# R/GRS.MLtest.R In GRS.test: GRS Test for Portfolio Efficiency, Its Statistical Power Analysis, and Optimal Significance Level Calculation

#### Documented in GRS.MLtest

```GRS.MLtest <-
function(ret.mat,factor.mat){
ret.mat=as.matrix(ret.mat); factor.mat=as.matrix(factor.mat)
N=ncol(ret.mat); T=nrow(ret.mat); K = ncol(factor.mat)

rmat=as.matrix(colMeans(factor.mat))
mat=factor.mat
V = cov(mat); V=V*(T-1)/(T)  # Use ML estimator as in GRS
theta2 = t(rmat) %*% solve(V) %*% rmat

rmat=rbind(as.matrix(colMeans(ret.mat)),as.matrix(colMeans(factor.mat)))
mat=cbind(ret.mat,factor.mat)
V = cov(mat); V=V*(T-1)/(T)  # Use ML estimator as in GRS
thetas2 = t(rmat) %*% solve(V) %*% rmat

tem3 = T/N; tem4 = (T-N-K)/(T-K-1)
tem1= sqrt(1+thetas2); tem2= sqrt(1+theta2)
F = tem3*tem4 *((tem1/tem2)^2 -1)
p.F = pf(F,df1=N,df2=T-N-K,lower.tail=FALSE)
ratio=sqrt(theta2/thetas2)

colnames(F) = "GRS"; colnames(p.F) = "GRS"

return(list(GRS.stat=F,GRS.pval=p.F,thetas=sqrt(thetas2),theta=sqrt(theta2),ratio=ratio))
}
```

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GRS.test documentation built on Dec. 4, 2017, 9:03 a.m.