考虑投资者主观预期的资产组合最优化
|
摘要
资产配置理论是现代投资理论中的重要组成部分。通过稳健合理的资产配置,不仅可以增加投资者利润,而且可以有效规避投资风险。资产配置策略作为基金操作的基本原则,可以解释91.5%的基金回报率波动。因此,资产配置对于机构投资者,尤其是基金管理人提高投资绩效、分散并且降低投资风险都起着非常重要的作用。近几年,随着我国基金市场的迅猛发展,国内对资产配置模型研究的关注也越来越多
目前,由高盛资产管理公司正式提出的Black-Litterman资产配置模型在国际上有着广泛的应用。但由于绝大多数的金融时间序列具有尖峰、厚尾、有偏的特征,常拒绝金融资产正态分布的假设,各资产之间还有着时变相关性、聚类效应及预测误差的异方差效应等其他无法被正态分布所刻画的特征的原凶,原始的Black-Litterman模型已经不能很好地解决上述问题带来的估计缺陷。因此本文在运用原始的Black-Litterman进行优化配置的过程中,还同时引入了Copula函数和DCC多元Garch模型对这一问题进行修正。通过Copula理论的应用,抹平了投资者对未来资产收益看法的分布与市场先验隐含分布之间的差异,并放开了投资者观点与市场先验的正态分布假设;通过DCC-MVGARCH的应用,在联合衡量资产间聚类效应以及异方差效应的同时还考虑了变量间相关系数的时变特征。这两方面都是这一领域相关研究中尚未涉及的。
本文选取了我国GICS行业一级指数,完成了混合方法的BLCOP-DCC模型参数估计和业绩比较。实证结果表明,在有无卖空的两种情况下,都取得了高于Markowitz以及GICS行业综合指数、上证综指的收益率表现;组合的波动性小于Markowitz以及GICS行业综合指数。在卖空限制条件下,于2008年的下跌行情中,BLCOP-DCC配置相对于Markowitz组合具有经风险调整后的更小损失。从整体来看,混合方法的BLCOP-DCC模型是一种较为理想的策略。
Asset allocation is the most important part of modern investment theory. Through the stable and reasonable asset allocation, investors can not only earn more profit, but also effectively avoid investment risk. As funds' basic operation principle, asset allocation strategy can interpret 91.5% of their return. So, for institutional investors, especially for fund managers, asset allocation plays a very important role in increasing the investment performance as well as diversification of risk. In recent years, along with the rapid development of the fund market, the research of asset allocation model is paid more and more attention.
Nowadays, an asset allocation model of Black-Litterman formally proposed by Fischer Black and Robert Litterman (1991) of Goldman Sachs is widely used in the world. However most of financial time serials have the property of excess peakness, fat tails and skewness, they often reject normal distribution hypothesis. Also, there exist time varied correlation, volatility clustering and heteroscedasticity. The original Black-Litterman model cannot solve above problems properly. This paper attempts to use the original Black-Litterman model to estimate and optimize, and meanwhile we introduce the Copula methods and DCC-MVGARCH. The Copula can erase the discrepancy of investor's view distribution and the implied market prior distribution, while the DCC model can help with the volatility clustering, heteroscedasticity and time varied correlation jointly.
This paper adopts GICS industry index in China to conduct the Empirical Analysis. The conclusion shows that whether under the constraint of short sale or not, our method does achieve superior returns to Markowitz method and benchmark of GICS and SSE Composite Index. The volatility of our portfolio is smaller than other methods mentioned above. Under the constraint of short sale, our method "BLCOP-DCC" portfolio has the less loss than Markowitz in 2008. Overall, the blended method—BLCOP-DCC can be a more desirable strategy .
目前,由高盛资产管理公司正式提出的Black-Litterman资产配置模型在国际上有着广泛的应用。但由于绝大多数的金融时间序列具有尖峰、厚尾、有偏的特征,常拒绝金融资产正态分布的假设,各资产之间还有着时变相关性、聚类效应及预测误差的异方差效应等其他无法被正态分布所刻画的特征的原凶,原始的Black-Litterman模型已经不能很好地解决上述问题带来的估计缺陷。因此本文在运用原始的Black-Litterman进行优化配置的过程中,还同时引入了Copula函数和DCC多元Garch模型对这一问题进行修正。通过Copula理论的应用,抹平了投资者对未来资产收益看法的分布与市场先验隐含分布之间的差异,并放开了投资者观点与市场先验的正态分布假设;通过DCC-MVGARCH的应用,在联合衡量资产间聚类效应以及异方差效应的同时还考虑了变量间相关系数的时变特征。这两方面都是这一领域相关研究中尚未涉及的。
本文选取了我国GICS行业一级指数,完成了混合方法的BLCOP-DCC模型参数估计和业绩比较。实证结果表明,在有无卖空的两种情况下,都取得了高于Markowitz以及GICS行业综合指数、上证综指的收益率表现;组合的波动性小于Markowitz以及GICS行业综合指数。在卖空限制条件下,于2008年的下跌行情中,BLCOP-DCC配置相对于Markowitz组合具有经风险调整后的更小损失。从整体来看,混合方法的BLCOP-DCC模型是一种较为理想的策略。
Asset allocation is the most important part of modern investment theory. Through the stable and reasonable asset allocation, investors can not only earn more profit, but also effectively avoid investment risk. As funds' basic operation principle, asset allocation strategy can interpret 91.5% of their return. So, for institutional investors, especially for fund managers, asset allocation plays a very important role in increasing the investment performance as well as diversification of risk. In recent years, along with the rapid development of the fund market, the research of asset allocation model is paid more and more attention.
Nowadays, an asset allocation model of Black-Litterman formally proposed by Fischer Black and Robert Litterman (1991) of Goldman Sachs is widely used in the world. However most of financial time serials have the property of excess peakness, fat tails and skewness, they often reject normal distribution hypothesis. Also, there exist time varied correlation, volatility clustering and heteroscedasticity. The original Black-Litterman model cannot solve above problems properly. This paper attempts to use the original Black-Litterman model to estimate and optimize, and meanwhile we introduce the Copula methods and DCC-MVGARCH. The Copula can erase the discrepancy of investor's view distribution and the implied market prior distribution, while the DCC model can help with the volatility clustering, heteroscedasticity and time varied correlation jointly.
This paper adopts GICS industry index in China to conduct the Empirical Analysis. The conclusion shows that whether under the constraint of short sale or not, our method does achieve superior returns to Markowitz method and benchmark of GICS and SSE Composite Index. The volatility of our portfolio is smaller than other methods mentioned above. Under the constraint of short sale, our method "BLCOP-DCC" portfolio has the less loss than Markowitz in 2008. Overall, the blended method—BLCOP-DCC can be a more desirable strategy .
引文
[1]Brinson G P,Singer B D,Beebower G L.Determinants of portfolio performance Ⅱ:An update[J].Financial Analysts Journal.1991,47(3):40-48.
[2]Markowitz H.Portfolio selection[J].Journal of finance.1952:77-91.
[3]Black F.Asset allocation:combining investor views with market equilibrium[J].The Journal of Fixed Income.1991(9).
[4]Black F,Litterman R.Global portfolio optimization[J].Financial Analysts Journal.1992:28-43.
[5]Meucci A.Risk and asset allocation[M].Springer,2005.
[6]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 and Portfolio Management.2007,21(2):147-166.
[7]Bollerslev T,Engle R F,Wooldridge J M.A capital asset pricing model with time-varying covariances[J].The journal of political economy.1988,96(1):116.
[8]Engle R F,Kroner K F.Multivariate simultaneous generalized ARCH[J].Econometric Theory.1995:122-150.
[9]Baba Y,Engle R F,Kraft D F,et al.Multivariate simultaneous generalized ARCH[J].Unpublished manuscript,Department of Economics,University of California,San Diego.1991.
[10]Bera A K,Kim S W.Testing constancy of conditional correlation in Divariate GARCH model [Z].1996.
[11]Tse Y K.The conditional heteroscedasticity of the Yen-Dollar exchange rate[J].Journal of Applied Econometrics.1998,13(1).
[12]Cappiello L,Engle R F,Sheppard K.Asymmetric dynamics in the correlations of global equity and bond returns[J].Journal of Financial Econometrics.2006,4(4):537.
[13]Sklar A.Fonctions de repartition a n dimensions et leurs margesfZ].1959:8,229-231.
[14]Nelsen R.An introduction to copulas[M].New York:1998.
[15]Frees E W,Valdez E A.Understanding relationships using copulas[J].North American Actuarial Journal.1998(2):1-25.
[16]Embrechts P,Lindskog F,Mcneil A.Modelling dependence with copulas and applications to risk management J].Handbook of heavy tailed distributions in finance.2003(8):329-384.
[17]Li D X.On default correlation:a copula function approach[J].The Journal of Fixed Income.2000,9(4):43-54.
[18]De Matteis R.Fitting copulas to data[D].2001.
[19]Rockinger M,Jondeau E.Entropy densities with an application to autoregressive conditional skewness and kurtosis[J].Journal of Econometrics.2002,106(1):119-142.
[20]Forbes K J,Rigobon R.No contagion,only interdependence:Measuring stock market comovements[J].Journal of Finance.2002:2223-2261.
[21]Scaillet O,Fermanian J D.Nonparametric estimation of copulas for time series[J].Journal of Risk.2003(5):25-54.
[22]Embrechts P,F L,J M A.Modeling depedence with copulas and applications to risk management[Z].2001.
[23]Hu L.Dependence patterns across financial markets:a mixed copula approach[J].Applied Financial Economics.2006,16(10):717-729.
[24]Sharpe W F.Capital asset prices:A theory of market equilibrium under conditions of risk[J].Journal of finance.1964:425-442.
[25]Bevan A,Winkelmann K.Using the Black-Litterman global asset allocation model:three years of practical experience[R].,1998.
[26]He G,Litterman R.The intuition behind Black-Litterman model portfolios[R].Goldman Sachs Asset Management,1999.
[27]Lee W.Theory and methodology of tactical asset allocation[M].Wiley,2000.
[28]Satchell S,Scowcroft A,Studies J I O M.A demystification of the Black-Littermann model:managing quantitative and traditional portfolio construction[Z].Judge Institute of Management Studies,University of Cambridge,1997.
[29]Herold U.Portfolio construction with qualitative forecasts[J].Journal of Portfolio Management.2003(3).
[30]Idzorek T M.A step-by-step guide to the Black-Litterman model[Z].2003.
[31]Satchell S,Scowcroft A,Studies J I O M.A demystification of the Black-Littermann model:managing quantitative and traditional portfolio construction[Z].Judge Institute of Management Studies,University of Cambridge,1997.
[32]Idzorek T M.A step-by-step guide to the Black-Litterman model:incorporating user-specified confidence levels[Z].2004.
[33]Mankert C.The Black-Litterman Model:mathematical and behavioral finance approaches towards its use in practice[Z].KTH,Industrial Economics and Management,2006.
[34]Meucci A.Risk and asset allocation[M].Springer,2005.
[35]Meucci A.Fully Flexible Views:Theory and Practice[Z].2008.
[36]Krishnan H,Mains N.The two-factor Black-Litterman model[J].RISK-LONDON-RISK MAGAZINE LIMITED-.2005,18(7):69.
[37]F(u|¨)ss R,Drobetz W,Stein M.Fixed Income Portfolio Allocation Including Hedge Fund Strategies:A Copula Opinion Pooling Approach2008.
[38]王敬,王颖.机构投资者资产配置方法研究[J].价值工程.2006(2):115-120.
[39]张士强.全球资产配置理论与实证研究-基于收益-风险分析的组合优化与BLACK-LITTERMAN模型的应用[D].南京理工大学,2008.
[40]Bollerslev T.A conditionally heteroskedastic time series model for speculative prices and rates of return[J].The review of economics and statistics.1987:542-547.
[41]Bollerslev T,Engle R F,Nelson D B,et al.ARCH models[J].1994(4):2959-3038.
[42]Bollerslev T.Modelling the coherence in short-run nominal exchange rates:a multivariate generalized ARCH model[J].The Review of Economics and Statistics.1990:498-505.
[43]Engle R.Dynamic conditional correlation[j].Journal of Business and Economic Statistics.2002,20(3):339-350.
[44]Bouy(?) E,Durrleman V,Nikeghbali A,et al.Copulas for finance-a reading guide and some applications[Z].2000.
[45]Bouy(?) E,Durrleman V,Nikeghbali A,et al.Copulas for finance-a reading guide and some applications[Z].2000.
[46]Genest C,Zidek J V.Combining probability distributions:A critique and an annotated bibliography[J].Statistical Science.1986:114-135.
[47]Joe H.Multivariate models and dependence concepts[Z].London,Chapman and Hall:Chapman & Hall/CRC,1997.
[48]Michaud R O.The Markowitz Optimization Enigma:Is' Optimized'Optimal?[J].Financial Analysts Journal.1989:31-42.
[49]lordanidis K.Global Asset Allocation Portfolio Contruction and Risk Management [Z].2002.
[50]Litterman B.Modern investment management:an equilibrium approach[M].Wiley,2004.
[51]Qian E,Gorman S.Conditional Distribution in Portfolio Theory[J].Financial Analysts Journal.2001,57(2):44-52.
[52]Best M J,Grauer R R.Sensitivity analysis for mean-variance portfolio problems[J].Management science.1991:980-989.
[53]Blamont D,Firoozye N.Asset Allocation Model[J].Global Market Research:Fixed Income Rsearch.Deutsche Bank,July.2003.
[54]Clemen R T,Winkler R L.Combining probability distributions from experts in risk analysis[J].Risk Analysis.1999,19(2):187-203.
[55]Grinold R C,Kahn R N.Active portfolio management[J].2000.
[56]Sharpe W F.Mutual fund performance[J],Journal of business.1966:119-138.
[2]Markowitz H.Portfolio selection[J].Journal of finance.1952:77-91.
[3]Black F.Asset allocation:combining investor views with market equilibrium[J].The Journal of Fixed Income.1991(9).
[4]Black F,Litterman R.Global portfolio optimization[J].Financial Analysts Journal.1992:28-43.
[5]Meucci A.Risk and asset allocation[M].Springer,2005.
[6]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 and Portfolio Management.2007,21(2):147-166.
[7]Bollerslev T,Engle R F,Wooldridge J M.A capital asset pricing model with time-varying covariances[J].The journal of political economy.1988,96(1):116.
[8]Engle R F,Kroner K F.Multivariate simultaneous generalized ARCH[J].Econometric Theory.1995:122-150.
[9]Baba Y,Engle R F,Kraft D F,et al.Multivariate simultaneous generalized ARCH[J].Unpublished manuscript,Department of Economics,University of California,San Diego.1991.
[10]Bera A K,Kim S W.Testing constancy of conditional correlation in Divariate GARCH model [Z].1996.
[11]Tse Y K.The conditional heteroscedasticity of the Yen-Dollar exchange rate[J].Journal of Applied Econometrics.1998,13(1).
[12]Cappiello L,Engle R F,Sheppard K.Asymmetric dynamics in the correlations of global equity and bond returns[J].Journal of Financial Econometrics.2006,4(4):537.
[13]Sklar A.Fonctions de repartition a n dimensions et leurs margesfZ].1959:8,229-231.
[14]Nelsen R.An introduction to copulas[M].New York:1998.
[15]Frees E W,Valdez E A.Understanding relationships using copulas[J].North American Actuarial Journal.1998(2):1-25.
[16]Embrechts P,Lindskog F,Mcneil A.Modelling dependence with copulas and applications to risk management J].Handbook of heavy tailed distributions in finance.2003(8):329-384.
[17]Li D X.On default correlation:a copula function approach[J].The Journal of Fixed Income.2000,9(4):43-54.
[18]De Matteis R.Fitting copulas to data[D].2001.
[19]Rockinger M,Jondeau E.Entropy densities with an application to autoregressive conditional skewness and kurtosis[J].Journal of Econometrics.2002,106(1):119-142.
[20]Forbes K J,Rigobon R.No contagion,only interdependence:Measuring stock market comovements[J].Journal of Finance.2002:2223-2261.
[21]Scaillet O,Fermanian J D.Nonparametric estimation of copulas for time series[J].Journal of Risk.2003(5):25-54.
[22]Embrechts P,F L,J M A.Modeling depedence with copulas and applications to risk management[Z].2001.
[23]Hu L.Dependence patterns across financial markets:a mixed copula approach[J].Applied Financial Economics.2006,16(10):717-729.
[24]Sharpe W F.Capital asset prices:A theory of market equilibrium under conditions of risk[J].Journal of finance.1964:425-442.
[25]Bevan A,Winkelmann K.Using the Black-Litterman global asset allocation model:three years of practical experience[R].,1998.
[26]He G,Litterman R.The intuition behind Black-Litterman model portfolios[R].Goldman Sachs Asset Management,1999.
[27]Lee W.Theory and methodology of tactical asset allocation[M].Wiley,2000.
[28]Satchell S,Scowcroft A,Studies J I O M.A demystification of the Black-Littermann model:managing quantitative and traditional portfolio construction[Z].Judge Institute of Management Studies,University of Cambridge,1997.
[29]Herold U.Portfolio construction with qualitative forecasts[J].Journal of Portfolio Management.2003(3).
[30]Idzorek T M.A step-by-step guide to the Black-Litterman model[Z].2003.
[31]Satchell S,Scowcroft A,Studies J I O M.A demystification of the Black-Littermann model:managing quantitative and traditional portfolio construction[Z].Judge Institute of Management Studies,University of Cambridge,1997.
[32]Idzorek T M.A step-by-step guide to the Black-Litterman model:incorporating user-specified confidence levels[Z].2004.
[33]Mankert C.The Black-Litterman Model:mathematical and behavioral finance approaches towards its use in practice[Z].KTH,Industrial Economics and Management,2006.
[34]Meucci A.Risk and asset allocation[M].Springer,2005.
[35]Meucci A.Fully Flexible Views:Theory and Practice[Z].2008.
[36]Krishnan H,Mains N.The two-factor Black-Litterman model[J].RISK-LONDON-RISK MAGAZINE LIMITED-.2005,18(7):69.
[37]F(u|¨)ss R,Drobetz W,Stein M.Fixed Income Portfolio Allocation Including Hedge Fund Strategies:A Copula Opinion Pooling Approach2008.
[38]王敬,王颖.机构投资者资产配置方法研究[J].价值工程.2006(2):115-120.
[39]张士强.全球资产配置理论与实证研究-基于收益-风险分析的组合优化与BLACK-LITTERMAN模型的应用[D].南京理工大学,2008.
[40]Bollerslev T.A conditionally heteroskedastic time series model for speculative prices and rates of return[J].The review of economics and statistics.1987:542-547.
[41]Bollerslev T,Engle R F,Nelson D B,et al.ARCH models[J].1994(4):2959-3038.
[42]Bollerslev T.Modelling the coherence in short-run nominal exchange rates:a multivariate generalized ARCH model[J].The Review of Economics and Statistics.1990:498-505.
[43]Engle R.Dynamic conditional correlation[j].Journal of Business and Economic Statistics.2002,20(3):339-350.
[44]Bouy(?) E,Durrleman V,Nikeghbali A,et al.Copulas for finance-a reading guide and some applications[Z].2000.
[45]Bouy(?) E,Durrleman V,Nikeghbali A,et al.Copulas for finance-a reading guide and some applications[Z].2000.
[46]Genest C,Zidek J V.Combining probability distributions:A critique and an annotated bibliography[J].Statistical Science.1986:114-135.
[47]Joe H.Multivariate models and dependence concepts[Z].London,Chapman and Hall:Chapman & Hall/CRC,1997.
[48]Michaud R O.The Markowitz Optimization Enigma:Is' Optimized'Optimal?[J].Financial Analysts Journal.1989:31-42.
[49]lordanidis K.Global Asset Allocation Portfolio Contruction and Risk Management [Z].2002.
[50]Litterman B.Modern investment management:an equilibrium approach[M].Wiley,2004.
[51]Qian E,Gorman S.Conditional Distribution in Portfolio Theory[J].Financial Analysts Journal.2001,57(2):44-52.
[52]Best M J,Grauer R R.Sensitivity analysis for mean-variance portfolio problems[J].Management science.1991:980-989.
[53]Blamont D,Firoozye N.Asset Allocation Model[J].Global Market Research:Fixed Income Rsearch.Deutsche Bank,July.2003.
[54]Clemen R T,Winkler R L.Combining probability distributions from experts in risk analysis[J].Risk Analysis.1999,19(2):187-203.
[55]Grinold R C,Kahn R N.Active portfolio management[J].2000.
[56]Sharpe W F.Mutual fund performance[J],Journal of business.1966:119-138.