*! version 1.2.1 07mar2013

Title

grstest2 -- Program to implement the Gibbons, Ross, Shanken (1989) test to assess asset pricing model performance.

Syntax

grstest2
varlist
[if]
, flist(string) [alphas nqui]

Main
flist Required option. Enter the factors here (e.g. market factor)

alphas Displays the magnitude of each individual intercept estimate

nqui Does not suppress regression output

Description

grstest2 calculates the Gibbons, Ross, Shanken (GRS) test statistic (1989) for the variables in
varlist and the factors when the data is in wide-format (each portfolio return has its own column). The GRS test statistic is:

J1 = (T-N-K)/N * (1+E[f]' var[f]^-1 E[f]') alpha sigma^-1 alpha ~ F(N,T-N-K)

where T is the number of observations in the time-series, N is the number of assets, K is the number of factors.
Further, E[f] is the sample mean of the factors, var[f] is their estimated variance-covariance matrix, alpha are the estimated intercepts from the individual time-series regressions and sigma is the estimated variance-covariance matrix of the intercepts.

grstest2 further reports an asymptotically valid chi-square test:

J0 = T(1+E[f]' var[f]^-1 E[f]') alpha sigma^-1 alpha ~ Chisquared(N)

To derive J1, normally distributed errors are assumed. J0 does not need that assumption but is only asymptotically valid.

Moreover, grstest2 displays the average intercept, the average adjusted R^2, the average standard error of the intercepts, the average absolute value of the intercepts and the sharpe ratio of the intercepts.

Remarks

1. grstest2 requires data to be in wide format, i.e. portfolio returns in columns, time in rows.

2. grstest2 uses excess returns (returns in excess of the risk-free rate), i.e. the time-series regression run to estimate the individual intercepts (alphas) is:

r_it - r_ft = alpha_i + beta_i' f_t + e_it

If you do not use excess returns, the test statistic will be wrong.

Examples

. grstest2 r*, flist(Rm)

. grstest2 r*, flist(Rm SMB HML WML) alphas

. grstest2 return1 return2, flist(Rm SMB HML WML) alphas nqui

References

Gibbons, M.R., Ross, S.A. & Shanken, J., 1989. A test of the efficiency of a given portfolio.
Econometrica, 57(5), 1121–1152.

Author

Markus Ibert
Swedish House of Finance
Stockholm School of Economics
markus.ibert@phdstudent.hhs.se