facmodTS (version 1.0)

fmCov: Covariance Matrix for assets' returns from fitted factor model.

Description

Computes the covariance matrix for assets' returns based on a fitted factor model. This is a generic function with methods for classes tsfm, sfm and ffm.

Usage

fmCov(object, ...)
# S3 method for tsfm
fmCov(object, factor.cov, use = "pairwise.complete.obs", ...)
# S3 method for sfm
fmCov(object, use = "pairwise.complete.obs", ...)
# S3 method for ffm
fmCov(object, use = "pairwise.complete.obs", ...)

Value

The computed N x N covariance matrix for asset returns based on the fitted factor model.

Arguments

object

fit object of class tsfm, sfm or ffm.

...

optional arguments passed to cov.

factor.cov

factor covariance matrix (optional); defaults to the sample covariance matrix.

use

method for computing covariances in the presence of missing values; one of "everything", "all.obs", "complete.obs", "na.or.complete", or "pairwise.complete.obs". Default is "pairwise.complete.obs".

Author

Eric Zivot, Yi-An Chen and Sangeetha Srinivasan.

Details

R(i, t), the return on asset i at time t, is assumed to follow a factor model of the form,

R(i,t) = alpha(i) + beta(i)*f(t) + e(i,t),

where, alpha(i) is the intercept, f(t) is a K x 1 vector of factor returns at time t, beta(i) is a 1 x K vector of factor exposures and the error terms e(i,t) are serially uncorrelated across time and contemporaneously uncorrelated across assets so that e(i,t) ~ iid(0,sig(i)^2). Thus, the variance of asset i's return is given by

var(R(i)) = beta(i)*cov(F)*tr(beta(i)) + sig(i)^2.

And, the N x N covariance matrix of asset returns is

var(R) = B*cov(F)*tr(B) + D,

where, B is the N x K matrix of factor betas and D is a diagonal matrix with sig(i)^2 along the diagonal.

The method for computing covariance can be specified via the ... argument. Note that the default of use="pairwise.complete.obs" for handling NAs restricts the method to "pearson".

References

Zivot, E., & Jia-hui, W. A. N. G. (2006). Modeling Financial Time Series with S-Plus Springer-Verlag.

See Also

fitTsfm

cov for more details on arguments use and method.

Examples

# Time Series Factor model example
 # load data
data(managers, package = 'PerformanceAnalytics')
 # Make syntactically valid column names
colnames(managers)
colnames(managers) <- make.names( colnames(managers))
colnames(managers)

fit <- fitTsfm(asset.names = colnames(managers[, (1:6)]), 
               factor.names = c("EDHEC.LS.EQ","SP500.TR"), 
               data = managers)                              
fmCov(fit)