# [R-SIG-Finance] Factor models and SDF with gmm

Petri Tötterman petri.totterman at hanken.fi
Tue Mar 1 13:50:31 CET 2011

```Dear all,

do you have experiences about estimating CAPM, Fama-French etc model
parameters in SDF form using gmm? I am trying to follow Cochrane
(Asset Pricing, 2005) chapter 13, where he suggests estimating the SDF

1 = E[mR]

where m is defined by factors f (1...N)

m = b1 * f1 + ... + bN * fN

Significant f factors would imply that they participate in pricing.
However, moment conditions should also be met, which is my main concern.

There is a good introduction in the gmm vignette, which I have used as
baseline. My code is

---
g <- function(Theta, x) {
gmat <- (Theta[1] * x[,1] + Theta[2] * x[,2] + Theta[3] *
x[,3]) * x[,4:ncol(n)] -1
return(gmat)
}

# z = portfolio excess return
# zm = market excess return
# zhml = high-low B/M portfolio excess return
# zsmb = small-big firm portfolio excess return

sdf <- gmm(g, x = as.matrix(cbind(z, zm, zhml, zsmb)), c(0, 0, 0))
summary(sdf)
---

but, using different datasets from Dr. French's homepage, either J
values from specTest() are very high, implying the moment conditions
do not hold, or the factors are not significantly different from zero.
Obviously, in both cases the model is rejected.

Any suggestions, how should the model and the moment conditions be expressed?

Best regards
/petri

--
Petri Tötterman

```