GRS 检验悬赏急求解答

如上图所示，分别有CAPM、Fama-French、新三因子模型对某个股市异象SUE进行解释。将股票根据SUE的大小平均分为10组，最小的一组为LOW，最大的一组叫HIGH，中间一组为第五组，H-L是最大的一组减去最小的一组的，分别对每组计算平均收益率。然后用那三个因子模型对每组进行回归，得到结果，这个我可以理解。我不理解的是这个GRS是怎么回事儿，是对哪一组做的GRS检验？或者说如果我也想做这样一个检验的话，该怎么做？

stata 中grs检验的方法：
STATA中GRS检验的解释：
-------------------------------------------------------------------------------
help for grstest
-------------------------------------------------------------------------------
grstest - module to implement the Gibbons et al. (1989) test in a single factor
>  or a multi factor setting
Syntax :
grstest varlist,flist(factorlist) [ret(string)]
Description :
multi factor setting
grstest implements the test by Gibbons et al.(1989) within a multi factor setti
> ng when the  
the number of factors in flist is greater than 1. Here, grstest computes the gr
> s test statistic as
GRS = ((`T'-`N'-`K')/(`N')) * w ~ F(df1,df2)
where w =  (bohat' * sigmahat^-1 * bohat) / (1 + fbar' * omegahat^-1 * fbar)
and,
T = total number of observations
N = Number of portfolios or assets
K = Number of factors in the flist
fbar= column vector of the factor means (K*1)
omegahat = variance-covariance matrix of the factors (K*K)
bohat = column vector of intercept estimates (N *1)
sigmahat = the residual variance-covariance matrix (N *N)
df1 = N
df2 = T-N-K
single factor setting
grstest implements the test by Gibbons et al.(1989) within a single factor sett
> ing when the  
the number of factors in flist is equal to 1. Here, grstest computes the grs te
> st statistic as
GRS = ((`T'-`N'-`K')/(`N')) * w ~ F(df1,df2)
where w =  (bohat' * sigmahat^-1 * bohat) / (1+ thetahat^2)
and,
T = total number of observations
N = Number of portfolios or assets
K = 1
thetahat= sample mean of the factor / sample standard deviation of the factor.
bohat = column vector of intercept estimates (N *1)
sigmahat = the  residual variance-covariance matrix (N *N)
df1 = N
df2 = T-N-1
Example Usage:
     . grstest p*, flist(rmrf smb hml) ret(r)
     . grstest p*, flist(f*) ret(r)
     . grstest s*b*_vwr, flist(mktrf smb hml)
     . grstest s*b*_vwr, flist(mktrf)
Options
flist (factorlist) : specifies the factors.  It is a required option.
ret (string): this must be specified as ret(r) if the returns are raw returns.
> If it is not specified or incorrectly
specified with anything other than r, the program will assume that the returns
> are excess returns. It is not a required
option.
Notes:
1. grstest requires that data be in the wide format i.e with each portfolio ret
> urn and factor in a separate variable.
2. grstest requires that the option ret(r) is to be specified if the portfolio/
> asset returns are raw returns.
   If ret(r) is specified, the excess returns will be computed automatically.Ho
> wever, if  ret(r) is specified,
   grstest requires that a variable rf containing  the relevant risk free rate
> is  present to calculate the excess
   returns. Specifying ret(r) without a rf variable will result in an error. If
>  the option ret() is not specified or  
   incorrectly specified then grstest will display the message "The option ret(
> ) is not specified or specified
   properly.grstest will assume that the returns are excess returns" and run th
> e test assuming that the returns are
   excess returns.
Author:
     Rajesh Tharyan
     Xfi- Centre for Finance and Investment
     University of Exeter
     r.tharyan@ex.ac.uk
References:
Fama, E.F. & French, K.R., 1993. Common risk factors in the returns on stocks a
> nd bonds. Journal of Financial Economics, 33(1), 3-56.
Gibbons, M.R., Ross, S.A. & Shanken, J., 1989. A test of the efficiency of a gi
> ven portfolio. Econometrica, 57(5), 1121?152.
{p_end}

理论上alpha必须等于零，GRS检验的就是这10组是否联合等于零；至于怎么用，说明书中已经说的很再清楚不过了

s.hsiao 发表于 2015-4-25 23:23
理论上alpha必须等于零，GRS检验的就是这10组是否联合等于零；至于怎么用，说明书中已经说的很再清楚不过了

上图中m.a.e是啥意思啊？括号里面的p-grs是啥意思？这个检验怎么用呢？比如说做GRS检验的结果是：
You are testing a multi factor model with 3 factors rmrf rmw cma and 3 portfolios.
The GRS test statistic is:  6.3442368 and the p-value is:  .00059609
这个值怎么判断检验结果的好坏啊？GRS检验结果越大越好吗？判断结果好坏的标准是什么啊？

s.hsiao 发表于 2015-4-25 23:23
理论上alpha必须等于零，GRS检验的就是这10组是否联合等于零；至于怎么用，说明书中已经说的很再清楚不过了

You are testing a multi factor model with 3 factors rmrf rmw cma and 3 portfolios.
The GRS test statistic is:  6.3442368 and the p-value is:  .00059609

以上为GRS检验的结果，怎么解读这个结果呢？是GRS值越大越好还是越小越好啊？上图中m.a.e是什么意思？GRS结果评判的标准是啥啊？

记得不是很清楚了 值应该是越小越好 p值越大越好 说明不能拒绝alpha联合零假设

ps: GRS检验是一个理想状态 一般都是通不过的 比较2个模型的好坏 一般看看GRS的值改进了多少

谁知道GRS检验的结果怎么判断呀？GRS大好还是小好？对应的P-VALUE是大好，还是小好？正确回答此问题者得到所有悬赏

bsgang 发表于 2015-5-3 23:41
谁知道GRS检验的结果怎么判断呀？GRS大好还是小好？对应的P-VALUE是大好，还是小好？正确回答此问题者得到所 ...

我也不是太知道，最近正好问了下。
因为原假设是说所有的alpha都等于零，所以如果P-value较大，说明不能拒绝原假设，也就是认为所有的alpha为零，那么就说明asset pricing model中的那些因子能够基本上解释returns，但是如果p value较小，则说明能够拒绝原假设。

原假设是 alpha=0，
通过GRS检验得出P值是否大于某一个值，如果是就可以拒绝原假设，即是模型里面alpha不是0，意味着模型解释力度不足
在论文那里提到了P值都比较大
GRS算法可以google到

您好  请教一下 做GRS检验的时  grstest 后面跟的是因变量吗 比如做FF 55分组的话，那么就是grstest r11 r12 ...r55, flist(rmrf smb hml) 这样吗？但是总是报错no observations, 请哪位看到的大神帮忙指点12，或者留言，或者邮箱我一下wdy_hnu@126.com  1019975351(QQ交流也✌)在此谢过啦