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#' @title Variance-covariance VaR for normally distributed returns
#'
#' @description Estimates the variance-covariance VaR of a
#' portfolio assuming individual asset returns are normally distributed,
#' for specified confidence level and holding period.
#'
#' @param vc.matrix Assumed variance covariance matrix for returns
#' @param mu Vector of expected position returns
#' @param positions Vector of positions
#' @param cl Confidence level and is scalar or vector
#' @param hp Holding period and is scalar or vector
#'
#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
#'
#' @author Dinesh Acharya
#'
#' @examples
#'
#' # Variance-covariance VaR for randomly generated portfolio
#' vc.matrix <- matrix(rnorm(16),4,4)
#' mu <- rnorm(4)
#' positions <- c(5,2,6,10)
#' cl <- .95
#' hp <- 280
#' VarianceCovarianceVaR(vc.matrix, mu, positions, cl, hp)
#'
#' @seealso AdjustedVarianceCovarianceVaR
#' @export
VarianceCovarianceVaR <- function(vc.matrix, mu, positions, cl, hp){
# Check that confidence level is read as a row vector
cl <- as.matrix(cl)
if (dim(cl)[1] > dim(cl)[2]){
cl <- t(cl)
}
# Check that hp is read as a column vector
hp <- as.matrix(hp)
if (dim(hp)[1] < dim(hp)[2]){
hp <- t(hp)
}
# Check that positions vector is read as a scalar or row vector
positions <- as.matrix(positions)
if (dim(positions)[1] > dim(positions)[2]){
positions <- t(positions)
}
# Check that expected returns vector is read as a scalar or row vector
mu <- as.matrix(mu)
if (dim(mu)[1] > dim(mu)[2]){
mu <- t(mu)
}
# Check that dimensions are correct
if (max(dim(mu)) != max(dim(positions))){
stop("Positions vector and expected returns vector must have same size")
}
vc.matrix <- as.matrix(vc.matrix)
if (max(dim(vc.matrix)) != max(dim(positions))){
stop("Positions vector and expected returns vector must have same size")
}
# Check that inputs obey sign and value restrictions
if (cl >= 1){
stop("Confidence level must be less than 1")
}
if (cl <= 0){
stop("Confidence level must be greater than 0");
}
if (hp <= 0){
stop("Holding period must be greater than 0");
}
# VaR estimation
VaR <- matrix(0, length(cl), length(hp))
for (i in 1:length(cl)) {
for (j in 1:length(hp)) {
VaR[i, j] <- - mu %*% t(positions) * hp[j] - qnorm(1-cl[i], 0, 1) * (positions %*% vc.matrix %*% t(positions)) * sqrt(hp[j])
}
}
y <- t(VaR)
return(y)
}
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