R/NormalVaRHotspots.R

In Dowd: Functions Ported from 'MMR2' Toolbox Offered in Kevin Dowd's Book Measuring Market Risk

#' @title Hotspots for normal VaR
#' 
#' @description Estimates the VaR hotspots (or vector of incremental VaRs) for 
#' a portfolio assuming individual asset returns are normally distributed, for
#' specified confidence level and holding period.
#' 
#' @param vc.matrix Variance covariance matrix for returns
#' @param mu Vector of expected position returns
#' @param positions Vector of positions
#' @param cl Confidence level and is scalar
#' @param hp Holding period and is scalar
#' @return Hotspots for normal VaR
#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
#' 
#' @author Dinesh Acharya
#' 
#' @examples
#' 
#'    # Hotspots for ES for randomly generated portfolio
#'    vc.matrix <- matrix(rnorm(16),4,4)
#'    mu <- rnorm(4,.08,.04)
#'    positions <- c(5,2,6,10)
#'    cl <- .95
#'    hp <- 280
#'    NormalVaRHotspots(vc.matrix, mu, positions, cl, hp)
#'    
#' @export
NormalVaRHotspots <- function(vc.matrix, mu, positions, cl, hp){
  
  # Check that positions vector 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 variance-covariance matrix must have compatible dimensions")
  }
  
  # 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 and ES estimation
  VaR <- - mu %*% t(positions) * hp - qnorm(1 - cl, 0, 1) * (positions %*% vc.matrix %*% t(positions)) * sqrt(hp) # VaR
  iVaR <- double(length(positions))
  for (i in 1:length(positions)){
    x <- positions
    x[i] <- 0
    iVaR[i] <- VaR + mu %*% t(x) %*% hp + qnorm(1 - cl, 0, 1) * (x %*% vc.matrix %*% t(x)) * sqrt(hp)
  }
  y <- iVaR
  return(y)
}