型在中国资本市场真的有效吗?.经济管理,2016,38(3):124-134.HAN Qiheng,WU Wensheng,CAO Zhiguang. The performance of asset allocation models in Chinese capital market.Economic Management Journal,2016,38(3):124-134.(in Chinese)
[10] JEGADEESH N,TITMAN S. Returns to buying winners and selling losers:implications for stock market efficiency. Journal of Finance,1993,48(1):65-91.
[11] LO A W,MACKINLAY A C. When are contrarian profits due to stock market overreaction?. Review of Financial Studies,1990,3(2):175-205.
[12] LEVINE A,PEDERSEN L H. Which trend is your friend?.Financial Analysts Journal,2016,72(3):1-16.
[13]赵大萍,张超梁,房勇.基于贝叶斯理论的长、短数据资产组合选择.中国管理科学,2015,23(S1):504-509.ZHAO Daping,ZHANG Chaoliang,FANG Yong. Portfolio selection of unequal histories of returns with Bayesian tramework. Chinese Journal of Management Science,2015,23(S1):504-509.(in Chinese)
[14] ANDERSON E W,CHENG A R. Robust Bayesian portfolio choices. Review of Financial Studies,2016,29(5):1330-1375.
[15]朱微亮,刘海龙.稳健的动态资产组合模型研究.中国管理科学,2007,15(3):19-24.ZHU Weiliang,LIU Hailong. Robust portfolio of dynamic asset allocation. Chinese Journal of Management Science,2007,15(3):19-24.(in Chinese)
[16] DEMIGUEL V,NOGALES F J. Portfolio selection with robust estimation. Operations Research,2009,57(3):560-577.
[17]PLAZZI A,TOROUS W N,VALKANOV R I. Exploiting property characteristics in commercial real estate portfolio allocation.Journal of Portfolio Management,2011,37(5):39-50.
[18] BRANDT M W,SANTACLARA P,VALKANOV R. Parametric portfolio policies:exploiting characteristics in the crosssection of equity returns. Review of Financial Studies,2009,22(9):3411-3447.
[19] KEMPF A,KORN O,SABNING S. Portfolio optimization using forward-looking information. Review of Finance,2015,19(1):467-490.
[20] HJALMARSSON E,MANCHEV P. Characteristic-based meanvariance portfolio choice. Journal of Banking&Finance,2012,36(5):1392-1401.
[21] PSTOR L,STAMBAUGH R F. Comparing asset pricing models:an investment perspective. Journal of Financial Economics,2000,56(3):335-381.
[22] DEMIGUEL V,PLYAKHA Y,UPPAL R,et al. Improving portfolio selection using option-implied volatility and skewness. Journal of Financial and Quantitative Analysis,2013,48(6):1813-1845.
[23] YEN Y M. Sparse weighted-norm minimum variance portfolios. Review of Finance,2016,20(3):1259-1287.
[24] LEDOIT O,WOLF M. Honey,I shrunk the sample covariance matrix. Journal of Portfolio Management,2003,30(4):110-119.
[25] LEDOIT O,WOLF M. Nonlinear shrinkage estimation of largedimensional covariance matrices. The Annals of Statistics,2011,40(2):1024-1060.
[26] DEMIGUEL V,MARTIN-UTRERA A,NOGALES F J. Size matters:optimal calibration of shrinkage estimators for portfolio selection. Journal of Banking&Finance,2013,37(8):3018-3034.
[27] LEDOIT O,WOLF M. Spectrum estimation:a unified framework for covariance matrix estimation and PCA in large dimensions. Journal of Multivariate Analysis,2015,139:360-384.
[28] CHOPRA V K,ZIEMBA W T. The effect of errors in means,variances,and co-variances on optimal portfolio choice. The Journal of Portfolio Management,1993,19(2):6-11.
[29]赵树然,姜亚萍,任培民.高频波动率矩阵估计的比较分析:基于有噪非同步的金融数据.中国管理科学,2015,23(10):19-29.ZHAO Shuran,JIANG Yaping,REN Peimin. Comparing estimators of the high-frequency volatility matrix in the presence of the non-synchronous trading and market micristructure noise. Chinese Journal of Management Science,2015,23(10):19-29.(in Chinese)
[30]JORION P. Bayes-Stein estimation for portfolio analysis. Journal of Financial and Quantitative Analysis,1986,21(3):279-292.
[31] KAN R,ZHOU G F. Optimal portfolio choice with parameter uncertainty. Journal of Financial and Quantitative Analysis,2007,42(3):621-656.
[32] DEMIGUEL V,GARLAPPI L,NOGALES F J,et al. A generalized approach to portfolio optimization:improving performance by constraining portfolio norms. Management Science,2009,55(5):798-812.
[33] TU J,ZHOU G F. Markowitz meets Talmud:a combination of sophisticated and naive diversification strategies. Journal of Financial Economics,2011,99(1):204-215.
[34] DEMIGUEL V,NOGALES F J,UPPAL R. Stock return serial dependence and out-of-sample portfolio performance. Review of Financial Studies,2014,27(4):1031-1073.
[35]李爱忠,任若恩,董纪昌.基于集成预测的均值-方差-熵的模糊投资组合选择.系统工程理论与实践,2013,33(5):1116-1125.LI Aizhong,REN Ruoen,DONG Jichang. Mean-variance-entropy fuzzy portfolio selection based on integrated forecast.System Engineering-Theory&Practice,2013,33(5):1116-1125.(in Chinese)
[36]姜富伟,凃俊,RAPACH D E,等.中国股票市场可预测性的实证研究.金融研究,2011(9):107-121.JIANG Fuwei,TU Jun,RAPACH D E,et al. How predictable is the Chinese stock market?. Journal of Financial Research,2011(9):107-121.(in Chinese)
[37]尹力博,韩立岩.国际大宗商品资产行业配置研究.系统工程理论与实践,2014,34(3):560-574.YIN Libo,HAN Liyan. Study of international commodity assets industry allocation strategy. System Engineering-Theory&Practice,2014,34(3):560-574.(in Chinese)
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