基于CVaR的动态套期保值比研究
|
摘要
从套期保值理论现有的研究成果来看,当前主流是从投资组合的角度来看待套期保值,要求在风险最小化或收益最大化的条件下,确定现货头寸与期货头寸的比例,因此套期保值比率的确定是研究的核心问题。
针对在一定风险假定下,通过条件风险价值(CVaR)来控制套期保值资产组合在极端情况下发生的超额损失,一些研究建立了相应的静态最优套期保值比决策模型。本文采用基于套期保值组合收益率的CVaR为目标函数来建立动态的最优套期保值比模型,通过在一定的置信水平下对套期保值资产组合的尾部损失进行控制,并利用移动窗口法来实现最优套期保值头寸的动态决策。
本文首先通过CVaR来控制套期保值资产组合在极端情况下发生的超额损失,建立组合收益率CVaR最小的套期保值模型,得到最优套期保值比。其次,通过GARCH模型来预测各资产及组合的方差和均值,将波动率聚集效应和时变方差效应考虑在预测过程中,从而解决套期保值比动态决策问题。最后,在实证部分分别以郑州商品交易所的白糖期货和香港期货交易所的恒生指数期货为样本数据进行检验。检验结果表明,与同类别的VaR法、Sharp法比较,在相近的单位风险收益条件下,本文研究方法在套期保值头寸规模与有效性方面具有较好的表现。
From the existing research of hedging theory, most of them examine hedging from a portfolio standpoint. It is required to find the ratio between spot position and futures position under the minimal risk or maximal return, thus, how to determine hedge ratio is crucial.
Under certain risk hypothesis, using CVaR to control the excess losses of hedged portfolio in extreme circumstances, some researches develop static optimal hedge ratio decision models. This article developed an optimal hedge ratio decision model based on the CVaR of hedged portfolio return as object, by controlling the tail loss of hedged portfolio under certain confidence level, and using moving window to achieving dynamic optimal hedge ratio.
Firstly, CVaR was used to control the excess losses of hedged portfolio under extreme circumstances, to minimize CVaR of portfolio return and achieve optimal hedge ratio. Secondly, by using GARCH model to forecast portfolio variance and mean values, fluctuation ratio mass effect and time-varying variance effect were considered in the forecasting process; thereby the problem of dynamic hedging was solved. Lastly, in the empirical test part, sugar futures of Zhengzhou Commodity Exchange and HSI futures of Hong Kong Security Exchange were used as sample data. The result shows that, comparing VaR and Sharpe methods, this model has better performance in hedging position scope and effectiveness under certain risk-return conditions.
针对在一定风险假定下,通过条件风险价值(CVaR)来控制套期保值资产组合在极端情况下发生的超额损失,一些研究建立了相应的静态最优套期保值比决策模型。本文采用基于套期保值组合收益率的CVaR为目标函数来建立动态的最优套期保值比模型,通过在一定的置信水平下对套期保值资产组合的尾部损失进行控制,并利用移动窗口法来实现最优套期保值头寸的动态决策。
本文首先通过CVaR来控制套期保值资产组合在极端情况下发生的超额损失,建立组合收益率CVaR最小的套期保值模型,得到最优套期保值比。其次,通过GARCH模型来预测各资产及组合的方差和均值,将波动率聚集效应和时变方差效应考虑在预测过程中,从而解决套期保值比动态决策问题。最后,在实证部分分别以郑州商品交易所的白糖期货和香港期货交易所的恒生指数期货为样本数据进行检验。检验结果表明,与同类别的VaR法、Sharp法比较,在相近的单位风险收益条件下,本文研究方法在套期保值头寸规模与有效性方面具有较好的表现。
From the existing research of hedging theory, most of them examine hedging from a portfolio standpoint. It is required to find the ratio between spot position and futures position under the minimal risk or maximal return, thus, how to determine hedge ratio is crucial.
Under certain risk hypothesis, using CVaR to control the excess losses of hedged portfolio in extreme circumstances, some researches develop static optimal hedge ratio decision models. This article developed an optimal hedge ratio decision model based on the CVaR of hedged portfolio return as object, by controlling the tail loss of hedged portfolio under certain confidence level, and using moving window to achieving dynamic optimal hedge ratio.
Firstly, CVaR was used to control the excess losses of hedged portfolio under extreme circumstances, to minimize CVaR of portfolio return and achieve optimal hedge ratio. Secondly, by using GARCH model to forecast portfolio variance and mean values, fluctuation ratio mass effect and time-varying variance effect were considered in the forecasting process; thereby the problem of dynamic hedging was solved. Lastly, in the empirical test part, sugar futures of Zhengzhou Commodity Exchange and HSI futures of Hong Kong Security Exchange were used as sample data. The result shows that, comparing VaR and Sharpe methods, this model has better performance in hedging position scope and effectiveness under certain risk-return conditions.
引文
[1]孙才仁.套期保值与企业风险管理实践[M].北京：中国经济出版社,2009.8：1-51
[2]Ederington L H. The hedging performance of the new futures markets [J]. Journal of Finance,1979,1 (34):157-170
[3]Cheung C S, and Kwan C C Y, and Yip C Y. The hedging effectiveness of options and futures:a mean-gini approach [J]. Journal of Futures Markets, 1990,1(10):61-74
[4]Lien D, Tse Y K. Hedging downside risk with futures contracts [J]. Applied Financial Economics,2000, (10):163-170
[5]Sharda R, and Musser K D. Financial futures hedging via goal programming [J]. Management Science,1986,32(8):933-946
[6]王征,樊治平和张权.期货套期保值的多期多目标规划模型[J].系统工程,1997, (2)：24-43
[7]Howard C T, and D' Antonio L J. A risk-return measure of hedging effectiveness [J]. Journal of Financial and Quantitative Analysis,1984, (19): 101-112
[8]Hsin C W, and Kuo J, and Lee C F. A new measure to compare the hedging effectiveness of foreign currency futures versus options [J]. Journal of Futures Markets,1994, (14):685-707
[9]Shalit H. Mean-gini hedging in futures markets [J]. Journal of Futures Markets, 1995, (15):617-635
[10]Lence S H. Relaxing the assumptions of minimum variance hedging [J]. Journal of Agricultural and Resource Economics,1996, (21):39-55
[11]Cecchetti S G, Cumby R E, and Figlewski S. Estimation of the optimal futures hedge [J]. Review of Economics and Statistics,1998, (70):623-630
[12]Rockafeller T, Uryasev S. Optimization of conditional Value-at -Risk. Journal of Risk,2000,2(3):21-24
[13]Jonas Palmquist, Stanislav Uryasev, and Patio Krokhmal. Portfolio Optimization with Conditional Value-at-Risk Objective and Constraints. http: //www.ise.ufl.edu/UI'yasev,1999
[14]Alexander G, Baptista A. Economic implications of using a mean-var model for portfolio selection. A comparison with mean-variance analysis[J]. Journal of Economic Dynamics & Control,2002,(26):1159-1193
[15]Fredrik Anderson, Helmut Mausser, Dan Rosen, and Stanislav Uryasev. Credit Risk Optimization with Conditional Value-at-Risk Criterion. Mathematical Program,2001,(89):273-291
[16]林孝贵,卢珍菊等.二重期货套期保值策略的统计分析[J].沿海企业与科技,2003,1：23-26
[17]林孝贵.基于收益与风险比率的期货套期保值策略[J].系统工程,2004,1：17-21
[18]林孝贵.期货套期保值最大概率与最小风险分析[J].数学的认识与实践,2004,4：33-37
[19]黄长征.期货套期保值决策模型研究[J].数量经济技术与经济研究,2004,7：14-18
[20]李国荣,吴大为,余方平.基于差异系数的期货套期保值优化策略[J].系统工程,2005,8：39-42
[21]吴文锋,刘太阳,吴冲锋.上海与伦敦期铜市场之间的波动溢出效应研究[J].管理工程学报,2007,3：23-26
[22]冯春山,吴家春等.石油期货套期保值时变套期比研究[J].上海理工大学学报,2004,5：34-38
[23]齐明亮.套期保值比率与套期保值的绩效-上海期铜合约的套期保值实证分析.华中科技大学学报(社会科学版),2004,2：45-48
[24]王赛德.套期保值期限、期货合约选择与最优套期保值比率-基于中国铜、铝期货市场的实证研究[J].上海理工大学学报,2004,5：58-63
[25]王骏,张宗成.石油期货套期保值时变套期比研究[J].上海理工大学学报,2004,5：73-76
[26]喻小军.套期保值决策在规避市场价格风险中的应用[J].武汉理工大学学报,2005,6：41-44
[27]梁朝晖,张维.期货市场组合保险策略及其实证研究[J].西安电子科技大学学报(社会科学版),2006,2：60-65
[28]陈金龙,张维.CVaR与投资组合优化统一模型[J].系统工程理论方法应用,2002,(1)：87-91
[29]林辉,何建敏.VaR在投资组合应用中存在的缺陷与CVaR模型[J].财贸经济,2003,(12)：46-49
[30]岳瑞锋,李振东,杨晓萍.风险管理的CVaR方法及其简化模型[J].河北省科学院学报,2003,(3)：134-138
[31]刘小茂,李楚霖,王建华.风险资产组合的均值-CVaR有效前沿[J].管理工程学报,2003,(1)：29-33
[32]田新民,黄海平.基于条件VaR(CVaR)的投资组合优化模型及比较研究[J].管理工程学报,2004,(7)：41-50
[33]王树娟,黄渝祥.基于GARCH-CVaR模型的我国股票市场风险分析.同济大学学报自然科学版,2005,(2)：121—124
[34]迟国泰,余平方,刘轶芳.基于VaR的期货最优套期保值模型及应用研究[J].系统工程学报,2008,(4)：417-423
[35]迟国泰,杨万武,余方平.基于资金限制的Sharp-ARIMA期货套期保值决策模型.预测,2007,26(3)：72—80
[36]菲利普·乔瑞.风险价值VAR[M].北京：中信出版社,2004.10
[37]Stambaugh F. Risk and value at risk. European Management Journal. 1996,14:612-621
[38]蒋敏.条件条件风险价值(cvar)模型的理论研究[D].博士学位论文,西安电子科技大学,2005
[39]Artzner P, Delbaen F, Eber J H, Heah D. Thinking coherently. Risk, 1997,(10):33-49
[40]Artzner P, Delbaen F, Eber J H, Heah D. Coherent Measure of Risk. Mathematical Finance,1999,(3):203-228
[41]高铁梅.计量经济分析方法与建模[M].北京：清华大学出版社,2006
[42]韩德宗.基于VaR的我国商品期货市场风险的预警研究[J].管理工程学报,2008(1)：117-121
[43]Howard C T, D'Antonio L J. A risk-return measure of hedging effectiveness [J]. Journal of Financial and Quantitative Analysis,1984, (19):101-112
[44]张学东,徐成贤,李栓劳,张芳.考虑交易成本的股价指数期货最优套期保值策略模型.西安交通大学学报,2002,36(12)：1317-1319
[45]熊维平,程晓红,周友生.商品保值性的定量分析.技术经济与管理研究,2000,(5)：45-47
[46]伍海军,马永开.期货市场多阶段展期套期保值的基本理论探讨.系统工程,2007,25(4)：83-87
[47]Fama E F, and French K R. Commodity Futures Prices:Some Evidence on Forecast Power, Premiums, and the Theory of Storage. The Journal of Business,1987,60(1):55-73
[48]Johnson L. The theory of hedging and speculation in commodity futures [J]. Review of Economic Studies,1960,27:139-151
[49]Baillie, and Myers R.J. Estimating Time Varying Optimal Hedge Ratios on Futures Markets [J]. Journal of Futures Markets,1991,11:39-53
[50]DeJong, DeRoon, and Veld. Out-of-sample Hedging Effectiveness of Currency Futures for Alternative Models and Hedging Strategies [J]. The Journal of Futures Markets,17:817-837
[51]Stein J L. The simultaneous determination of spot and futures price [J]. American Economic Review,1961,51:1012-1025
[52]Herbst, and Kare, and Marshall. A Time Varying, Convergence Adjusted Hedge Ratio Model [J]. Advances in Futures and Options Research,1989,6:13 7-151
[53]Schweizer M. Mean-variance hedging for general claims [J]. Annals of Applied Probability,1992, (2):171-179
[54]Ghosh. Hedging with Stock Index Futures:Estimation and Forecasting with Error Correction Model[J]. The Journal of Futures Markets,1933,8:743-752
[55]Myers R J, and Thompson S R. Generalized Optimal Hedge Ratio Estimation. American Journal of Agricultural Economics,1989,71:858-867
[56]]Cecchetti, and Cumby, and Figlewski, Estimation of the Optimal Futures Hedge[J]. Review of Economics and Statistics,1988,17:623-630
[57]Mathew, and Holthausen. A simple multiperiod minimum risk hedge model [J]. American Journal of Agricultural Economics,1991,5:123-128
[58]Baillie, and Myers R.J. Estimating Time Varying Optimal Hedge Ratios on Futures Markets[J].Journal of Futures Markets,1991,11:39-53
[59]DeJong, DeRoon, and Veld. Out-of-sample Hedging Effectiveness of Currency Futures for Alternative Models and Hedging Strategies[J]. The Journal of Futures Markets,1977,6:817-837
[60]Chen, Lee, and Shrestha.On A Mean-Generalized Semi-variance Approach to Determining the Hedge Ratio[J].The Journal of Futures Markets,21:581-598
[61]Lien, and Tse. Fractional Cointegration and Futures Hedging[J]. The Journal of Futures Markets,1999,9:457-474
[62]Michael, and Mathew. Hedging Foreign currency, Freight and Commodity Futures Portfolios:A Note[J]. Journal of Futures Markets,2002,22:1205-1221
[63]Lien D, and Wang Y. Cross-hedging with futures and options:The effects of disappointment aversion [J]. Journal of Multinational Financial Management, 2006,16(1):16-26
[64]Amir Alizadeh, and Nikos Nomikos. A Markov Regime Switching Approach for Hedging Stock Indices [J].The Journal of Futures Markets,2004,24(7):649-674
[65]Zhang, R. C, J. E. Houston, D. V. Vedenov, and B. J. Barnett, Impacts of government risk management policies on hedging in futures and options: LPM2 hedge model vs. EU hedge model,2008 NCCC-134 Conference on Applied Commodity Price Analysis, Forecasting, and Market Risk Management.
[66]Lien D, and Y. K. Tse. Hedging downside risk with futures contracts. Applied Financial Economics,2000,10:321-331
[67]Lien, D., and Y. K. Tse. Hedging downside risk:futures vs. options. International Review of Economics and Finance,2001,10:78-84
[68]Lien, D., and Y. K. Tse. Hedging Time-varying Down side Risk[J]. The Journal of Futures Markets,1998,10:705-722
[2]Ederington L H. The hedging performance of the new futures markets [J]. Journal of Finance,1979,1 (34):157-170
[3]Cheung C S, and Kwan C C Y, and Yip C Y. The hedging effectiveness of options and futures:a mean-gini approach [J]. Journal of Futures Markets, 1990,1(10):61-74
[4]Lien D, Tse Y K. Hedging downside risk with futures contracts [J]. Applied Financial Economics,2000, (10):163-170
[5]Sharda R, and Musser K D. Financial futures hedging via goal programming [J]. Management Science,1986,32(8):933-946
[6]王征,樊治平和张权.期货套期保值的多期多目标规划模型[J].系统工程,1997, (2)：24-43
[7]Howard C T, and D' Antonio L J. A risk-return measure of hedging effectiveness [J]. Journal of Financial and Quantitative Analysis,1984, (19): 101-112
[8]Hsin C W, and Kuo J, and Lee C F. A new measure to compare the hedging effectiveness of foreign currency futures versus options [J]. Journal of Futures Markets,1994, (14):685-707
[9]Shalit H. Mean-gini hedging in futures markets [J]. Journal of Futures Markets, 1995, (15):617-635
[10]Lence S H. Relaxing the assumptions of minimum variance hedging [J]. Journal of Agricultural and Resource Economics,1996, (21):39-55
[11]Cecchetti S G, Cumby R E, and Figlewski S. Estimation of the optimal futures hedge [J]. Review of Economics and Statistics,1998, (70):623-630
[12]Rockafeller T, Uryasev S. Optimization of conditional Value-at -Risk. Journal of Risk,2000,2(3):21-24
[13]Jonas Palmquist, Stanislav Uryasev, and Patio Krokhmal. Portfolio Optimization with Conditional Value-at-Risk Objective and Constraints. http: //www.ise.ufl.edu/UI'yasev,1999
[14]Alexander G, Baptista A. Economic implications of using a mean-var model for portfolio selection. A comparison with mean-variance analysis[J]. Journal of Economic Dynamics & Control,2002,(26):1159-1193
[15]Fredrik Anderson, Helmut Mausser, Dan Rosen, and Stanislav Uryasev. Credit Risk Optimization with Conditional Value-at-Risk Criterion. Mathematical Program,2001,(89):273-291
[16]林孝贵,卢珍菊等.二重期货套期保值策略的统计分析[J].沿海企业与科技,2003,1：23-26
[17]林孝贵.基于收益与风险比率的期货套期保值策略[J].系统工程,2004,1：17-21
[18]林孝贵.期货套期保值最大概率与最小风险分析[J].数学的认识与实践,2004,4：33-37
[19]黄长征.期货套期保值决策模型研究[J].数量经济技术与经济研究,2004,7：14-18
[20]李国荣,吴大为,余方平.基于差异系数的期货套期保值优化策略[J].系统工程,2005,8：39-42
[21]吴文锋,刘太阳,吴冲锋.上海与伦敦期铜市场之间的波动溢出效应研究[J].管理工程学报,2007,3：23-26
[22]冯春山,吴家春等.石油期货套期保值时变套期比研究[J].上海理工大学学报,2004,5：34-38
[23]齐明亮.套期保值比率与套期保值的绩效-上海期铜合约的套期保值实证分析.华中科技大学学报(社会科学版),2004,2：45-48
[24]王赛德.套期保值期限、期货合约选择与最优套期保值比率-基于中国铜、铝期货市场的实证研究[J].上海理工大学学报,2004,5：58-63
[25]王骏,张宗成.石油期货套期保值时变套期比研究[J].上海理工大学学报,2004,5：73-76
[26]喻小军.套期保值决策在规避市场价格风险中的应用[J].武汉理工大学学报,2005,6：41-44
[27]梁朝晖,张维.期货市场组合保险策略及其实证研究[J].西安电子科技大学学报(社会科学版),2006,2：60-65
[28]陈金龙,张维.CVaR与投资组合优化统一模型[J].系统工程理论方法应用,2002,(1)：87-91
[29]林辉,何建敏.VaR在投资组合应用中存在的缺陷与CVaR模型[J].财贸经济,2003,(12)：46-49
[30]岳瑞锋,李振东,杨晓萍.风险管理的CVaR方法及其简化模型[J].河北省科学院学报,2003,(3)：134-138
[31]刘小茂,李楚霖,王建华.风险资产组合的均值-CVaR有效前沿[J].管理工程学报,2003,(1)：29-33
[32]田新民,黄海平.基于条件VaR(CVaR)的投资组合优化模型及比较研究[J].管理工程学报,2004,(7)：41-50
[33]王树娟,黄渝祥.基于GARCH-CVaR模型的我国股票市场风险分析.同济大学学报自然科学版,2005,(2)：121—124
[34]迟国泰,余平方,刘轶芳.基于VaR的期货最优套期保值模型及应用研究[J].系统工程学报,2008,(4)：417-423
[35]迟国泰,杨万武,余方平.基于资金限制的Sharp-ARIMA期货套期保值决策模型.预测,2007,26(3)：72—80
[36]菲利普·乔瑞.风险价值VAR[M].北京：中信出版社,2004.10
[37]Stambaugh F. Risk and value at risk. European Management Journal. 1996,14:612-621
[38]蒋敏.条件条件风险价值(cvar)模型的理论研究[D].博士学位论文,西安电子科技大学,2005
[39]Artzner P, Delbaen F, Eber J H, Heah D. Thinking coherently. Risk, 1997,(10):33-49
[40]Artzner P, Delbaen F, Eber J H, Heah D. Coherent Measure of Risk. Mathematical Finance,1999,(3):203-228
[41]高铁梅.计量经济分析方法与建模[M].北京：清华大学出版社,2006
[42]韩德宗.基于VaR的我国商品期货市场风险的预警研究[J].管理工程学报,2008(1)：117-121
[43]Howard C T, D'Antonio L J. A risk-return measure of hedging effectiveness [J]. Journal of Financial and Quantitative Analysis,1984, (19):101-112
[44]张学东,徐成贤,李栓劳,张芳.考虑交易成本的股价指数期货最优套期保值策略模型.西安交通大学学报,2002,36(12)：1317-1319
[45]熊维平,程晓红,周友生.商品保值性的定量分析.技术经济与管理研究,2000,(5)：45-47
[46]伍海军,马永开.期货市场多阶段展期套期保值的基本理论探讨.系统工程,2007,25(4)：83-87
[47]Fama E F, and French K R. Commodity Futures Prices:Some Evidence on Forecast Power, Premiums, and the Theory of Storage. The Journal of Business,1987,60(1):55-73
[48]Johnson L. The theory of hedging and speculation in commodity futures [J]. Review of Economic Studies,1960,27:139-151
[49]Baillie, and Myers R.J. Estimating Time Varying Optimal Hedge Ratios on Futures Markets [J]. Journal of Futures Markets,1991,11:39-53
[50]DeJong, DeRoon, and Veld. Out-of-sample Hedging Effectiveness of Currency Futures for Alternative Models and Hedging Strategies [J]. The Journal of Futures Markets,17:817-837
[51]Stein J L. The simultaneous determination of spot and futures price [J]. American Economic Review,1961,51:1012-1025
[52]Herbst, and Kare, and Marshall. A Time Varying, Convergence Adjusted Hedge Ratio Model [J]. Advances in Futures and Options Research,1989,6:13 7-151
[53]Schweizer M. Mean-variance hedging for general claims [J]. Annals of Applied Probability,1992, (2):171-179
[54]Ghosh. Hedging with Stock Index Futures:Estimation and Forecasting with Error Correction Model[J]. The Journal of Futures Markets,1933,8:743-752
[55]Myers R J, and Thompson S R. Generalized Optimal Hedge Ratio Estimation. American Journal of Agricultural Economics,1989,71:858-867
[56]]Cecchetti, and Cumby, and Figlewski, Estimation of the Optimal Futures Hedge[J]. Review of Economics and Statistics,1988,17:623-630
[57]Mathew, and Holthausen. A simple multiperiod minimum risk hedge model [J]. American Journal of Agricultural Economics,1991,5:123-128
[58]Baillie, and Myers R.J. Estimating Time Varying Optimal Hedge Ratios on Futures Markets[J].Journal of Futures Markets,1991,11:39-53
[59]DeJong, DeRoon, and Veld. Out-of-sample Hedging Effectiveness of Currency Futures for Alternative Models and Hedging Strategies[J]. The Journal of Futures Markets,1977,6:817-837
[60]Chen, Lee, and Shrestha.On A Mean-Generalized Semi-variance Approach to Determining the Hedge Ratio[J].The Journal of Futures Markets,21:581-598
[61]Lien, and Tse. Fractional Cointegration and Futures Hedging[J]. The Journal of Futures Markets,1999,9:457-474
[62]Michael, and Mathew. Hedging Foreign currency, Freight and Commodity Futures Portfolios:A Note[J]. Journal of Futures Markets,2002,22:1205-1221
[63]Lien D, and Wang Y. Cross-hedging with futures and options:The effects of disappointment aversion [J]. Journal of Multinational Financial Management, 2006,16(1):16-26
[64]Amir Alizadeh, and Nikos Nomikos. A Markov Regime Switching Approach for Hedging Stock Indices [J].The Journal of Futures Markets,2004,24(7):649-674
[65]Zhang, R. C, J. E. Houston, D. V. Vedenov, and B. J. Barnett, Impacts of government risk management policies on hedging in futures and options: LPM2 hedge model vs. EU hedge model,2008 NCCC-134 Conference on Applied Commodity Price Analysis, Forecasting, and Market Risk Management.
[66]Lien D, and Y. K. Tse. Hedging downside risk with futures contracts. Applied Financial Economics,2000,10:321-331
[67]Lien, D., and Y. K. Tse. Hedging downside risk:futures vs. options. International Review of Economics and Finance,2001,10:78-84
[68]Lien, D., and Y. K. Tse. Hedging Time-varying Down side Risk[J]. The Journal of Futures Markets,1998,10:705-722