R/factorModelCovariance.r

In R-Finance/FactorAnalytics: factor analysis

#' Compute Factor Model Covariance Matrix.
#' 
#' Compute asset return covariance matrix from factor model.
#' 
#' The return on asset \code{i} is assumed to follow the
#' factor model 
#' \cr \code{R(i,t) = alpha + t(beta)*F(t) + e(i,t), e(i,t) ~ iid(0, sig(i)^2)} \cr
#' where \code{beta} is a \code{K x 1} vector of factor
#' exposures. The return variance is then \cr \code{var(R(i,t) =
#' t(beta)*var(F(t))*beta + sig(i)^2}, \cr and the \code{N x N} covariance
#' matrix of the return vector \code{R} is \cr \code{var(R) = B*var(F(t))*t(B)
#' + D} \cr where B is the \code{N x K} matrix of asset betas and \code{D} is a
#' diagonal matrix with \code{sig(i)^2} values along the diagonal.
#' 
#' @param beta \code{N x K} matrix of factor betas, where \code{N} is the
#' number of assets and \code{K} is the number of factors.
#' @param factor.cov \code{K x K} factor return covariance matrix.
#' @param resid.variance \code{N x 1} vector of asset specific residual
#' variances from the factor model.
#' @return \code{N x N} return covariance matrix based on factor model
#' parameters.
#' @author Eric Zivot and Yi-An Chen.
#' @references Zivot, E. and J. Wang (2006), \emph{Modeling Financial Time
#' Series with S-PLUS, Second Edition}, Springer-Verlag.
#' @export
#' @examples
#'  \dontrun{
#' # Time Series model
#' 
#' data(managers.df)
#' factors    = managers.df[,(7:9)]
#' fit <- fitTimeSeriesFactorModel(assets.names=colnames(managers.df[,(1:6)]),
#'                                 factors.names=c("EDHEC.LS.EQ","SP500.TR"),
#'                                 data=managers.df,fit.method="OLS")
#' factors    = managers.df[,(7:8)]                               
#' factorModelCovariance(fit$beta,var(factors),fit$resid.variance)
#' 
#' # Statistical Model
#' data(stat.fm.data)
#' sfm.pca.fit <- fitStatisticalFactorModel(sfm.dat,k=2)
#' #' factorModelCovariance(t(sfm.pca.fit$loadings),var(sfm.pca.fit$factors),sfm.pca.fit$resid.variance)
#' 
#' sfm.apca.fit <- fitStatisticalFactorModel(sfm.apca.dat,k=2)
#' 
#' factorModelCovariance(t(sfm.apca.fit$loadings),
#'                        var(sfm.apca.fit$factors),sfm.apca.fit$resid.variance)
#'
#'  # fundamental factor model example
#'  #' 
#'  data(stock)
#' # there are 447 assets  
#' exposure.names <- c("BOOK2MARKET", "LOG.MARKETCAP") 
#' beta.mat <- subset(stock,DATE == "2003-12-31")[,exposure.names]
#' beta.mat1 <- cbind(rep(1,447),beta.mat1)
# FM return covariance 
#' fit.fund <- fitFundamentalFactorModel(exposure.names=c("BOOK2MARKET", "LOG.MARKETCAP")
#'                                      , data=stock,returnsvar = "RETURN",datevar = "DATE",  
#'                                      assetvar = "TICKER",
#'                                      wls = TRUE, regression = "classic", 
#'                                      covariance = "classic", full.resid.cov = FALSE)
#' ret.cov.fundm <- factorModelCovariance(beta.mat1,fit.fund$factor.cov$cov,fit.fund$resid.variance)
#' fit.fund$returns.cov$cov == ret.cov.fundm
#' }
#' @export
#' 

factorModelCovariance <-
function(beta, factor.cov, resid.variance) {

  beta = as.matrix(beta)
	factor.cov = as.matrix(factor.cov)
	sig.e = as.vector(resid.variance)
	if (length(sig.e) > 1) {
	 D.e = diag(as.vector(sig.e))
  } else {
   D.e =  as.matrix(sig.e)
  }
	if (ncol(beta) != ncol(factor.cov))
		stop("beta and factor.cov must have same number of columns")
		
	if (nrow(D.e) != nrow(beta))
		stop("beta and D.e must have same number of rows")
	cov.fm = beta %*% factor.cov %*% t(beta) + D.e
	if (any(diag(chol(cov.fm)) == 0))
    warning("Covariance matrix is not positive definite")
	return(cov.fm)
}