fmCov: Covariance Matrix for assets' returns from fitted factor...
In factorAnalytics: Factor Analytics

Description Usage Arguments Details Value Author(s) References See Also Examples

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.

fmCov(object, ...)

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

## S3 method for class 'sfm'
fmCov(object, ...)

## S3 method for class 'ffm'
fmCov(object, ...)

`object`	fit object of class `tsfm`, `sfm` or `ffm`.
`...`	optional arguments passed to `cov`.
`factor.cov`	optional user specified factor covariance matrix with named columns; 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".

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.

For the time series factor model, the user can specify a factor covariance matrix; otherwise the default is to use the sample covariance from factor returns. 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".

For the statistical and fundamental factor model, the factor model covariances already computed via the model fitting functions are simply recalled by this method for user convenience.

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

Eric Zivot, Yi-An Chen and Sangeetha Srinivasan.

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

fitTsfm, fitSfm, fitFfm

cov for more details on arguments use and method.

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

# Statistical Factor Model
data(StockReturns)
sfm.pca.fit <- fitSfm(r.M, k=2)
fmCov(sfm.pca.fit)

# Fundamental factor Model
data(Stock.df)
exposure.vars <- c("BOOK2MARKET", "LOG.MARKETCAP", "GICS.SECTOR")
fit2 <- fitFfm(data=stock, asset.var="TICKER", ret.var="RETURN", 
              date.var="DATE", exposure.vars=exposure.vars)
fmCov(fit2)