铝期货套期保值最佳比例的实证分析

铝期货套期保值最佳比例的实证分析1 引言套期保值是指以回避现货价格风险为目的的期货交易行为。企业为了回避价格波动所带来的不利影响而参与期货交易，在期货市场上买进（卖出）与其将要在现货市场上买进（卖出）的现货商品数量相当，期限相近的同种商品的期货合约。希望在未来某一时间内，在现货市场上卖出（买进）原来买进（卖出）的期货合约，从而将价格波动的风险降到最小，是交易者将现货与期货结合运作的一种经营管理模式。套期保值表明企业参与交易的目的和途径，保值是目的，即保住目前认为合理的价格和利润，回避以后价格不利带来的风险，套期是实现保值的途径，即套用期货合约，参与期货交易。因此，我国铝期货套期保值绩效进行验证检验，分别采用OLS模型、ECM模型和B-VAM模型估计铝期货套期保值比率，并比较各种模型的优劣。2 实证研究2.1数据搜集与整理由于每个期货合约都将在一定时间到期，因此，期货价格具有不连续的特点，即对每一个期货合约，合约的时间跨度是有限，任一交割月份合约在合约到期以后，该合约将不复存在。另外，在同一个交易日，同时有若干不同交割月份的期货合约在进行交易，因此，同一期货品种在同一交易日会有若干不同交割月份的期货数据存在。为研究需要，克服期货价格不连续的缺点，必须产生连续的期货价格序列，为此，我们选取铝期货价格和现货价格（有色金属现货每日最高价格与最低价格的平均价）。表一 铝现货期货价2010年01月04日至2010年12月31日数据序号现货 S期货 F序号现货 S期货 F序号现货 S期货 F116270168308215200156501631582015360216260171308315120153301641588015430316240177458415120155401651588015465416210175108515080154951661576015570516210171808615120154401671598015630616210178408715090155151681612015580716250178808815150154851691610015360816250170508915200148551701604015550916200172159015340149001711606015520101620017250911526014815172160301540011161801733592152001490017316120153701216140173009315120148451741637015370131605017150941507015010175163901542514159901714095152201493517616360154901516020167259615280149301771636015440161598016935971532014940178163601564017160201675098152801505017916200156301816000167209915340150051801617015660191601016090100152901500018116200155902016070158601011533014800182161501582021160301619010215280148251831604016330221608016215103151001463518416000161602315860165601041510013900185159801630024159201635010515060140251861602016295251592016115106150401440018715980162702615980161601071500014285188159301605027160301633010814880144501891593016205281603016470109148001439019016090160602916070164601101480014355191161801602030161501666011114740147701921618016200311615016800112147001457019316200164053216070168551131471014620194162301637033159801664011414660147001951619016165341637016670115146601461019616170161003516280165601161463014725197162301616036164201667511714680146101981630016360371664016395118146601455019916300163303816610165151191466014535200163101633539165001653512014660147102011630016480401648016565121146401473020216260168104116500167201221460014745203162101665042162301662512314500147002041621016730431627016730124144501481020516200167104416120165851251443014800206162301678545161501657512614720147002071625016295461607016330127146901466020816250163804716040163651281463014725209163301630048162201648012914640147252101635015670491630016340130144801480521116500161305016220164901311456014720212165001620051160101635513214370148502131623016110521602016265133143501484021416140158855316000162401341442014860215160601602554161401608013514270150702161586015990551607016215136140801519521715810159205616050162351371396015080218158001592557161401629013813780152802191598015880581612016200139138501519022015950160255916020164801401455015065221158001616560160601653014114640154902221564016130611561016630142148401544522315940161756215570166001431490015450224162601617063156001644014414920154402251670016060641561016515145150001544522616780161356515520166801461485015490227167601613066153801660514714900152552281691016155671540016695148149201524522917110161656815280166701491492015130230171801620569152301663015014790153402311732016215701521016205151149001531023217150162507115280163001521480015335233172801623572153001630015314740153202341715016310731517016320154150701530023517080163907415180162201551533015130236173301644075153301629015615320151402371720016395761540016115157153201510523817180163757715300158201581535015120239173801638578152501585515915320151402401712016420791525015915160153201513524116650164258015200159501611558015315242165801644081151801576016215610152502.2运用单方程时间序列模型估计最优套期比2.2.1用OLS模型估计最优套期比建立S关于F的回归方程：Dependent Variable: SMethod: Least SquaresDate: 06/14/12 Time: 20:36Sample: 1 242Included observations: 242VariableCoefficientStd. Errort-StatisticProb. F0.6528820.04381014.902410.0000C5358.104695.84237.7001700.0000R-squared0.480612 Mean dependent var15715.37Adjusted R-squared0.478448 S.D. dependent var734.6375S.E. of regression530.5448 Akaike info criterion15.39392Sum squared resid67554674 Schwarz criterion15.42275Log likelihood-1860.664 F-statistic222.0820Durbin-Watson stat0.115910 Prob(F-statistic)0.000000图1 S关于F回归方程得回归方程：系数的值接近0，回归系数是显著的。回归结果得到每单位现货用0.652882单位期货进行空头保值，即最优套期比是0.652882。结论1：由现货价S关于期货价F回归模型得到的套期比是0.652882。评价：1）虽然模型系数显著，但是模型精度离1较远，精度不太高。所以不能排除此模型是伪回归。2）这一结论只能保证在保值策略实施前（建模的样本内），模型在一定程度上是有效的，不能保证在策略实施期（样本外）模型同样有效，所以使用这一结论进行套期保值需要注意到这些情况。建立关于的回归方程：Dependent Variable: DSMethod: Least SquaresDate: 06/14/12 Time: 21:02Sample(adjusted): 2 242Included observations: 241 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. DF-0.0537880.043371-1.2401600.2161C1.1992658.0248980.1494430.8813R-squared0.006394 Mean dependent var1.286307Adjusted R-squared0.002237 S.D. dependent var124.7147S.E. of regression124.5751 Akaike info criterion12.49596Sum squared resid3709033. Schwarz criterion12.52488Log likelihood-1503.763 F-statistic1.537998Durbin-Watson stat1.683643 Prob(F-statistic)0.216132图2 关于的回归方程（含常数项）常数项概率很大，接受常数为0的假设，重新定义回归方程：Dependent Variable: DSMethod: Least SquaresDate: 06/14/12 Time: 21:04Sample(adjusted): 2 242Included observations: 241 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. DF-0.0538440.043281-1.2440510.2147R-squared0.006301 Mean dependent var1.286307Adjusted R-squared0.006301 S.D. dependent var124.7147S.E. of regression124.3212 Akaike info criterion12.48775Sum squared resid3709380. Schwarz criterion12.50221Log likelihood-1503.774 Durbin-Watson stat1.683486图3 关于的回归方程（不含常数项）得回归结果：系数的值小，回归系数是显著的，但每单位现货用-0.053844单位期货进行空头保值，即最优套期比是-0.053844。可见，分别用套期比公式得到有结果k是不同的：，结论2：由现货价差分关于期货价差分回归模型得到的套期比是-0.053844。评价：1）虽然这一模型系数显著，但模型精度，精度非常低。而且也不能排除模型是伪回归。2）结论2只能保证在保值策略实施前（建模的样本内），与在一定程度上满足此模型，不能保证在策略实施期（样本外）模型同样有效。3）差分模型一般用于分析短期波动情况，所以此模型在不顾伪回归下，也只用于动态套期保值。2.2.2用ECM模型估计最优套期比（1）对和分别进行平衡性检验，如图：Date: 06/14/12 Time: 21:28Sample: 1 242Included observations: 242AutocorrelationPartial CorrelationAC PAC Q-Stat Prob .|*| .|*|10.9680.968229.370.000 .|*| .|* |20.9410.076447.250.000 .|*| .|* |30.9190.066655.940.000 .|*| .|. |40.894-0.045854.270.000 .|*| .|. |50.869-0.0211042.30.000 .|* | .|. |60.841-0.0541219.40.000 .|* | .|. |70.815-0.0061386.20.000 .|* | .|. |80.7900.0111543.70.000 .|* | .|. |90.7680.0351693.10.000 .|* | .|. |100.744-0.0251833.90.000 .|* | .|. |110.7210.0051966.90.000 .|* | .|. |120.698-0.0252092.00.000 .|* | .|. |130.6760.0092209.90.000 .|* | .|. |140.6580.0452322.00.000 .|* | .|. |150.6430.0492429.50.000 .|* | *|. |160.622-0.0822530.40.000 .|* | .|. |170.6060.0592626.80.000 .|* | .|. |180.5940.0502719.90.000 .|* | .|. |190.5850.0612810.60.000 .|* | .|. |200.573-0.0482897.90.000 .|* | *|. |210.557-0.0702980.70.000 .|* | .|. |220.540-0.0453058.90.000 .|* | .|. |230.522-0.0433132.40.000 .|* | .|. |240.5070.0403202.10.000 .|* | .|* |250.4960.0763269.20.000图4 序列相关分析图从图4的序列自相关系数（AC）没有很快趋近0，说明序列F是非平稳的。又因为期货价格往往有一定的趋势和截距，所以对ADF单位根检验时，选择同时具有趋势项和常数项的模型。滞后项p要精确确定就是AIC准则，粗略确定由系统默认。由上面分析，选择模型进行单位检验，假设；备择假设。ADF Test Statistic-1.803424 1% Critical Value*-3.9993 5% Critical Value-3.4297 10% Critical Value-3.1381*MacKinnon critical values for rejection of hypothesis of a unit root.Augmented Dickey-Fuller Test EquationDependent Variable: D(F)Method: Least SquaresDate: 06/14/12 Time: 21:35Sample(adjusted): 2 242Included observations: 241 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. F(-1)-0.0284640.015784-1.8034240.0726C440.3672256.92451.7139950.0878TREND(1)0.0785450.1767760.4443170.6572R-squared0.017051 Mean dependent var-1.618257Adjusted R-squared0.008791 S.D. dependent var185.4052S.E. of regression184.5885 Akaike info criterion13.28650Sum squared resid8109351. Schwarz criterion13.32988Log likelihood-1598.024 F-statistic2.064217Durbin-Watson stat2.242207 Prob(F-statistic)0.129184图5 序列单位根检验期货价格序列的ADF检验统计量观察值为，比概率1%、5%和10%对应的三个临界值都大。所以这次ADF检验接受F非平稳的原假设，即认为F是非平稳的。对F序列一次差分进行ADF检验：ADF Test Statistic-17.92129 1% Critical Value*-3.9994 5% Critical Value-3.4297 10% Critical Value-3.1381*MacKinnon critical values for rejection of hypothesis of a unit root.Augmented Dickey-Fuller Test EquationDependent Variable: D(F,2)Method: Least SquaresDate: 06/14/12 Time: 21:41Sample(adjusted): 3 242Included observations: 240 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. D(F(-1)-1.1444000.063857-17.921290.0000C-29.4442223.89626-1.2321690.2191TREND(1)0.2166710.1708861.2679290.2061R-squared0.575429 Mean dependent var-1.187500Adjusted R-squared0.571846 S.D. dependent var279.8007S.E. of regression183.0833 Akaike info criterion13.27018Sum squared resid7944118. Schwarz criterion13.31369Log likelihood-1589.422 F-statistic160.6054Durbin-Watson stat2.050737 Prob(F-statistic)0.000000图6 序列一次差分单位根检验从图6看到，期货价格F一次差分序列的ADF检验统计量观察值为，比概率1%、5%和10%对应的三个临界值都小。所以这次ADF检验拒绝F一次差分序列非平稳的原假设。即认为F一次差分序列是平稳的。所以，因此。同理检验得到，因此。（2）进行和的协整检验由于和都是一阶单整的，满足协整检验的前提。由前面已用OLS方法建立了关于的回归方程：根据协整检验要求，还要检验残差是否平稳。观察如下：ADF Test Statistic-7.737753 1% Critical Value*-2.5743 5% Critical Value-1.9410 10% Critical Value-1.6164*MacKinnon critical values for rejection of hypothesis of a unit root.Augmented Dickey-Fuller Test EquationDependent Variable: D(E)Method: Least SquaresDate: 06/14/12 Time: 21:53Sample(adjusted): 8 242Included observations: 235 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. E(-1)-1.2350490.159613-7.7377530.0000D(E(-1)0.1923460.1405111.3689060.1724D(E(-2)0.0544570.1201310.4533130.6508D(E(-3)0.0589280.0912450.6458150.5190D(E(-4)0.0448280.0619870.7231860.4703R-squared0.532768 Mean dependent var-0.725530Adjusted R-squared0.524643 S.D. dependent var248.2038S.E. of regression171.1270 Akaike info criterion13.14374Sum squared resid6735423. Schwarz criterion13.21734Log likelihood-1539.389 Durbin-Watson stat1.902889图7 关于协整回归残差的单位根检验从图7看到，关于协整回归残差的ADF检验统计量观察值为，比概率1%，5%、10%对应的两个临界值都小。ADF检验得到拒绝残差序列非平稳的原假设。即认残差序列是平稳的，即残差。（3）建立误差修正模型由以上可知，与序列存在协整关系。建立误差修正模型可分析向长期均衡状态调整的非均衡动态调整过程。原来协整模型形式如下：变成为误差修正模型其中要建立的修正误差模型的简单形式为最小二乘估计命令建立修正误差模型OLS：DS C DF E(-1)得到回归结果为：Dependent Variable: DSMethod: Least SquaresDate: 06/14/12 Time: 22:03Sample(adjusted): 4 242Included observations: 239 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. DF-0.0684260.045693-1.4974970.1356E(-1)-0.0662180.045205-1.4648290.1443C1.0509268.0761900.1301260.8966R-squared0.015239 Mean dependent var1.422594Adjusted R-squared0.006894 S.D. dependent var125.2278S.E. of regression124.7954 Akaike info criterion12.50370Sum squared resid3675439. Schwarz criterion12.54734Log likelihood-1491.192 F-statistic1.826047Durbin-Watson stat1.693248 Prob(F-statistic)0.163317图8 修正误差模型输出结果（包含常数）从图8的结果得到，常数非常不显著，所以省去常数项，重新定义方程如下：Dependent Variable: DSMethod: Least SquaresDate: 06/14/12 Time: 22:05Sample(adjusted): 4 242Included observations: 239 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. DF-0.0686090.045577-1.5053540.1336E(-1)-0.0662540.045111-1.4686940.1432R-squared0.015168 Mean dependent var1.422594Adjusted R-squared0.011013 S.D. dependent var125.2278S.E. of regression124.5363 Akaike info criterion12.49540Sum squared resid3675703. Schwarz criterion12.52450Log likelihood-1491.201 Durbin-Watson stat1.693095图9修正误差模型输出结果（不包含常数）由图9得到所要建ECM为：从统计量看出该方程整体上系数是显著的，自变量系数和误差修正项系数的t统计量都很显著，故该回归模型拟合得很好。ECM得到每单位现货头寸要用-0.068609单位相同的期货头寸进行合作。这一结果与序列差分的OLS模型估计出的结果-0.053844相近；但与序列的OLS模型估计出的结果0.652882相差较大。结论3：由ECM得到的套期比是-0.068609。评价：1）虽然这一模型系数显著，但模型精度，精度不高。2）此模型排除了伪回归。3）结论3的依据是ECM，理论上保证了样本内和样本外都有效，但ECM是用于分析短期波动的。4）可见ECM用于动态套期保值较好。2.2.3用B-VAR模型估计最优套期比Dependent Variable: DSMethod: Least SquaresDate: 06/14/12 Time: 22:29Sample(adjusted): 3 242Included observations: 240 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. DF-0.0691130.043752-1.5796310.1155DS(-1)