| fmCov {facmodCS} | R Documentation |
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, factor.cov, ...)
## S3 method for class 'ffm'
fmCov(object, factor.cov, use = "pairwise.complete.obs", ...)
Arguments
object |
fit object of class |
factor.cov |
factor covariance matrix (optional); defaults to the sample covariance matrix. |
... |
optional arguments passed to |
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". |
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".
Value
The computed N x N covariance matrix for asset returns based
on the fitted factor model.
Author(s)
Eric Zivot, Yi-An Chen and Sangeetha Srinivasan.
References
Zivot, E., & Jia-hui, W. A. N. G. (2006). Modeling Financial Time Series with S-Plus Springer-Verlag.
See Also
cov for more details on arguments use and
method.