------------------------------------------------------------------------------- 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) * ((T-N-K) / (T-K-1)) * 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 fo factors in the flist fbar= column vector of the factor means (K*1) omegahat = variance-covariance matrix for the factors (K*K) bohat = column vector of intercept estimates (N *1) sigmahat = the unbaised residual 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 * (T-N-1) / (N *(T-2)) * 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 variance of the factor. bohat = column vector of intercept estimates (N *1) sigmahat = the unbaised residual 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 pogram will assume that the returns a > re 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), 11211152.

Moore,J.D.,2009, Using the GRS test statistic to asses factor model fit. Availa > ble at http://djmphd.googlepages.com/epublications. {p_end}