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#' Figure of t - VaR and ES and pdf against L/P
#'
#' Gives figure showing the VaR and ES and probability distribution function assuming P/L 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
#'
#' cl VaR confidence level and should be scalar
#'
#' hp VaR holding period in days and should be 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
#'
#' # Plots lognormal VaR, ES and pdf against L/P data for given returns data
#' data <- runif(5, min = 0, max = .2)
#' tESFigure(returns = data, df = 10, cl = .95, hp = 90)
#'
#' # Plots lognormal VaR, ES and pdf against L/P data with given parameters
#' tESFigure(mu = .012, sigma = .03, df = 10, cl = .95, hp = 90)
#'
#' @export
tESFigure <- function(...){
# Determine if there are four or five 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$mu
cl <- args$cl
df <- args$df
sigma <- args$sigma
hp <- args$hp
}
if (nargs() == 4) {
mu <- mean(args$returns)
cl <- args$cl
df <- args$df
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 scalar or 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")
}
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 scalar or a vector")
}
# Check that cl and hp are read as row and column vectors respectively
if (cl.row > cl.col) {
cl <- t(cl)
}
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")
}
# Message to indicate how matrix of results is to be interpreted, if cl and hp both vary and results are given in matrix form
if (max(cl.row, cl.col) > 1 & max(hp.row, hp.col) > 1) {
print('VaR results with confidence level varying across row and holding period down column')
}
# VaR estimation
cl.row <- dim(cl)[1]
cl.col <- dim(cl)[2]
VaR <- - sigma[1,1] * sqrt(hp) * sqrt((df - 2) / df) %*% qt(1 - cl, df) - mu[1,1] * hp %*% matrix(1, cl.row, cl.col) # VaR
# ES Estimation
n <- 1000 # Number of slices into which tail is divided
cl0 <- cl # Initial confidence level
w <- VaR
delta.cl <- (1 - cl) / n # Increment to confidence level as each slice is taken
for (i in 1:(n-1)) {
cl <- cl0 + i * delta.cl
w <- w - sigma[1,1] * sqrt(hp) * sqrt((df - 2) / df) %*% qt(1 - cl, df) - mu[1,1] * hp %*% matrix(1, cl.row, cl.col)
}
ES <- w/n
# Plotting
x.min <- -mu - 5 * sigma
x.max <- -mu + 5 * sigma
delta <- (x.max-x.min) / 100
x <- seq(x.min, x.max, delta)
p <- dt((x-mu) / sigma, df)
plot(x, p, type = "l", xlim = c(x.min, x.max), ylim = c(0, max(p)*1.1), xlab = "Loss (+) / Profit (-)", ylab = "Probability", main = "t- VaR and ES")
# VaR line
u <- c(VaR, VaR)
v <- c(0, .6*max(p))
lines(u, v, type = "l", col = "blue")
# ES line
w <- c(ES, ES)
z <- c(0, .45*max(p))
lines(w, z, type = "l", col = "blue")
# Input Labels
cl.for.label <- 100 * cl0
xpos <- -mu-2.5*sigma
text(xpos,.95*max(p), pos = 1, 'Input parameters', cex=.75, font = 2)
text(xpos, .875*max(p),pos = 1, paste('Daily mean L/P = ', -mu), cex=.75)
text(xpos, .8*max(p),pos = 1, paste('St. dev. of daily L/P = ', sigma), cex=.75)
text(xpos, .725*max(p),pos = 1, paste('Degrees of freedom', df), cex=.75)
text(xpos, .65*max(p),pos = 1, paste('Holding period = ', hp,' day(s)'), cex=.75)
# VaR label
text(VaR, .7*max(p),pos = 2, paste('VaR at ', cl.for.label,'% CL'), cex=.75)
text(VaR, .65 * max(p),pos = 2, paste('= ',VaR), cex=.75)
# ES label
text(ES, .55*max(p),pos = 2, 'ES =', cex=.75)
text(ES, .65 * max(p),pos = 2, paste(ES), cex=.75)
}
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