Fama-French等人在检验和拒绝多因子模型的时候，用的一个检验叫做GRS检验。但是我不知道这个检验的原理是什么，也不知道检验的目的是怎样的，也不知道如何用STATA进行GRS检验，及出结果之后怎么利用这个检验的结果。
我找到了英文原稿，但是我还是看不懂，英文太垃圾了。
求大神用通俗语言给我介绍一下，解释一下这个检验，多谢
GRS原稿为：http://wenku.baidu.com/link?url=mSbN3ufzgr9Z4y31wo8ojzvdcxq1zDiQSmnbpO7JoUes-Zl3mcawrkHK3SC8fH8wN8nXo-uOik0cKbL8sjryeFjleFBOQspmPoQmtAPwks3
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}
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