factorModelSdDecomposition: Compute factor model standard deviation decomposition

In R-Finance/FactorAnalytics: factor analysis

Description

Compute the factor model factor standard deviation decomposition for an asset based on Euler's theorem given factor model parameters.

Usage

  factorModelSdDecomposition(beta.vec, factor.cov, sig2.e)

Arguments

beta.vec	k x 1 vector of factor betas with factor names in the rownames.
factor.cov	k x k factor excess return covariance matrix.
sig2.e	scalar, residual variance from factor model.

Details

The factor model has the form
R(t) = beta'F(t) + e(t) = beta.star'F.star(t)
where beta.star = (beta, sig.e)' and F.star(t) = [F(t)', z(t)]'. By Euler's theorem:
Sd.fm = sum(cSd.fm) = sum(beta.star*mSd.fm)

Value

an S3 object containing

• Sd.fm Scalar, std dev based on factor model.

• mSd.fm (K+1) x 1 vector of factor marginal contributions to sd.

• cSd.fm (K+1) x 1 vector of factor component contributions to sd.

• pcSd.fm (K+1) x 1 vector of factor percentage component contributions to sd.

Author(s)

Eric Zivot and Yi-An Chen

References

1. Hallerback (2003), "Decomposing Portfolio Value-at-Risk: A General Analysis", The Journal of Risk 5/2.

2. Yamai and Yoshiba (2002)."Comparative Analyses of Expected Shortfall and Value-at-Risk: Their Estimation Error, Decomposition, and Optimization Bank of Japan.

3. Meucci (2007). "Risk Contributions from Generic User-Defined Factors," Risk.

#'

Examples

# load data from the database
data("stat.fm.data")
fit.stat <- fitStatisticalFactorModel(sfm.dat,k=2)
cov.factors = var(fit.stat$factors)
names = colnames(fit.stat$asset.ret)
factor.sd.decomp.list = list()
for (i in names) {
 factor.sd.decomp.list[[i]] =
   factorModelSdDecomposition(fit.stat$loadings[,i],
                              cov.factors, fit.stat$resid.variance[i])
}

R-Finance/FactorAnalytics documentation built on May 8, 2019, 3:51 a.m.