[Returnanalytics-commits] r3674 - in pkg/Dowd: . R man
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Mon Jun 15 12:05:50 CEST 2015
Author: dacharya
Date: 2015-06-15 12:05:49 +0200 (Mon, 15 Jun 2015)
New Revision: 3674
Added:
pkg/Dowd/R/AdjustedNormalESHotspots.R
pkg/Dowd/R/AdjustedNormalVaRHotspots.R
pkg/Dowd/man/AdjustedNormalESHotspots.Rd
pkg/Dowd/man/AdjustedNormalVaRHotspots.Rd
Modified:
pkg/Dowd/NAMESPACE
pkg/Dowd/R/FrechetVaRPlot2DCl.R
pkg/Dowd/man/FrechetVaRPlot2DCl.Rd
Log:
AdjustedNormalESHotspots, AdjustedNormalVaRHotspots: source and documentation
Modified: pkg/Dowd/NAMESPACE
===================================================================
--- pkg/Dowd/NAMESPACE 2015-06-12 16:43:18 UTC (rev 3673)
+++ pkg/Dowd/NAMESPACE 2015-06-15 10:05:49 UTC (rev 3674)
@@ -1,6 +1,8 @@
# Generated by roxygen2 (4.1.1): do not edit by hand
export(ADTestStat)
+export(AdjustedNormalESHotspots)
+export(AdjustedNormalVaRHotspots)
export(BinomialBacktest)
export(BlancoIhleBacktest)
export(BootstrapES)
Added: pkg/Dowd/R/AdjustedNormalESHotspots.R
===================================================================
--- pkg/Dowd/R/AdjustedNormalESHotspots.R (rev 0)
+++ pkg/Dowd/R/AdjustedNormalESHotspots.R 2015-06-15 10:05:49 UTC (rev 3674)
@@ -0,0 +1,114 @@
+#' @title Hotspots for ES adjusted by Cornish-Fisher correction
+#'
+#' @description Estimates the ES hotspots (or vector of incremental ESs) for a
+#' portfolio with portfolio return adjusted for non-normality by Cornish-Fisher
+#' corerction, 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. Measurh ing Market Risk, Wiley, 2007.
+#'
+#' @author Dinesh Acharya
+#'
+#' @examples
+#'
+#' # Hotspots for ES for randomly generated portfolio
+#' vc.matrix <- matrix(rnorm(16),4,4)
+#' return <- rnorm(4)
+#' skew <- .5
+#' kurtosis <- 1.2
+#' positions <- c(5,2,6,10)
+#' cl <- .95
+#' hp <- 280
+#' AdjustedNormalESHotsopts(vc.matrix, mu, skew, kurtosis, positions, cl, hp)
+#'
+#' @export
+AdjustedNormalESHotspots <- function(vc.matrix, mu, skew, kurtosis, 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")
+ }
+ 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 and ES estimation
+ # Begin with portfolio ES
+ z <- qnorm(1 - cl, 0 ,1)
+ sigma <- positions %*% vc.matrix %*% t(positions)/(sum(positions)^2) # Initial
+ # standard deviation of portfolio returns
+ adjustment <- (1 / 6) * (z ^ 2 - 1) * skew + (1 / 24) * (z ^ 3 - 3 * z) *
+ (kurtosis - 3) - (1 / 36) * (2 * z ^ 3 - 5 * z) * skew ^ 2
+ VaR <- - mu %*% t(positions) * hp - (z + adjustment) * sigma *
+ (sum(positions)^2) * sqrt(hp) # Initial VaR
+ n <- 1000 # Number of slives into which tail is divided
+ cl0 <- cl # Initial confidence level
+ term <- VaR
+ delta.cl <- (1 - cl) / n # Increment to confidence level
+ for (k in 1:(n - 1)) {
+ cl <- cl0 + k * delta.cl # Revised cl
+ z <- qnorm(1 - cl, 0, 1)
+ adjustment=(1 / 6) * (z ^ 2 - 1) * skew + (1 / 24) * (z ^ 3 - 3 * z) *
+ (kurtosis - 3) - (1 / 36) * (2 * z ^ 3 - 5 * z) * skew ^ 2
+ term <- term - mu %*% t(positions) * hp - (z + adjustment) * sigma *
+ (sum(positions)^2) * sqrt(hp)
+ }
+ portfolio.ES <- term/n
+
+ # Portfolio ES
+ es <- double(length(positions))
+ ies <- double(length(positions))
+ for (j in range(1: length(positions))) {
+ x <- positions
+ x[j] <- 0
+ sigma <- x %*% vc.matrix %*% t(x) / (sum(x)^2)
+ term[j] <- - mu %*% t(x) * hp - qnorm(1-cl, 0, 1) * x %*%
+ vc.matrix %*% t(x) * sqrt(hp)
+
+ for (k in 1:(n - 1)){
+ cl <- cl0 + k * delta.cl # Revised cl
+ z <- qnorm(1-cl, 0, 1)
+ adjustment=(1 / 6) * (z ^ 2 - 1) * skew + (1 / 24) * (z ^ 3 - 3 * z) *
+ (kurtosis - 3) - (1 / 36) * (2 * z ^ 3 - 5 * z) * skew ^ 2
+ term[j] <- term[j] - mu %*% t(positions) * hp - (z + adjustment) *
+ sigma * (sum(positions)^2) * sqrt(hp)
+ }
+ es[j] <- term[j]/n # ES on portfolio minus position j
+ ies [j] <- portfolio.ES - es[j] # Incremental ES
+
+ }
+ y <- ies
+ return(ies)
+
+}
Added: pkg/Dowd/R/AdjustedNormalVaRHotspots.R
===================================================================
--- pkg/Dowd/R/AdjustedNormalVaRHotspots.R (rev 0)
+++ pkg/Dowd/R/AdjustedNormalVaRHotspots.R 2015-06-15 10:05:49 UTC (rev 3674)
@@ -0,0 +1,85 @@
+#' @title Hotspots for VaR adjusted by Cornish-Fisher correction
+#'
+#' @description Estimates the VaR hotspots (or vector of incremental VaRs) for a
+#' portfolio with portfolio return adjusted for non-normality by Cornish-Fisher
+#' corerction, 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. Measurh ing Market Risk, Wiley, 2007.
+#'
+#' @author Dinesh Acharya
+#'
+#' @examples
+#'
+#' # Hotspots for ES for randomly generated portfolio
+#' vc.matrix <- matrix(rnorm(16),4,4)
+#' return <- rnorm(4)
+#' skew <- .5
+#' kurtosis <- 1.2
+#' positions <- c(5,2,6,10)
+#' cl <- .95
+#' hp <- 280
+#' AdjustedNormalESHotsopts(vc.matrix, mu, skew, kurtosis, positions, cl, hp)
+#'
+#' @export
+AdjustedNormalVaRHotspots <- function(vc.matrix, mu, skew, kurtosis, 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 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 and ES estimation
+ z <- qnorm(1 - cl, 0 ,1)
+ sigma <- positions %*% vc.matrix %*% t(positions)/(sum(positions)^2) # Initial standard deviation of portfolio returns
+ adjustment <- (1 / 6) * (z ^ 2 - 1) * skew + (1 / 24) * (z ^ 3 - 3 * z) * (kurtosis - 3) - (1 / 36) * (2 * z ^ 3 - 5 * z) * skew ^ 2
+ VaR <- - mu %*% t(positions) * hp - (z + adjustment) * sigma * (sum(positions)^2) * sqrt(hp)
+
+ # VaR
+ x <- double(length(positions))
+ sigma <- double(length(positions))
+ iVaR <- double(length(positions))
+ for (i in 1:length(positions)){
+ x <- positions
+ x[i] <- 0
+ sigma[i] <- x %*% vc.matrix %*% t(x)/sum(x)^2 # standard deviation of portfolio returns
+ iVaR[i] <- VaR + mu %*% t(x) %*% hp + (z + adjustment) * sigma[i] * (sum(x))^2 * sqrt(hp) # Incremental VaR
+ }
+ y <- iVaR
+ return(y)
+
+}
\ No newline at end of file
Modified: pkg/Dowd/R/FrechetVaRPlot2DCl.R
===================================================================
--- pkg/Dowd/R/FrechetVaRPlot2DCl.R 2015-06-12 16:43:18 UTC (rev 3673)
+++ pkg/Dowd/R/FrechetVaRPlot2DCl.R 2015-06-15 10:05:49 UTC (rev 3674)
@@ -1,6 +1,6 @@
-#' Plots Frechet Value at Risk against Cl
+#' @title Plots Frechet Value at Risk against Cl
#'
-#' Plots the VaR of a portfolio against confidence level assuming extreme losses
+#' @description Plots the VaR of a portfolio against confidence level assuming extreme losses
#' are Frechet distributed, for specified range of confidence level and a given
#' holding period.
#'
@@ -14,7 +14,7 @@
#' @param cl Confidence level and should be a vector
#' @param hp Holding period and should be a scalar
#'
-#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
+#' @references Dowd, K. Measurh ing Market Risk, Wiley, 2007.
#'
#' Embrechts, P., Kluppelberg, C. and Mikosch, T., Modelling Extremal Events for
#' Insurance and Finance. Springer, Berlin, 1997, p. 324.
@@ -24,6 +24,7 @@
#' 15-18.
#'
#' @author Dinesh Acharya
+#'
#' @examples
#'
#' # Plots VaR against vector of cl assuming Frechet Distribution for given parameters
Added: pkg/Dowd/man/AdjustedNormalESHotspots.Rd
===================================================================
--- pkg/Dowd/man/AdjustedNormalESHotspots.Rd (rev 0)
+++ pkg/Dowd/man/AdjustedNormalESHotspots.Rd 2015-06-15 10:05:49 UTC (rev 3674)
@@ -0,0 +1,46 @@
+% Generated by roxygen2 (4.1.1): do not edit by hand
+% Please edit documentation in R/AdjustedNormalESHotspots.R
+\name{AdjustedNormalESHotspots}
+\alias{AdjustedNormalESHotspots}
+\title{Hotspots for ES adjusted by Cornish-Fisher correction}
+\usage{
+AdjustedNormalESHotspots(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{
+Estimates the ES hotspots (or vector of incremental ESs) for a
+portfolio with portfolio return adjusted for non-normality by Cornish-Fisher
+corerction, for specified confidence level and holding period.
+}
+\examples{
+# Hotspots for ES for randomly generated portfolio
+ vc.matrix <- matrix(rnorm(16),4,4)
+ return <- rnorm(4)
+ skew <- .5
+ kurtosis <- 1.2
+ positions <- c(5,2,6,10)
+ cl <- .95
+ hp <- 280
+ AdjustedNormalESHotsopts(vc.matrix, mu, skew, kurtosis, positions, cl, hp)
+}
+\author{
+Dinesh Acharya
+}
+\references{
+Dowd, K. Measurh ing Market Risk, Wiley, 2007.
+}
+
Added: pkg/Dowd/man/AdjustedNormalVaRHotspots.Rd
===================================================================
--- pkg/Dowd/man/AdjustedNormalVaRHotspots.Rd (rev 0)
+++ pkg/Dowd/man/AdjustedNormalVaRHotspots.Rd 2015-06-15 10:05:49 UTC (rev 3674)
@@ -0,0 +1,46 @@
+% Generated by roxygen2 (4.1.1): do not edit by hand
+% Please edit documentation in R/AdjustedNormalVaRHotspots.R
+\name{AdjustedNormalVaRHotspots}
+\alias{AdjustedNormalVaRHotspots}
+\title{Hotspots for VaR adjusted by Cornish-Fisher correction}
+\usage{
+AdjustedNormalVaRHotspots(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{
+Estimates the VaR hotspots (or vector of incremental VaRs) for a
+portfolio with portfolio return adjusted for non-normality by Cornish-Fisher
+corerction, for specified confidence level and holding period.
+}
+\examples{
+# Hotspots for ES for randomly generated portfolio
+ vc.matrix <- matrix(rnorm(16),4,4)
+ return <- rnorm(4)
+ skew <- .5
+ kurtosis <- 1.2
+ positions <- c(5,2,6,10)
+ cl <- .95
+ hp <- 280
+ AdjustedNormalESHotsopts(vc.matrix, mu, skew, kurtosis, positions, cl, hp)
+}
+\author{
+Dinesh Acharya
+}
+\references{
+Dowd, K. Measurh ing Market Risk, Wiley, 2007.
+}
+
Modified: pkg/Dowd/man/FrechetVaRPlot2DCl.Rd
===================================================================
--- pkg/Dowd/man/FrechetVaRPlot2DCl.Rd 2015-06-12 16:43:18 UTC (rev 3673)
+++ pkg/Dowd/man/FrechetVaRPlot2DCl.Rd 2015-06-15 10:05:49 UTC (rev 3674)
@@ -23,8 +23,7 @@
Plots the VaR of a portfolio against confidence level assuming extreme losses
are Frechet distributed, for specified range of confidence level and a given
holding period.
-}
-\details{
+
Note that the long-right-hand tail is fitted to losses, not profits.
}
\examples{
@@ -36,7 +35,7 @@
Dinesh Acharya
}
\references{
-Dowd, K. Measuring Market Risk, Wiley, 2007.
+Dowd, K. Measurh ing Market Risk, Wiley, 2007.
Embrechts, P., Kluppelberg, C. and Mikosch, T., Modelling Extremal Events for
Insurance and Finance. Springer, Berlin, 1997, p. 324.
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