CAPM模型在中国有效性论证

一.研究方法

CAPM模型的形式为:Ri=Rf+i(Rm-Rf)(1)。其中:Ri为第i种股票的收益率。Rf为无风险利率，Rm为市场组合的收益率,i是风险系数。

检验该模型是否有效，首先要估计个股的系数。本文采用的方法是对单个股票的收益率Ri与市场指数的收益率Rm进行时间序列的回归

确定系数之后，就可以将作为自变量对单个股票的收益率与系数再进行一次回归，进行检验。 二.样本选择 1、股票品种

本文随机选择股票，为以下十只 1.浦发银行 2.招商银行 3.兴业银行 4.南方航空 5.同仁堂 6.日照港 7.万科A 8.大唐发电 9.中国宝安 10.盐田港 2、市场指数

本文选择上证综合指数作为市场组合指数 3、无风险利率 Rf=0.025

三．所选股票数据的年份：2010.1.4-2010.12.31 四．具体操作

（一）回归求beta系数

1、浦发银行

Dependent Variable: Y Method: Least Squares Date: 12/25/11 Time: 14:26 Sample: 1/04/2010 12/31/2010 Included observations: 242

CoefficiVariable ent Std. Error t-Statistic

-0.027-26.3029C 818 0.001058 5

0.0061

X 86 0.000605 10.22709 0.3035 Mean dependent

R-squared 27 var Adjusted 0.3006 S.D. dependent R-squared 25 var

Prob. 0.0000 0.0000 -0.027912 0.0196

73

0.0164

S.E. of regression 52 Sum squared 0.0649resid 61

651.58

Log likelihood 93 Durbin-Watson 1.4747stat 69

2、招商银行

Akaike criterion

info

Schwarz criterion F-statistic Prob(F-statistic)

-5.368

507 -5.339673 104.59

34 0.0000

00 Dependent Variable: Y Method: Least Squares Date: 12/25/11 Time: 14:33 Sample: 1/04/2010 12/31/2010 Included observations: 242

CoefficStd. Variable ient Error t-Statistic

-0.0260.00096-26.8375C 016 9 4

0.00600.0005510.8452

X 13 4 1 0.3288 Mean dependent

R-squared 94 var Adjusted 0.3260 S.D. dependent R-squared 98 var S.E. of 0.0150 Akaike info regression 80 criterion Sum squared 0.0545resid 76 Schwarz criterion

672.66

Log likelihood 53 F-statistic Durbin-Watson 1.6737stat 52 Prob(F-statistic)

3、兴业银行

Dependent Variable: Y Method: Least Squares Date: 12/25/11 Time: 14:38

Prob. 0.0000 0.0000

-0.026108 0.0183

70 -5.542689 -5.513854 117.61

87 0.0000

00

Sample: 1/04/2010 12/31/2010 Included observations: 242

Coeffici

Variable ent Std. Error t-Statistic

-0.026-20.6908C 554 0.001283 5

0.0073

X 86 0.000734 10.06317 0.2967 Mean dependent

R-squared 39 var Adjusted 0.2938R-squared 09 S.D. dependent var

0.0199 Akaike info

S.E. of regression 64 criterion Sum squared 0.0956resid 53 Schwarz criterion

604.76

Log likelihood 88 F-statistic Durbin-Watson 1.7593stat 53 Prob(F-statistic)

4、南方航空

Dependent Variable: Y Method: Least Squares Date: 12/25/11 Time: 14:43 Sample: 1/04/2010 12/31/2010 Included observations: 242

CoefficiVariable ent Std. Error t-Statistic

-0.022-15.5321C 864 0.001472 2

0.0121

X 31 0.000842 14.40960 0.4638 Mean dependent

R-squared 51 var Adjusted 0.4616R-squared 17 S.D. dependent var S.E. of regression 0.0228 Akaike info

Prob. 0.0000 0.0000 -0.026666 0.0237

57 -4.9815

60 -4.9527

26 101.26

75 0.0000

00

Prob. 0.0000 0.0000 -0.023048 0.0312

08 -4.7072

98 criterion 66

Sum squared 0.1258-4.6784resid 41 Schwarz criterion 31

571.57207.63

Log likelihood 91 F-statistic 65 Durbin-Watson 1.81550.0000stat 10 Prob(F-statistic) 00

5、同仁堂

Dependent Variable: Y Method: Least Squares Date: 12/25/11 Time: 14:47 Sample (adjusted): 1/04/2010 12/01/2010 Included observations: 220 after adjustments

CoefficiVariable ent Std. Error t-Statistic Prob.

-0.022-13.8466C 327 0.001612 5 0.0000

0.0093

X 07 0.000907 10.26638 0.0000 0.3259 Mean dependent -0.0223

R-squared 09 var 63 Adjusted 0.32280.0290R-squared 17 S.D. dependent var 63

0.0239 Akaike info -4.6194

S.E. of regression 16 criterion 71 Sum squared 0.1246-4.5886resid 93 Schwarz criterion 20

510.14105.39

Log likelihood 18 F-statistic 86 Durbin-Watson 1.88970.0000stat 25 Prob(F-statistic) 00

6、日照港

Dependent Variable: Y Method: Least Squares Date: 12/25/11 Time: 14:50 Sample: 1/04/2010 12/31/2010 Included observations: 242

Coeffic

Variable ient Std. Error t-Statistic

-0.025-23.9964C 535 0.001064 7

0.0078

X 23 0.000609 12.85477 0.4077 Mean dependent

R-squared 66 var Adjusted 0.4052 S.D. dependent R-squared 98 var

0.0165 Akaike info

S.E. of regression 53 criterion Sum squared 0.0657resid 64 Schwarz criterion

650.10

Log likelihood 26 F-statistic Durbin-Watson 1.7268stat 77 Prob(F-statistic)

7、万科A

Dependent Variable: Y Method: Least Squares Date: 12/25/11 Time: 15:07 Sample: 1/04/2010 12/31/2010 Included observations: 242

CoefficiVariable ent Std. Error t-Statistic

-0.027-13.3316

C 602 0.002070 7

0.0063

X 18 0.001184 5.335586 0.1060 Mean dependent

R-squared 40 var Adjusted 0.1023R-squared 15 S.D. dependent var

0.0322 Akaike info

S.E. of regression 06 criterion Sum squared 0.2489resid 42 Schwarz criterion Log likelihood 489.03 F-statistic

Prob.

0.0000 0.0000 -0.025654 0.0214

65 -5.356220 -5.327385 165.24

51 0.0000

00

Prob. 0.0000 0.0000 -0.027698 0.0339

92 -4.0250

68 -3.9962

34 28.468

Durbin-Watson stat

8、大唐发电

Dependent Variable: Y Method: Least Squares Date: 12/25/11 Time: 15:10 Sample: 1/04/2010 12/31/2010 Included observations: 242

CoefficiVariable ent Std. Error t-Statistic

-0.024-10.8815

C 475 0.002249 5

0.0058

X 79 0.001286 4.570003 0.0800 Mean dependent

R-squared 54 var Adjusted 0.0762R-squared 21 S.D. dependent var

0.0349 Akaike info

S.E. of regression 88 criterion Sum squared 0.2937resid 94 Schwarz criterion

468.98

Log likelihood 85 F-statistic Durbin-Watson 1.1836stat 46 Prob(F-statistic)

9、中国宝安

Dependent Variable: Y Method: Least Squares Date: 12/25/11 Time: 15:13 Sample: 1/04/2010 12/31/2010 Included observations: 242

CoefficiVariable ent Std. Error t-Statistic

-0.023-13.9893

C 052 0.001648 1

33

1.2358

06 Prob(F-statistic) 48

0.0000

00

Prob. 0.0000 0.0000 -0.024564 0.0364

03 -3.8594

09 -3.8305

75 20.884

93 0.0000

08

Prob. 0.0000

0.0130

X 54 0.000942 13.85118

0.4442 Mean dependent

R-squared 58 var Adjusted 0.4419R-squared 43 S.D. dependent var

0.0256 Akaike info

S.E. of regression 33 criterion Sum squared 0.1576resid 93 Schwarz criterion

544.27

Log likelihood 80 F-statistic Durbin-Watson 2.1489stat 78 Prob(F-statistic)

10、盐田港

Dependent Variable: Y Method: Least Squares Date: 12/25/11 Time: 15:16 Sample: 1/04/2010 12/31/2010 Included observations: 242

CoefficiVariable ent Std. Error t-Statistic

-0.026-32.0389C 141 0.000816 7

0.0076

X 93 0.000467 16.48540

0.5310 Mean dependent

R-squared 38 var Adjusted 0.5290R-squared 84 S.D. dependent var

0.0126 Akaike info

S.E. of regression 92 criterion Sum squared 0.0386resid 60 Schwarz criterion

714.38

Log likelihood 42 F-statistic Durbin-Watson 2.1605stat 07 Prob(F-statistic)

0.0000

-0.0232

50 0.0343

13 -4.4816

37 -4.4528

02 191.85

52 0.0000

00

Prob. 0.0000 0.0000 -0.0262

57 0.0184

95 -5.8874

72 -5.8586

38 271.76

84 0.0000

00

 Beta系数：

1. 浦发银行：0.006186 2. 招商银行：0.006013 3. 兴业银行：0.007386 4. 南方航空：0.012131 5. 同仁堂：0.009307 6. 日照港：0.007823 7. 万科A：0.006318 8. 大唐发电：0.005879 9. 中国宝安：0.013054 10. 盐田港：0.007693

 个股平均收益率： 11. 浦发银行：-0.00828 12. 招商银行：-0.00429 13. 兴业银行：-0.01637 14. 南方航空：0.009657 15. 同仁堂：-0.02085 16. 日照港：0.00495 17. 万科A：-0.00167 18. 大唐发电：-0.00179 19. 中国宝安：-0.00247 20. 盐田港：-0.00182

（二）Beta系数和平均收益率的回归： Dependent Variable: Y Method: Least Squares Date: 12/25/11 Time: 22:35 Sample: 1 10 Included observations: 10

Coeffici

Variable ent Std. Error t-Statistic

-0.010-1.04969C 900 0.010384 8

0.8077

X 28 1.217043 0.663681 0.0521 Mean dependent

R-squared 86 var Adjusted -0.066 S.D. dependent R-squared 291 var

Prob. 0.3245 0.5256 -0.004294 0.0090

58

0.0093 Akaike info -6.3292

S.E. of regression 53 criterion 90 Sum squared 0.0007-6.2687resid 00 Schwarz criterion 73

33.6460.4404

Log likelihood 45 F-statistic 73 Durbin-Watson 3.29330.5255stat 57 Prob(F-statistic) 55

（三）结果：回归结果显示，R-squared=0.009058，数值很小，说明系统风险对股票预期收益率的解释能力很弱。这些情况都表明CAPM模型在中国股票市场是不适用的。

（四）结论：CAPM模型在中国证券市场是非有效的，综合来看，有两个原因。一是CAPM模型存在着一系列严格的假定，而中国证券市场不可能满足它所有的假定，这是造成CAPM模型非有效的一个重主要因素。二是市场指数的选择。目前我国普遍使用的是市场指数是深交所成分指数和上证综合指数。但是其中有相当一部分股票不能上市流通，而编制的指数却将他们考虑在内，从而不能反映股票市场的真实状况。因此它在一定程度上存在着不合理性。