期货价格期限结构隐含信息及其应用研究
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摘要
期货价格的期限结构是指在某一时点期货价格与不同到期期限的关系,也是不同到期期限的期货合约的跨期价格关系的呈现,描述了不同时点期货价格与现货价格的变动关系。期货价格期限结构是市场上所有可得信息的综合反映,是投资者对未来价格趋势的综合预期,对实现期货套期保值和价格发现功能意义重大。
金融资产价格的信息提炼近年来越来越为学者们关注,相关研究已渗透到金融市场的各个领域,包括股票、债券和期货等,但对期货价格期限结构中可能隐含的投资策略和套期保值等信息的研究,国内还尚未有文献涉及。由于我国期货市场上金融期货上市较迟,相比于商品期货市场还很稚嫩,而且可得数据较少,故本文的研究主要是针对商品期货价格的期限结构。
本文以2004年10月到2010年7月上海期货交易所、大连商品交易所和郑州商品交易所三大商品期货交易所中最具代表性的9个品种的周结算价数据为样本,包括金属、能源、农产品等,对我国商品期货价格期限结构进行主成分分析(Principal component analysis,PCA),根据商品期货价格期限结构曲线的不同变动方式,揭示期货价格期限结构隐含信息的应用价值,主要包括投资策略信息和套期保值信息。主成分分析得出的结论是,前三因素基本解释了期货价格期限结构曲线变化方差的85%以上,第一主成分为水平因素,对应期货价格相关系数矩阵的最大特征根,反映了平行移动的因素在期货价格期限结构曲线变动中发挥了主导作用,该因素的增加会使所有期货合约近似同等的增加；斜度因素对应第二特征根,它和期限结构曲线的倾斜程度相关,该因素将使短期期货合约和长期期货合约朝着不同的方向变化,从而将改变期限结构曲线的斜率；凸度因素对应第三特征根,该因素和期限结构曲线的曲率关系密切,该因素对短期和长期期货合约的影响与对中期期货合约的影响相反,从而改变期限结构曲线的曲率。
基于期限结构我们构建了3个不同的投资策略,结果发现,即使是第一成分解释能力较低的组合都能获得超过基本持有策略的超额收益；根据不同的期限结构变动形式,得出期限结构对套期保值的决策和风险都有不同的影响。
The term structure of futures price refers to the relation between futures price and different maturities at a point. Also the term structure is a representation of the inter-temporal price relationship between futures contracts with different maturities, indicating changes between futures price and spot price over time. It is the comprehensive reaction to all the market information available, also the the investors'comprehensive expect to the future price trend, so it plays an important part to the hedging and price discovering of futures.
In recent years, scholars pay more and more attention to the information extraction of financial assets prices. Studies related to this have been involving every field of the financial market, including securities,bonds and futures, but researchs on the term structure of futures price which may contains implied information about investment stratege and hedging still untapped. This paper, therefore, largely studies the term structure of commodity futures price because of the young financial futures relative to the commodity futures in China and no enough data available.
We use weekly settlement prices of 9 most representative underlying from Shanghai Futures Exchange(SHFE), Dalian Commodity Exchange(DCE) and Zhengzhou Commodity Exchange(CZCE), covering the period from October 2004 to July 2010, including mental,energy and agricultural. This paper applies principal component analysis(PCA) to the term structure of commodity futures price in China to explore the application value of implied imformation in the term structure of futures price according to the different change of the term structure curve of commodity futures price, mainly including implication of investment stratege and hedging. Findings from principal component analysis of commodity futures price term structures are, the first three principal component(PCs) basically explains the 85% of variance of the dynamic futures price term structures, the first principal components (PCs) derived from our sample of 9 underlyings can be interpreted as level factors, corresponding to the biggest eigenvalue of futures price variance-covariance matrix, reflecting that parallel shift factors play a leading role to the dynamic futures price term structures, so the increase of this factor can lead to increase of all futures contracts; The second PCs represent steepness factors corresponding to the second eigenvalue which are relative to the slope of the term structures curve, so this factor can make short-term and long-term futures contract change in different directions,and therefore change the solpe of the term structures curve; The third PCs, corresponding to the third eigenvalue, can be interpreted as curvature factors which is closely related to the curvature of the term structures curve, so this factor can make mid-term futures move toward opposite direction comparing to short-term and long-term, and therefore change the curvature of the term structures curve.
Based on the term structures, we construct three different investment strategies, and the results tell us that even the proflio with low explanatory power of the first PCs can gain excess profits more than basic hold strategy; According to the different changes of the term structure, we can conclude that the term structure make different influence to the decision and risk of hedging.
金融资产价格的信息提炼近年来越来越为学者们关注,相关研究已渗透到金融市场的各个领域,包括股票、债券和期货等,但对期货价格期限结构中可能隐含的投资策略和套期保值等信息的研究,国内还尚未有文献涉及。由于我国期货市场上金融期货上市较迟,相比于商品期货市场还很稚嫩,而且可得数据较少,故本文的研究主要是针对商品期货价格的期限结构。
本文以2004年10月到2010年7月上海期货交易所、大连商品交易所和郑州商品交易所三大商品期货交易所中最具代表性的9个品种的周结算价数据为样本,包括金属、能源、农产品等,对我国商品期货价格期限结构进行主成分分析(Principal component analysis,PCA),根据商品期货价格期限结构曲线的不同变动方式,揭示期货价格期限结构隐含信息的应用价值,主要包括投资策略信息和套期保值信息。主成分分析得出的结论是,前三因素基本解释了期货价格期限结构曲线变化方差的85%以上,第一主成分为水平因素,对应期货价格相关系数矩阵的最大特征根,反映了平行移动的因素在期货价格期限结构曲线变动中发挥了主导作用,该因素的增加会使所有期货合约近似同等的增加；斜度因素对应第二特征根,它和期限结构曲线的倾斜程度相关,该因素将使短期期货合约和长期期货合约朝着不同的方向变化,从而将改变期限结构曲线的斜率；凸度因素对应第三特征根,该因素和期限结构曲线的曲率关系密切,该因素对短期和长期期货合约的影响与对中期期货合约的影响相反,从而改变期限结构曲线的曲率。
基于期限结构我们构建了3个不同的投资策略,结果发现,即使是第一成分解释能力较低的组合都能获得超过基本持有策略的超额收益；根据不同的期限结构变动形式,得出期限结构对套期保值的决策和风险都有不同的影响。
The term structure of futures price refers to the relation between futures price and different maturities at a point. Also the term structure is a representation of the inter-temporal price relationship between futures contracts with different maturities, indicating changes between futures price and spot price over time. It is the comprehensive reaction to all the market information available, also the the investors'comprehensive expect to the future price trend, so it plays an important part to the hedging and price discovering of futures.
In recent years, scholars pay more and more attention to the information extraction of financial assets prices. Studies related to this have been involving every field of the financial market, including securities,bonds and futures, but researchs on the term structure of futures price which may contains implied information about investment stratege and hedging still untapped. This paper, therefore, largely studies the term structure of commodity futures price because of the young financial futures relative to the commodity futures in China and no enough data available.
We use weekly settlement prices of 9 most representative underlying from Shanghai Futures Exchange(SHFE), Dalian Commodity Exchange(DCE) and Zhengzhou Commodity Exchange(CZCE), covering the period from October 2004 to July 2010, including mental,energy and agricultural. This paper applies principal component analysis(PCA) to the term structure of commodity futures price in China to explore the application value of implied imformation in the term structure of futures price according to the different change of the term structure curve of commodity futures price, mainly including implication of investment stratege and hedging. Findings from principal component analysis of commodity futures price term structures are, the first three principal component(PCs) basically explains the 85% of variance of the dynamic futures price term structures, the first principal components (PCs) derived from our sample of 9 underlyings can be interpreted as level factors, corresponding to the biggest eigenvalue of futures price variance-covariance matrix, reflecting that parallel shift factors play a leading role to the dynamic futures price term structures, so the increase of this factor can lead to increase of all futures contracts; The second PCs represent steepness factors corresponding to the second eigenvalue which are relative to the slope of the term structures curve, so this factor can make short-term and long-term futures contract change in different directions,and therefore change the solpe of the term structures curve; The third PCs, corresponding to the third eigenvalue, can be interpreted as curvature factors which is closely related to the curvature of the term structures curve, so this factor can make mid-term futures move toward opposite direction comparing to short-term and long-term, and therefore change the curvature of the term structures curve.
Based on the term structures, we construct three different investment strategies, and the results tell us that even the proflio with low explanatory power of the first PCs can gain excess profits more than basic hold strategy; According to the different changes of the term structure, we can conclude that the term structure make different influence to the decision and risk of hedging.
引文
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[2]Breeden D. and Litzenberger R H, Prices of State Contingent Claims Implicit in Options Prices[J]. Journal of Business,1978,51(4):621-651.
[3]Britten-Jones M, Neuberger A. Option prices, implied price processes, and stochastic volatility[J]. Journal of Finance,2000,55(2):839-866.
[4]Jiang G J, Tian Y S. The model-free implied volatility and its information content[J]. Review of Financial Studies,2005,18(4):1305-1342.
[5]Chiras D. P, Manaster S. The information content of option prices and a test for market efficiency [J]. Journal of Financial Economics,1978(6):213-234.
[6]Beckers S. Standard Deviations Implied in Option Prices as Predictors of Duture Stock Price Variability [J]. Journal of Banking and Finance,1981(53):63-381.
[7]Mishkin F.S., Frederic S. The information in the longer maturity term structure about future inflation[J]. The Quarterly Journal of economics,1990a(3):815-828.
[8]Mishkin F S., Frederic S. What does the term structure tell us about the future inflation[J]. Journal of Monetary Economics,1990b (25):77-99.
[9]Fama E.F. Term structure forecast of interest rate inflation and real return[J]. Journal of Monetary Economics,1990(25):59-76.
[10]Gerlach S. The information content of the term structure:evidence for Germany[J].BIS working paper 1995 (29).
[11]Estrella A. and Mishkin F.S. The Predictive Power of The Term Structure of Interest Rates In Europe And The United States:Implication For The European Central Bank[J]. European Economic Review,1997(41):1375-1401.
[12]Nielsen C.M. The Information Content Of The Term Structure Of Interest Rates About Future Inflation——An Illustration Of The Importance of Accounting For A Time-Varying Real Interest Rate And Inflation Risk Premium [J]. working paper,2005.
[13]Jorion, Philippe & Mishkin, Frederic. A multicountry comparison of term-structure forecasts at long horizons[J]. Journal of Financial Economics,1991(29):59-80.
[14]范龙振,王晓丽.上交所国债市场利率期限结构及其信息价值[J].管理工程学报,2004(1)：72-75.
[15]石柱鲜,孙皓,邓创.中国主要宏观经济变量与利率期限结构的关系：基于VAR-ATSM模型的分析[J].世界经济,2008(3)：53-59.
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