影响封闭式基金定价的因素分析(1)

1、影响封闭式基金定价的因素分析论文成员：陶露露，喻昭阳，夏雨潇一.问题的提出随着证券市场的逐步发展,我国机构投资者(包括基金管理公司、保险公司、证券公司、投资信托公司等)在我国证券市场上的发展非常迅速,虽然市场份额占有率与发达国家相比还有很大的差距,但已然成为影响证券市场波动变化的一个重要因素,因此证券投资基金的波动也引起了各方的广泛关注。封闭式基金进入我国的时间较早,发展也相对成熟。在经历过繁荣、衰退后,封闭式基金现在又重新回到人们的视野。但是大量的研究发现，封闭式基金单位份额交易的价格不等于其净资产现值，并且折价交易是一种普遍的现象。这与有效市场假设互相矛盾的价格表现，本文的研究和探索是希望

2、能够找到影响封闭式基金价格波动的影响因素，并从中分离出最主要的成分,从而帮助投资者决策和规避风险,同时帮助决策者进行政策的制定和市场的调控。封闭式基金上市后，其交易价格主要受下列因素的影响:1、 基金单位的资产净值。这是基金交易价格的价值基础，基金的交易价格就以基金单位的资产净值为中心上下波动。2、基金的供求关系。因为封闭式基金的发行单位有限，投资者对基金单位的需求有可能超过或者低于市场的供应量，会因此导致基金交易价格的溢价或者折价。3、市场的异常因素。如投资者对基金的不正确认识和人为的炒作，都有可能造成基金价格的上下波动。而市场的异常因素较为复杂，无法用具体的变量来解释，故本论文选择用基金指

3、数来代替市场因素以及基金的供求关系对基金的交易价格的影响。二.研究设计根据经济意义，基金的交易价格主要受基金单位的资产净值影响，其次，用基金指数代替市场的不确定因素来分析对基金交易价格的影响。1.模型形式的设定被解释变量：Y基金价格解释变量：X2基金单位净值X3基金指数Y=1+2X2+3X3+u2.数据的收集本文收集了从2008-9-5至2012-9-7，以一周为时间单位的一只基金的收盘价格，基金单位净值，该基金为基金泰和，源自上交所。还有来自上交所的上证基金指数。'500002'基金价格单位净值基金指数日期YX2X32008-9-50.3830.7262902.262008-

4、9-120.3590.6972760.012008-9-190.3770.7112785.082008-9-260.4260.7462939.882008-10-100.3740.6592579.52008-10-170.3040.6242431.962008-10-240.310.6332392.52008-10-310.2840.6212281.482008-11-70.3010.622348.452008-11-140.3440.692630.392008-11-210.310.6952524.322008-11-280.2840.6782408.422008-12-50.3230.73

5、92629.882008-12-120.3130.7122593.972008-12-190.3250.7522656.352008-12-260.3130.6932502.222008-12-310.3110.6882512.492009-1-90.3240.7032620.472009-1-160.3460.7212761.552009-1-230.3520.742788.512009-2-60.3990.7883018.632009-2-130.4160.8313110.222009-2-200.3890.8233011.272009-2-270.3420.7662788.392009-

6、3-60.3650.8092938.622009-3-130.3540.7872874.522009-3-200.3780.8243057.862009-3-270.4070.863185.912009-4-30.4310.8733271.32009-4-100.4450.8743277.092009-4-170.4690.8853301.822009-4-240.4680.8563258.322009-4-300.4810.8563322.822009-5-80.5410.9023546.012009-5-150.5770.9023606.722009-5-220.570.8933595.1

7、82009-5-270.5720.8943621.62009-6-50.6120.9433834.462009-6-120.5960.9343823.592009-6-190.60.9783952.172009-6-260.5990.9893991.082009-7-30.6181.0544201.472009-7-100.621.0664234.712009-7-170.6181.0824339.952009-7-240.6991.1094654.42009-7-310.6691.1164664.812009-8-70.6161.0884391.112009-8-140.5461.04841

8、35.852009-8-210.531.024045.922009-8-280.5250.9933894.212009-9-40.5361.0063943.352009-9-110.561.0484098.862009-9-180.581.0384089.992009-9-250.551.0193997.182009-9-300.5461.0033961.382009-10-90.5711.0424125.512009-10-160.5941.0594248.512009-10-230.6411.144492009-10-300.6361.0954321.792009-11-60.6811.1

9、384567.652009-11-130.6851.1624614.292009-11-200.7291.1764761.862009-11-270.6711.1274437.862009-12-40.7141.1834762.882009-12-110.7021.1794676.72009-12-180.6671.124513.962009-12-250.6761.1564528.842009-12-310.7041.1734765.742010-1-80.7141.1424694.52010-1-150.7441.164706.172010-1-220.7371.1224625.53201

10、0-1-290.7211.0924449.132010-2-50.7041.0764398.642010-2-120.7381.1014566.592010-2-260.7411.134566.072010-3-50.7331.1194553.522010-3-120.7221.1014544.22010-3-190.7441.1224613.342010-3-260.7351.1264606.162010-4-20.7861.1634804.832010-4-90.7991.1284772.822010-4-160.7861.1294715.322010-4-230.7481.1214474

11、.192010-4-300.7461.0694399.162010-5-70.741.0474189.852010-5-140.7681.0444272.192010-5-210.7641.0334154.582010-5-280.7711.054213.782010-6-40.7511.0414077.852010-6-110.7631.0574092.092010-6-180.7571.0244046.822010-6-250.7541.0374090.822010-7-20.6950.9833837.32010-7-90.7431.0243974.912010-7-160.7451.01

12、73928.262010-7-230.7641.0624118.432010-7-300.7751.0874208.692010-8-60.7781.1114237.112010-8-130.7741.1164143.352010-8-200.7761.1124175.572010-8-270.7881.1194131.462010-9-30.8051.1534180.992010-9-100.8161.1564214.292010-9-170.8251.174167.622010-9-210.8431.1624186.042010-9-300.8731.1944313.422010-10-8

13、0.9011.2134473.592010-10-150.8941.1964780.292010-10-220.8981.2474764.642010-10-290.9391.2534752.852010-11-51.0071.2914988.072010-11-120.9731.2644725.732010-11-190.9941.3024630.962010-11-261.0171.3044635.72010-12-30.9921.2834573.972010-12-100.9831.30645682010-12-1711.3374624.012010-12-241.0551.285460

14、3.182010-12-311.0531.34557.662011-1-71.0981.2794646.052011-1-141.0311.2234569.682011-1-210.9951.1764433.62011-1-280.9961.1844496.992011-2-10.9971.1964544.942011-2-111.0161.2174569.612011-2-181.0161.2344651.172011-2-251.0091.234623.572011-3-41.0141.2434728.152011-3-110.9991.2474676.042011-3-180.9961.

15、2354647.72011-3-251.0191.244730.272011-4-11.0221.0434750.232011-4-81.0091.0544822.92011-4-1511.044836.342011-4-220.9991.054767.222011-4-290.9951.0164668.432011-5-60.9661.0064541.732011-5-130.9511.0094542.932011-5-200.9440.9994555.952011-5-270.9190.9624405.72011-6-30.9310.9914404.272011-6-100.9430.97

16、94377.532011-6-170.9180.9744301.622011-6-240.9631.0214461.512011-7-10.9841.0464472.672011-7-81.0071.0664536.292011-7-151.0031.084546.492011-7-221.0121.0664485.22011-7-290.9851.0594368.312011-8-50.9771.0424268.342011-8-120.9711.0474256.042011-8-260.9561.0224312.162011-9-90.9170.9644154.012011-9-160.9

17、030.9594114.022011-9-230.8740.9544017.912011-9-300.8510.9333895.332011-10-140.8750.953978.332011-10-210.8390.8933808.952011-11-40.9020.974137.442011-11-110.8840.9584056.472011-11-180.8660.9293936.422011-12-20.8460.9093877.212011-12-90.8180.8938152011-12-160.7770.8843674.792011-12-300.7790.8743592.26

18、2012-1-60.7720.8473534.772012-1-200.7960.8733782.32012-2-240.8190.9243937.542012-3-160.8270.943892.372012-3-230.8170.9133824.692012-3-300.7980.8973705.722012-4-60.8140.9183772.482012-4-130.8260.9313855.782012-4-200.8290.9313917.412012-4-270.8260.933919.992012-5-40.8450.9544014.42012-5-110.8460.94739

19、28.32012-5-180.8450.9333853.062012-5-250.8410.9393850.742012-6-10.8640.9693927.562012-6-80.8620.9543805.192012-6-150.8850.983878.732012-6-210.8810.9673813.962012-6-290.8840.9763765.92012-7-60.9060.9923778.742012-7-130.90713746.482012-7-200.8830.9573699.942012-7-270.8810.9533647.782012-8-30.890.96736

20、56.422012-8-100.9050.9923720.422012-8-170.8920.9653608.792012-8-240.8790.9593566.892012-8-310.8550.9263481.652012-9-70.8980.9673632.63注：Y为基金泰和的收盘交易价格X2为基金泰和的单位基金净值X3为上证基金指数三.模型的估计与调整从线图可以看出，Y,X2，X3都具有相同的变化，而X3比Y的波动幅度较大，故有可能是数据过大造成的。1. 基金单位净值和基金指数对基金价格的回归Dependent Variable: YMethod: Least SquaresDate

21、: 01/07/13 Time: 19:13Sample (adjusted): 9/05/2008 9/07/2012Included observations: 210 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.  C-0.2272830.065836-3.4522320.0007X20.1867650.1626281.1484190.2521X30.0001993.96E-055.0386200.0000R-squared0.534651    M

22、ean dependent var0.751648Adjusted R-squared0.530155    S.D. dependent var0.210560S.E. of regression0.144329    Akaike info criterion-1.019260Sum squared resid4.311990    Schwarz criterion-0.971444Log likelihood110.0223   

23、0;F-statistic118.9138Durbin-Watson stat0.012986    Prob(F-statistic)0.000000回归方程：Y=-0.227283 + 0.186765 X2 + 0.000199 X3 Std. Error = (0.065836) (0.162628) (3.96E-05) t-Statistic = (-3.452232) (1.148419) (5.038620) Prob.值 = (0.0007) (0.2521) (0.0000) R-squared=0.534651; Adjusted

24、R-squared=0.530155; F=118.9138;df=n-3=217;从表中可以看出，解释变量X2的t值不显著，而且解释变量x2的p值偏大；解释变量X3系数较小，故考虑到基金指数与单个基金价格数据相差较大，改变模型设定形式，将X3的值取对数为LNX3。2. 基金单位净值和基金指数取对数对基金价格的回归Dependent Variable: YMethod: Least SquaresDate: 01/07/13 Time: 19:24Sample (adjusted): 9/05/2008 9/07/2012Included observations: 210 after adj

25、ustmentsVariableCoefficientStd. Errort-StatisticProb.  C-6.2908700.966174-6.5111170.0000X20.0594600.1524340.3900730.6969LNX30.8442270.1334336.3269910.0000R-squared0.562235    Mean dependent var0.751648Adjusted R-squared0.558006    S.D. dependent var0

26、.210560S.E. of regression0.139986    Akaike info criterion-1.080366Sum squared resid4.056390    Schwarz criterion-1.032550Log likelihood116.4384    F-statistic132.9284Durbin-Watson stat0.015032    Prob(F-statistic)0.0000

27、00回归方程：Y=-6.290870 + 0.059460 X2 + 0.844227 LNX3 Std. Error = (0.966174) ( 0.152434) (0.133433) t-Statistic = (-6.511117) (0.390073) (6.326991) Prob.值 = (0.0000) (0.6969) (0.0000) R-squared=0.562235; Adjusted R-squared=0.558006; F=132.9284;df=n-3=217;从表中可以看出，解释变量X2的t值不显著，而且解释变量x2的p值偏大，而X3取对数比未取对数所估计

28、的更为准确；故可能X2与LNX3存在多重共线性。根据X2与LNX3的相关性检验X2LNX3X2 1.000000 0.912097LNX3 0.912097 1.000000相关系数为0.912097，表示X2与LNX3的相关程度较高。由于经济意义中的基金价格与基金净值存在很大的相关性，所以也有可能是变量间存在异方差和自相关（DW=0.015032）所引起的。3.异方差检验(1)残差图形分析由图可以初步判断出，残差平方e2对解释变量X2和LNX3的散点图主要分布在图形中的下三角部分，可看出残差平方e2随解释变量X2和LNX3的变动呈增大趋势，因此模型可能

29、存在异方差。但是需通过更进一步的检验。(2)ARCH检验ARCH Test:F-statistic1075.043    Probability0.000000Obs*R-squared194.7423    Probability0.000000Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 01/11/13 Time: 00:13Sample (adjusted): 9/26/2008 9/07/2012Included ob

30、servations: 207 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.  C0.0007990.0004391.8199260.0702RESID2(-1)0.9286570.06908013.443140.0000RESID2(-2)0.2109720.0940932.2421710.0260RESID2(-3)-0.1751760.069660-2.5147380.0127R-squared0.940784    Mean dependent v

31、ar0.019492Adjusted R-squared0.939909    S.D. dependent var0.016744S.E. of regression0.004105    Akaike info criterion-8.134305Sum squared resid0.003420    Schwarz criterion-8.069904Log likelihood845.9005    F-statistic10

32、75.043Durbin-Watson stat1.989930    Prob(F-statistic)0.000000给定显著性水平=0.05，查2分布表得临界值2（3）=7.81473，因为Obs*R-squared=194.74232（3）=7.81473，故表明模型中的随机误差项存在异方差。（3）异方差的修正Dependent Variable: YMethod: Least SquaresDate: 01/11/13 Time: 08:36Sample (adjusted): 9/05/2008 9/07/2012Included obser

33、vations: 210 after adjustmentsWeighting series: W2VariableCoefficientStd. Errort-StatisticProb.  C-8.2681560.918139-9.0053380.0000X2-0.1808560.174451-1.0367180.3011LNX31.1126800.1310448.4908700.0000Weighted StatisticsR-squared0.363942    Mean dependent var0.693156Adjust

34、ed R-squared0.357796    S.D. dependent var0.162016S.E. of regression0.129835    Akaike info criterion-1.230914Sum squared resid3.489452    Schwarz criterion-1.183098Log likelihood132.2460    F-statistic352.2040Durbin-Wat

35、son stat0.036138    Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.552751    Mean dependent var0.751648Adjusted R-squared0.548429    S.D. dependent var0.210560S.E. of regression0.141494    Sum squared resid4.14

36、4277Durbin-Watson stat0.020198运用加权最小二乘法（WLS）估计过程中，我们分别选用了权数w1=1/x2, w2=1/x22, w3=1/sqr(x2)。生成权数后，经估计检验发现用权数w2的效果最好。但是，从表中可以看出，X2的系数变为负数，这与经济意义有些不相符合，而且X2的P值也是相对偏大的，Adjusted R-squared=0.357796，说明拟合优度不是很好。根据表中Durbin-Watson stat=0.036138，表明模型中极有可能存在自相关性。4.自相关检验（1）图示法检验图一为绘制的E（-1）和E的散点图，表明随机误差项u存在着正自相关。

37、图二为按照时间顺序绘制回归残差项E的图形，根据E随着时间的变化逐次有规律的变化，且一段时间为正后，又一段时间为负，表明随机误差项u存在着正自相关。（2）DW检验法样本量为210，两个解释变量的模型，在0.05显著水平上，查DW统计表可知，dL=1.748，dU=1.789模型中的DW=0，.036138dL=1.748，说明模型中显然存在自相关。Date: 01/07/13 Time: 19:33Sample: 9/05/2008 11/22/2012Included observations: 208AutocorrelationPartial CorrelationAC 

38、0;PAC Q-Stat Prob    *|. |    *|. |1-0.491-0.49150.8170.000       .|. |      *|. |20.042-0.26151.1970.000       *|. |     *|.

39、 |3-0.144-0.34855.6260.000       .|* |       *|. |40.155-0.15760.7940.000       *|. |       *|. |5-0.060-0.13061.5760.000      

40、60;.|. |      *|. |6-0.031-0.18961.7820.000       .|. |       *|. |70.021-0.13961.8800.000       .|. |       *|. |80.037-0.08062.1

41、840.000       .|. |       .|. |90.0250.00862.3260.000       *|. |       .|. |10-0.058-0.00563.0750.000       *|. |  

42、;     *|. |11-0.074-0.15064.2750.000       .|* |       .|. |120.122-0.03467.5740.000       .|. |       .|. |13-0.035-0.03567.8460.000&#

43、160;      *|. |       *|. |14-0.065-0.15768.7830.000       .|* |       .|. |150.095-0.00470.8330.000       .|. |   

44、    .|. |16-0.026-0.01970.9840.000       .|. |       .|. |17-0.011-0.05471.0100.000       *|. |       *|. |18-0.067-0.10672.0440.000 &#

45、160;     .|* |       .|. |190.1430.05576.7580.000       *|. |       .|. |20-0.103-0.01479.2070.000       .|* |    &

46、#160;  .|* |210.0980.09981.4500.000       *|. |       .|. |22-0.1060.05484.0930.000       .|. |       .|. |230.011-0.03284.1210.000   &

47、#160;   .|. |       *|. |24-0.000-0.06184.1210.000       .|. |       .|. |250.055-0.00984.8350.000       .|. |      

48、; .|. |26-0.0220.04184.9510.000       .|. |       .|. |270.0050.04084.9580.000       .|. |       *|. |28-0.050-0.06385.5530.000    

49、0;  .|. |       .|. |290.035-0.03585.8530.000       .|. |       .|. |30-0.003-0.00685.8550.000       .|. |       .|

50、* |310.0570.07786.6680.000       *|. |       .|. |32-0.0940.03088.8520.000       .|* |       .|* |330.0800.07990.4370.000根据残差E的相关图，可以看出模型中存在一阶自相关，滞后期数为一期。（3）自相关问题的处理Dependent Variable: YMethod: Least SquaresDate: 01/07/13 Time: 19:38Sample (adjusted): 9/12/2008 9/07/2012Included observations: 209 after adjustmentsConvergence achieved after 7 iterationsVariableCoefficientStd. Errort-StatisticProb.  C-3.5830160.674493-5.3121660.0000X20.