Nothing
#' Plots t ES against holding period
#'
#' Plots the ES of a portfolio against holding period assuming that L/P is t distributed, for specified confidence level and holding periods.
#'
#' @param ... The input arguments contain either return data or else mean and
#' standard deviation data. Accordingly, number of input arguments is either 4
#' or 5. In case there 4 input arguments, the mean and standard deviation of
#' data is computed from return data. See examples for details.
#'
#' returns Vector of daily P/L data
#'
#' mu Mean of daily P/L data
#'
#' sigma Standard deviation of daily P/L data
#'
#' df Number of degrees of freedom in the t distribution
#'
#' cl ES confidence level and must be a scalar
#'
#' hp ES holding period and must be a vector
#'
#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
#'
#' Evans, M., Hastings, M. and Peacock, B. Statistical Distributions, 3rd
#' edition, New York: John Wiley, ch. 38,39.
#'
#' @author Dinesh Acharya
#' @examples
#'
#' # Computes ES given geometric return data
#' data <- runif(5, min = 0, max = .2)
#' tESPlot2DHP(returns = data, df = 6, cl = .95, hp = 60:90)
#'
#' # Computes v given mean and standard deviation of return data
#' tESPlot2DHP(mu = .012, sigma = .03, df = 6, cl = .99, hp = 40:80)
#'
#' @export
tESPlot2DHP <- function(...){
if (nargs() < 4) {
stop("Too few arguments")
}
if (nargs() > 5) {
stop("Too many arguments")
}
args <- list(...)
if (nargs() == 5) {
mu <- args$mu
df <- args$df
cl <- args$cl
sigma <- args$sigma
hp <- args$hp
}
if (nargs() == 4) {
mu <- mean(args$returns)
df <- args$df
cl <- args$cl
sigma <- sd(args$returns)
hp <- args$hp
}
# Check that inputs have correct dimensions
mu <- as.matrix(mu)
mu.row <- dim(mu)[1]
mu.col <- dim(mu)[2]
if (max(mu.row, mu.col) > 1) {
stop("Mean must be a scalar")
}
sigma <- as.matrix(sigma)
sigma.row <- dim(sigma)[1]
sigma.col <- dim(sigma)[2]
if (max(sigma.row, sigma.col) > 1) {
stop("Standard deviation must be a scalar")
}
cl <- as.matrix(cl)
cl.row <- dim(cl)[1]
cl.col <- dim(cl)[2]
if (max(cl.row, cl.col) > 1) {
stop("Confidence level must be a scalar")
}
hp <- as.matrix(hp)
hp.row <- dim(hp)[1]
hp.col <- dim(hp)[2]
if (min(hp.row, hp.col) > 1) {
stop("Holding period must be a vector")
}
df <- as.matrix(df)
df.row <- dim(df)[1]
df.col <- dim(df)[2]
if (max(df.row, df.col) > 1) {
stop("Number of degrees of freedom must be a scalar")
}
# Check that hp is read as row vector
if (hp.row > hp.col) {
hp <- t(hp)
}
# Check that inputs obey sign and value restrictions
if (sigma < 0) {
stop("Standard deviation must be non-negative")
}
if (df < 3) {
stop("Number of degrees of freedom must be at least 3 for first two moments of distribution to be defined")
}
if (max(cl) >= 1){
stop("Confidence level(s) must be less than 1")
}
if (min(cl) <= 0){
stop("Confidence level(s) must be greater than 0")
}
if (min(hp) <= 0){
stop("Holding period(s) must be greater than 0")
}
# VaR estimation
VaR <- (-sigma[1,1] * sqrt(t(hp)) %*% sqrt((df - 2) / df) %*% qt(1 - cl, df)) + (- mu[1,1] * t(hp)) # VaR
# ES etimation
n <- 1000 # Number of slices into which tail is divided
cl0 <- cl # Initial confidence level
delta.cl <- (1 - cl) / n # Increment to confidence level as each slice is taken
v <- VaR
for (i in 1:(n-1)) {
cl <- cl0 + i * delta.cl # Revised cl
v <- v + (-sigma[1,1] * sqrt(t(hp)) %*% sqrt((df - 2) / df) %*% qt(1 - cl, df)) + (- mu[1,1] * t(hp) %*% matrix(1, cl.row, cl.col))
}
v <- v/n
# Plotting
plot(hp, v, type = "l", xlab = "Holding Period", ylab = "ES")
title("t ES against holding period")
xmin <-min(hp)+.25*(max(hp)-min(hp))
cl.label <- cl0 * 100
text(xmin,max(v)-.5*(max(v)-min(v)),
'Input parameters', cex=.75, font = 2)
text(xmin,max(v)-.55*(max(v)-min(v)),
paste('Daily mean L/P data = ', round(mu[1,1], 3)),cex=.75)
text(xmin,max(v)-.6*(max(v)-min(v)),
paste('Stdev. of daily L/P data = ',round(sigma[1,1],3)),cex=.75)
text(xmin,max(v)-.65*(max(v)-min(v)),
paste('Degrees of freedom = ',df),cex=.75)
text(xmin,max(v)-.7*(max(v)-min(v)),
paste('Confidence level = ',cl.label,'%'),cex=.75)
}
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.