#' @title Decompose portfolio standard deviation into individual factor contributions
#'
#' @description Compute the factor contributions to standard deviation (Sd) of
#' portfolio returns based on Euler's theorem, given the fitted factor model.
#'
#' @importFrom stats quantile residuals cov resid qnorm
#' @importFrom xts as.xts
#' @importFrom zoo index as.Date
#'
#' @details The factor model for a portfolio's return at time \code{t} has the
#' form \cr \cr \code{R(t) = beta'f(t) + e(t) = beta.star'f.star(t)} \cr \cr
#' where, \code{beta.star=(beta,sig.e)} and \code{f.star(t)=[f(t)',z(t)]'}.
#' \cr \cr By Euler's theorem, the standard deviation of the portfolio's return
#' is given as: \cr \cr
#' \code{portSd = sum(cSd_k) = sum(beta.star_k*mSd_k)} \cr \cr
#' where, summation is across the \code{K} factors and the residual,
#' \code{cSd} and \code{mSd} are the component and marginal
#' contributions to \code{Sd} respectively. Computing \code{portSd} and
#' \code{mSd} is very straight forward. The formulas are given below and
#' details are in the references. The covariance term is approximated by the
#' sample covariance. \cr \cr
#' \code{portSd = sqrt(beta.star''cov(F.star)beta.star)} \cr
#' \code{mSd = cov(F.star)beta.star / portSd}
#'
#' @param object fit object of class \code{tsfm}, or \code{ffm}.
#' @param weights a vector of weights of the assets in the portfolio. Default is NULL,
#' in which case an equal weights will be used.
#' @param factor.cov optional user specified factor covariance matrix with
#' named columns; defaults to the sample covariance matrix.
#' @param use an optional character string giving a method for computing
#' covariances in the presence of missing values. This must be (an
#' abbreviation of) one of the strings "everything", "all.obs",
#' "complete.obs", "na.or.complete", or "pairwise.complete.obs". Default is
#' "pairwise.complete.obs".
#' @param ... optional arguments passed to \code{\link[stats]{cov}}.
#'
#' @return A list containing
#' \item{portSd}{factor model Sd of portfolio return.}
#' \item{mSd}{length-(K + 1) vector of marginal contributions to Sd.}
#' \item{cSd}{length-(K + 1) vector of component contributions to Sd.}
#' \item{pcSd}{length-(K + 1) vector of percentage component contributions to Sd.}
#' Where, K is the number of factors.
#'
#' @author Douglas Martin, Lingjie Yi
#'
#'
#' @seealso \code{\link{fitTsfm}}, \code{\link{fitFfm}}
#' for the different factor model fitting functions.
#'
#' \code{\link{portVaRDecomp}} for portfolio factor model VaR decomposition.
#' \code{\link{portEsDecomp}} for portfolio factor model ES decomposition.
#'
#'
#' @examples
#' # Time Series Factor Model
#' data(managers)
#' fit.macro <- factorAnalytics::fitTsfm(asset.names=colnames(managers[,(1:6)]),
#' factor.names=colnames(managers[,(7:9)]),
#' rf.name=colnames(managers[,10]), data=managers)
#' decomp <- portSdDecomp(fit.macro)
#' # get the factor contributions of risk
#' decomp$cSd
#'
#' # random weights
#' wts = runif(6)
#' wts = wts/sum(wts)
#' names(wts) <- colnames(managers)[1:6]
#' portSdDecomp(fit.macro, wts)
#'
#' # Fundamental Factor Model
#' data("stocks145scores6")
#' dat = stocks145scores6
#' dat$DATE = as.yearmon(dat$DATE)
#' dat = dat[dat$DATE >=as.yearmon("2008-01-01") &
#' dat$DATE <= as.yearmon("2012-12-31"),]
#'
#' # Load long-only GMV weights for the return data
#' data("wtsStocks145GmvLo")
#' wtsStocks145GmvLo = round(wtsStocks145GmvLo,5)
#'
#' # fit a fundamental factor model
#' fit.cross <- fitFfm(data = dat,
#' exposure.vars = c("SECTOR","ROE","BP","MOM121","SIZE","VOL121",
#' "EP"),date.var = "DATE", ret.var = "RETURN", asset.var = "TICKER",
#' fit.method="WLS", z.score = "crossSection")
#'
#' decomp = portSdDecomp(fit.cross)
#' # get the factor contributions of risk
#' decomp$cSd
#' portSdDecomp(fit.cross, wtsStocks145GmvLo)
#'
#' @export
portSdDecomp <- function(object, ...){
# check input object validity
if (!inherits(object, c("tsfm", "ffm"))) {
stop("Invalid argument: Object should be of class 'tsfm', or 'ffm'.")
}
UseMethod("portSdDecomp")
}
#' @rdname portSdDecomp
#' @method portSdDecomp tsfm
#' @export
portSdDecomp.tsfm <- function(object, weights = NULL, factor.cov,
use="pairwise.complete.obs", ...) {
# get beta.star: 1 x (K+1)
beta <- object$beta
beta[is.na(beta)] <- 0
n.assets = nrow(beta)
asset.names <- object$asset.names
# check if there is weight input
if(is.null(weights)){
weights = rep(1/n.assets, n.assets)
}else{
# check if number of weight parameter matches
if(n.assets != length(weights)){
stop("Invalid argument: incorrect number of weights")
}
if(!is.null(names(weights))){
weights = weights[asset.names]
}else{
stop("Invalid argument: names of weights vector should match with asset names")
}
}
# get portfolio beta.star: 1 x (K+1)
beta.star <- as.matrix(cbind(weights %*% as.matrix(beta), sqrt(sum(weights^2 * object$resid.sd^2))))
colnames(beta.star)[dim(beta.star)[2]] <- "Residuals"
# get cov(F): K x K
# get cov(F): K x K
factor <- as.matrix(object$data[, object$factor.names])
if (missing(factor.cov)) {
factor.cov = cov(factor, use=use, ...)
} else {
if (!identical(dim(factor.cov), as.integer(c(ncol(factor), ncol(factor))))) {
stop("Dimensions of user specified factor covariance matrix are not
compatible with the number of factors in the fitTsfm object")
}
}
# get cov(F.star): (K+1) x (K+1)
K <- ncol(object$beta)
factor.star.cov <- diag(K+1)
factor.star.cov[1:K, 1:K] <- factor.cov
colnames(factor.star.cov) <- c(colnames(factor.cov),"Residuals")
rownames(factor.star.cov) <- c(colnames(factor.cov),"Residuals")
# compute factor model sd; a vector of length 1
Sd.fm <- sqrt(rowSums(beta.star %*% factor.star.cov * beta.star))
# compute marginal, component and percentage contributions to sd
# each of these have dimensions: N + 1
mSd <- drop((t(factor.star.cov %*% t(beta.star)))/Sd.fm)
cSd <- drop(mSd * beta.star)
pcSd <- drop(100* cSd/Sd.fm)
fm.sd.decomp <- list(portSd=Sd.fm, mSd=mSd, cSd=cSd, pcSd=pcSd)
return(fm.sd.decomp)
}
#' @rdname portSdDecomp
#' @method portSdDecomp ffm
#' @export
portSdDecomp.ffm <- function(object, weights = NULL, factor.cov, ...) {
beta <- object$beta
beta[is.na(beta)] <- 0
n.assets = nrow(beta)
asset.names <- unique(object$data[[object$asset.var]])
# check if there is weight input
if(is.null(weights)){
weights = rep(1/n.assets, n.assets)
}else{
# check if number of weight parameter matches
if(n.assets != length(weights)){
stop("Invalid argument: incorrect number of weights")
}
if(!is.null(names(weights))){
weights = weights[asset.names]
}else{
stop("Invalid argument: names of weights vector should match with asset names")
}
}
# get portfolio beta.star: 1 x (K+1)
beta.star <- as.matrix(cbind(weights %*% beta, sqrt(sum(weights^2 * object$resid.var))))
colnames(beta.star)[dim(beta.star)[2]] <- "Residuals"
# get cov(F): K x K
if (missing(factor.cov)) {
factor.cov = object$factor.cov
} else {
if (!identical(dim(factor.cov), dim(object$factor.cov))) {
stop("Dimensions of user specified factor covariance matrix are not
compatible with the number of factors (including dummies) in the
fitFfm object")
}
}
# get cov(F.star): (K+1) x (K+1)
K <- ncol(beta)
factor.star.cov <- diag(K+1)
factor.star.cov[1:K, 1:K] <- factor.cov
colnames(factor.star.cov) <- c(colnames(factor.cov),"Residuals")
rownames(factor.star.cov) <- c(colnames(factor.cov),"Residuals")
# compute factor model sd; a vector of length 1
Sd.fm <- drop(sqrt(rowSums(beta.star %*% factor.star.cov * beta.star)))
# compute marginal, component and percentage contributions to sd
# each of these have dimensions: N+K
mSd <- drop((t(factor.star.cov %*% t(beta.star)))/Sd.fm)
cSd <- drop(mSd * beta.star)
pcSd <- drop(100* cSd/Sd.fm)
fm.sd.decomp <- list(portSd=Sd.fm, mSd=mSd, cSd=cSd, pcSd=pcSd)
return(fm.sd.decomp)
}
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