Black-Litterman模型的参数优化及其在行业资产配置中的应用
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摘要
针对Black-Litterman模型中投资者观点的量化问题,运用梯度提升回归树(gradient boosting regression tree,GBRT)算法对收益率进行预测,将预测值作为观点收益的替代变量,算法迭代收敛时的均方误差作为观点误差。采用上证380的10个行业指数数据检验文中提出的参数优化方法的有效性及合理性。结果表明,结合GBRT算法的Black-Litterman模型的投资绩效优于市场策略和Markowitz模型。
For the problem of the quantification of investor views in the Black-Litterman model,this paper proposes to use gradient boosting regression tree(GBRT)algorithm to predict the returns,regarding the predictive values as view returns and take the mean square errors when the algorithm converges iteratively as the view errors.The data of Shanghai 380 industry index are used to test the validity and rationality of the parameter optimization method proposed in this paper.Results show that the investment performance of Black-Litterman model combined with GBRT algorithm outperforms the market strategy and Markowitz model.
For the problem of the quantification of investor views in the Black-Litterman model,this paper proposes to use gradient boosting regression tree(GBRT)algorithm to predict the returns,regarding the predictive values as view returns and take the mean square errors when the algorithm converges iteratively as the view errors.The data of Shanghai 380 industry index are used to test the validity and rationality of the parameter optimization method proposed in this paper.Results show that the investment performance of Black-Litterman model combined with GBRT algorithm outperforms the market strategy and Markowitz model.
引文
[1]MARKOWITZ H.Portfolio selection[J].Journal of Finance,1952,7(1):77-91.
[2]BLACK F,LITTERMAN R.Global portfolio optimization[J].Financial Analysts Journal,1992,48(5):28-43.
[3]MEUCCI A.Beyond Black-Litterman in practice:a five-step recipe to input views on non-normal markets[M].New York:Social Science Electronic Publishing,2005:119-124.
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[6]NORELL J,DOVE E.Black-Litterman portfolio allocation stability and financial performance with MGARCH-M derived views[D].Sikanna,sweden:Lund University,2016.
[7]ECHAUST K,PIASECKI K.Black-Litterman model with intuitionistic fuzzy posterior return[J].The IEBInternational Journal of Finance,2017,15(1):8-19.
[8]温琪,陈敏,梁斌.基于Black-Litterman框架的资产配置策略研究[J].数理统计与管理,2011,30(4):741-751.WEN Qi,CHEN Min,LIANG Bin.The study of asset allocation strategy based on Black-Litterman framework[J].Journal of Applied Statistics and Management,2011,30(4):741-751.(in Chinese)
[9]孟勇.对Black-Litterman模型加入主观收益方法的改进[J].统计研究,2012,29(2):94-99.MENG Yong.The improvement of Black-Litterman model containing subjective returns method[J].Statistical Research,2012,29(2):94-99.(in Chinese)
[10]符永健,程希骏,刘峰.基于量化观点和Black-Litterman模型的期货投资组合[J].中国科学院大学学报,2014,31(4):570-575.FU Yongjian,CHENG Xijun,LIU Feng.The futures portfolio research based on the quantitatives and BlackLitterman model[J].Journal of University of Chinese Academy of Sciences,2014,31(4):570-575.(in Chinese)
[11]苏展辉.机构投资者基于Black-Litterman模型的资产配置研究[D].北京:对外经济贸易大学,2014.SU Zhanhui.Asset allocation of institutional investors based on Black-Litterman model[D].Beijing:University of International Business and Economics,2014.(in Chinese)
[12]李知常.基于Black-Litterman模型的资产配置策略研究[D].济南:山东大学,2017.LI Zhichang.Asset allocation strategies based on BlackLitterman model[D].Jinan:Shandong University,2017.(in Chinese)
[13]WEI S.Optimal and actual portfolio choices[D].Dekalb America:Northern Illinois University,2012.
[14]FRIEDMAN J H.Stochastic gradient boosting[J].Computatianal Statistics&Data Analysis,2002,38(4):367-378.
[15]游皓麟.R语言预测实战[M].北京:电子工业出版社,2016:308-320.YOU Haolin.Predictive action with R[M].Beijing:Publishing House of Electronics Industry,2016:308-320.(in Chinese)
[2]BLACK F,LITTERMAN R.Global portfolio optimization[J].Financial Analysts Journal,1992,48(5):28-43.
[3]MEUCCI A.Beyond Black-Litterman in practice:a five-step recipe to input views on non-normal markets[M].New York:Social Science Electronic Publishing,2005:119-124.
[4]BEACH S L,ORLOV A G.An application of the Black-Litterman model with EGARCH-M derived views for international portfolio management[J].Financial Markets&Portfolio Management,2007,21(2):147-166.
[5]SIMONIAN J,DAVIS J.Incorporating uncertainty into the Black-Litterman portfolio selection model[J].Applied Economics Letters,2011,18(17):1719-1722.
[6]NORELL J,DOVE E.Black-Litterman portfolio allocation stability and financial performance with MGARCH-M derived views[D].Sikanna,sweden:Lund University,2016.
[7]ECHAUST K,PIASECKI K.Black-Litterman model with intuitionistic fuzzy posterior return[J].The IEBInternational Journal of Finance,2017,15(1):8-19.
[8]温琪,陈敏,梁斌.基于Black-Litterman框架的资产配置策略研究[J].数理统计与管理,2011,30(4):741-751.WEN Qi,CHEN Min,LIANG Bin.The study of asset allocation strategy based on Black-Litterman framework[J].Journal of Applied Statistics and Management,2011,30(4):741-751.(in Chinese)
[9]孟勇.对Black-Litterman模型加入主观收益方法的改进[J].统计研究,2012,29(2):94-99.MENG Yong.The improvement of Black-Litterman model containing subjective returns method[J].Statistical Research,2012,29(2):94-99.(in Chinese)
[10]符永健,程希骏,刘峰.基于量化观点和Black-Litterman模型的期货投资组合[J].中国科学院大学学报,2014,31(4):570-575.FU Yongjian,CHENG Xijun,LIU Feng.The futures portfolio research based on the quantitatives and BlackLitterman model[J].Journal of University of Chinese Academy of Sciences,2014,31(4):570-575.(in Chinese)
[11]苏展辉.机构投资者基于Black-Litterman模型的资产配置研究[D].北京:对外经济贸易大学,2014.SU Zhanhui.Asset allocation of institutional investors based on Black-Litterman model[D].Beijing:University of International Business and Economics,2014.(in Chinese)
[12]李知常.基于Black-Litterman模型的资产配置策略研究[D].济南:山东大学,2017.LI Zhichang.Asset allocation strategies based on BlackLitterman model[D].Jinan:Shandong University,2017.(in Chinese)
[13]WEI S.Optimal and actual portfolio choices[D].Dekalb America:Northern Illinois University,2012.
[14]FRIEDMAN J H.Stochastic gradient boosting[J].Computatianal Statistics&Data Analysis,2002,38(4):367-378.
[15]游皓麟.R语言预测实战[M].北京:电子工业出版社,2016:308-320.YOU Haolin.Predictive action with R[M].Beijing:Publishing House of Electronics Industry,2016:308-320.(in Chinese)