# R/LogtVaRPlot2DCL.R In Dowd: Functions Ported from 'MMR2' Toolbox Offered in Kevin Dowd's Book Measuring Market Risk

#### Documented in LogtVaRPlot2DCL

```#' Plots log-t VaR against confidence level
#'
#' Plots the VaR of a portfolio against confidence level assuming that geometric
#'  returns are Student-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 5
#'  or 6. In case there 5 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
#'
#'  investment Size of investment
#'
#'  df Number of degrees of freedom in the t distribution
#'
#'  cl VaR confidence level and must be a vector
#'
#'  hp VaR holding period and must be a scalar
#'
#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
#'
#' @author Dinesh Acharya
#' @examples
#'
#'    # Plots VaR against confidene level given geometric return data
#'    data <- runif(5, min = 0, max = .2)
#'    LogtVaRPlot2DCL(returns = data, investment = 5, df = 6, cl = seq(.85,.99,.01), hp = 60)
#'
#'    # Computes VaR against confidence level given mean and standard deviation of return data
#'    LogtVaRPlot2DCL(mu = .012, sigma = .03, investment = 5, df = 6, cl = seq(.85,.99,.01), hp = 40)
#'
#'
#' @export
LogtVaRPlot2DCL <- function(...){
# Determine if there are four or five arguments, and ensure that arguments are read as intended
if (nargs() < 5) {
stop("Too few arguments")
}
if (nargs() > 6) {
stop("Too many arguments")
}
args <- list(...)
if (nargs() == 6) {
mu <- args\$mu
investment <- args\$investment
df <- args\$df
cl <- args\$cl
sigma <- args\$sigma
hp <- args\$hp
}
if (nargs() == 5) {
mu <- mean(args\$returns)
investment <- args\$investment
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")
}

# Check that cl 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 (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 <- investment - exp(((df-2)/df)*sigma[1,1] * sqrt(hp[1,1]) * qt(1 - cl, df)+mu[1,1]*hp[1,1]*matrix(1,cl.row,cl.col) + log(investment)
) # VaR
# Plotting
plot(cl, VaR, type = "l", xlab = "Confidence Level", ylab = "VaR")
title("Log-t VaR against confidence level")
xmin <-min(cl)+.3*(max(cl)-min(cl))
text(xmin,max(VaR)-.1*(max(VaR)-min(VaR)),
'Input parameters', cex=.75, font = 2)
text(xmin,max(VaR)-.15*(max(VaR)-min(VaR)),
paste('Daily mean geometric return = ',round(mu[1,1],3)),cex=.75)
text(xmin,max(VaR)-.2*(max(VaR)-min(VaR)),
paste('Stdev. of daily geometric returns = ',round(sigma[1,1],3)),cex=.75)
text(xmin,max(VaR)-.25*(max(VaR)-min(VaR)),
paste('Degrees of freedom = ',df),cex=.75)
text(xmin,max(VaR)-.3*(max(VaR)-min(VaR)),
paste('Investment size = ',investment),cex=.75)
text(xmin,max(VaR)-.35*(max(VaR)-min(VaR)),
paste('Holding period = ',hp,'days'),cex=.75)
}
```

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