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

```#' @title Cornish-Fisher adjusted Variance-Covariance ES
#'
#' @description Function estimates the Variance-Covariance ES of a multi-asset
#' portfolio using the Cornish - Fisher adjustment for portfolio return
#' non-normality, for specified confidence level and holding period.
#'
#' @param vc.matrix Variance covariance matrix for returns
#' @param mu Vector of expected position returns
#' @param skew Return skew
#' @param kurtosis Return kurtosis
#' @param positions Vector of positions
#' @param cl Confidence level and is scalar
#' @param hp Holding period and is scalar
#'
#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
#'
#' @author Dinesh Acharya
#'
#' @examples
#'
#'    # Variance-covariance ES for randomly generated portfolio
#'    vc.matrix <- matrix(rnorm(16), 4, 4)
#'    mu <- rnorm(4)
#'    skew <- .5
#'    kurtosis <- 1.2
#'    positions <- c(5, 2, 6, 10)
#'    cl <- .95
#'    hp <- 280
#'    AdjustedVarianceCovarianceES(vc.matrix, mu, skew, kurtosis, positions, cl, hp)
#'
#' @export
AdjustedVarianceCovarianceES <- function(vc.matrix, mu, skew, kurtosis,
positions, cl, hp){

# Check that cl 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 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")
}
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");
}

# Portfolio return standard deviation
sigma <- positions %*% vc.matrix %*% t(positions)/(sum(positions)^2) # Initial
# standard deviation of portfolio returns
# VaR and ES estimation
z <- double(length(cl))
VaR <- matrix(0, length(cl), length(hp))
cl0 <- cl
term <- VaR
es <- VaR
delta.cl <- cl
for (i in 1:length(cl)) {

z[i] <- qnorm(1 - cl[i], 0 ,1)
adjustment[i] <- (1 / 6) * (z[i] ^ 2 - 1) * skew + (1 / 24) *
(z[i] ^ 3 - 3 * z[i]) * (kurtosis - 3) - (1 / 36) *
(2 * z[i] ^ 3 - 5 * z[i]) * skew ^ 2

for (j in 1:length(hp)){

VaR[i,j] <- - mu %*% t(positions) * hp[j] - (z[i] + adjustment[i]) *
sigma * (sum(positions)^2) * sqrt(hp[j]) # VaR
# ES Estimation
n <- 1000 # Number of slices into which tail is divided
cl0[i] <- cl[i] # Initial confidence level
term[i, j] <- VaR[i, j]
delta.cl[i] <- (1 - cl[i]) / n # Increment to confidence level as each
# slice is taken

for (k in 1:(n - 1)) {

cl[i] <- cl0[i] + k * delta.cl[i] # Revised cl
z[i] <- qnorm(1 - cl[i], 0, 1)
adjustment[i]=(1 / 6) * (z[i] ^ 2 - 1) * skew + (1 / 24) *
(z[i] ^ 3 - 3 * z[i]) * (kurtosis - 3) - (1 / 36) *
(2 * z[i] ^ 3 - 5 * z[i]) * skew ^ 2
term[i, j] <- term[i, j] - mu %*% t(positions) * hp[j] -
(z[i] + adjustment) * sigma * (sum(positions)^2) * sqrt(hp[j])

}
es[i, j] <- term[i, j]/n

}
}
y <- t(es)
return(y)

}
```

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Dowd documentation built on May 30, 2017, 1:30 a.m.