[Returnanalytics-commits] r3680 - in pkg/Dowd: . R man
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Thu Jun 18 23:54:56 CEST 2015
Author: dacharya
Date: 2015-06-18 23:54:56 +0200 (Thu, 18 Jun 2015)
New Revision: 3680
Added:
pkg/Dowd/R/AdjustedVarianceCovarianceES.R
pkg/Dowd/man/AdjustedVarianceCovarianceES.Rd
Modified:
pkg/Dowd/NAMESPACE
Log:
AdjustedVarianceCovarianceES: source and documentation
Modified: pkg/Dowd/NAMESPACE
===================================================================
--- pkg/Dowd/NAMESPACE 2015-06-18 00:11:57 UTC (rev 3679)
+++ pkg/Dowd/NAMESPACE 2015-06-18 21:54:56 UTC (rev 3680)
@@ -3,6 +3,7 @@
export(ADTestStat)
export(AdjustedNormalESHotspots)
export(AdjustedNormalVaRHotspots)
+export(AdjustedVarianceCovarianceES)
export(BinomialBacktest)
export(BlancoIhleBacktest)
export(BootstrapES)
Added: pkg/Dowd/R/AdjustedVarianceCovarianceES.R
===================================================================
--- pkg/Dowd/R/AdjustedVarianceCovarianceES.R (rev 0)
+++ pkg/Dowd/R/AdjustedVarianceCovarianceES.R 2015-06-18 21:54:56 UTC (rev 3680)
@@ -0,0 +1,125 @@
+#' @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 kurtisos 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)
+#' 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))
+ adjustment <- z
+ VaR <- matrix(0, length(cl), length(hp))
+ cl0 <- cl
+ term <- VaR
+ es <- VaR
+ delta.cl <- cl
+ for (i in 1:length(cl)) {
+
+ # Cornish-Fisher adjustment
+ 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 slives 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(es)
+
+}
Added: pkg/Dowd/man/AdjustedVarianceCovarianceES.Rd
===================================================================
--- pkg/Dowd/man/AdjustedVarianceCovarianceES.Rd (rev 0)
+++ pkg/Dowd/man/AdjustedVarianceCovarianceES.Rd 2015-06-18 21:54:56 UTC (rev 3680)
@@ -0,0 +1,45 @@
+% Generated by roxygen2 (4.1.1): do not edit by hand
+% Please edit documentation in R/AdjustedVarianceCovarianceES.R
+\name{AdjustedVarianceCovarianceES}
+\alias{AdjustedVarianceCovarianceES}
+\title{Cornish-Fisher adjusted Variance-Covariance ES}
+\usage{
+AdjustedVarianceCovarianceES(vc.matrix, mu, skew, kurtosis, positions, cl, hp)
+}
+\arguments{
+\item{vc.matrix}{Variance covariance matrix for returns}
+
+\item{mu}{Vector of expected position returns}
+
+\item{skew}{Return skew}
+
+\item{positions}{Vector of positions}
+
+\item{cl}{Confidence level and is scalar}
+
+\item{hp}{Holding period and is scalar}
+
+\item{kurtisos}{Return kurtosis}
+}
+\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.
+}
+\examples{
+# Variance-covariance ES for randomly generated portfolio
+ vc.matrix <- matrix(rnorm(16), 4, 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)
+}
+\author{
+Dinesh Acharya
+}
+\references{
+Dowd, K. Measuring Market Risk, Wiley, 2007.
+}
+
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