# R/tESPlot2DCL.R In Dowd: Functions Ported from 'MMR2' Toolbox Offered in Kevin Dowd's Book Measuring Market Risk

#### Documented in tESPlot2DCL

```#' Plots t- ES against confidence level
#'
#' Plots the ES of a portfolio against confidence level, assuming that L/P is
#' t distributed, for specified confidence level and holding period.
#'
#' @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 geometric return data
#'
#'  mu Mean of daily geometric return data
#'
#'  sigma Standard deviation of daily geometric return data
#'
#'  df Number of degrees of freedom in the t distribution
#'
#'  cl ES confidence level and must be a vector
#'
#'  hp ES holding period and must be a scalar
#'
#' @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)
#'    tESPlot2DCL(returns = data, df = 6, cl = seq(.9,.99,.01), hp = 60)
#'
#'    # Computes v given mean and standard deviation of return data
#'    tESPlot2DCL(mu = .012, sigma = .03, df = 6, cl = seq(.9,.99,.01), hp = 40)
#'
#'
#' @export
tESPlot2DCL <- function(...){
# Determine if there are five or six arguments, and ensure that arguments are read as intended
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 (min(cl.row, cl.col) > 1) {
stop("Confidence level must be a vector")
}
hp <- as.matrix(hp)
hp.row <- dim(hp)[1]
hp.col <- dim(hp)[2]
if (max(hp.row, hp.col) > 1) {
stop("Holding period must be a scalar")
}
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 (cl.row > cl.col) {
cl <- t(cl)
}

# 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
cl.row <- dim(cl)[1]
cl.col <- dim(cl)[2]
VaR <-  (-sigma[1,1] * sqrt(hp[1,1]) * sqrt((df - 2) / df) %*% qt(1 - cl, df)) + (- mu[1,1] * hp[1,1] * matrix(1, cl.row, cl.col)) # 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(hp[1,1]) * sqrt((df - 2) / df) %*% qt(1 - cl, df)) + (- mu[1,1] * hp[1,1] * matrix(1, cl.row, cl.col))
}
v <- v/n

# Plotting
plot(cl0, v, type = "l", xlab = "Holding Period", ylab = "ES")
title("t ES against confidence level")
xmin <-min(cl0)+.25*(max(cl0)-min(cl0))
text(xmin,max(v)-.1*(max(v)-min(v)),
'Input parameters', cex=.75, font = 2)
text(xmin,max(v)-.15*(max(v)-min(v)),
paste('Daily mean L/P = ',round(mu[1,1],3)),cex=.75)
text(xmin,max(v)-.2*(max(v)-min(v)),
paste('Stdev. of daily L/P = ',round(sigma[1,1],3)),cex=.75)
text(xmin,max(v)-.25*(max(v)-min(v)),
paste('Degrees of freedom = ',df),cex=.75)
text(xmin,max(v)-.3*(max(v)-min(v)),
paste('Holding Period = ',hp),cex=.75)
}
```

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