# R/LogNormalVaRPlot3D.R In Dowd: Functions Ported from 'MMR2' Toolbox Offered in Kevin Dowd's Book Measuring Market Risk

#### Documented in LogNormalVaRPlot3D

```#' Plots log normal VaR against confidence level and holding period
#'
#' Plots the VaR of a portfolio against confidence level and holding period assuming that geometric
#'  returns are normal 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
#'
#'  investment Size of investment
#'
#'  cl VaR confidence level and must be a vector
#'
#'  hp VaR holding period and must be a vector
#'
#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
#'
#' @author Dinesh Acharya
#' @examples
#'
#'    # Plots VaR against confidene level given geometric return data
#'    data <- rnorm(5, .09, .03)
#'    LogNormalVaRPlot3D(returns = data, investment = 5, cl = seq(.9,.99,.01), hp = 1:100)
#'
#'    # Computes VaR against confidence level given mean and standard deviation of return data
#'    LogNormalVaRPlot3D(mu = .012, sigma = .03, investment = 5, cl = seq(.9,.99,.01), hp = 1:100)
#'
#'
#' @export
LogNormalVaRPlot3D <- 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
investment <- args\$investment
cl <- args\$cl
sigma <- args\$sigma
hp <- args\$hp
}
if (nargs() == 4) {
mu <- mean(args\$returns)
investment <- args\$investment
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 (min(hp.row, hp.col) > 1) {
stop("Holding period must be a vector")
}

# Check that cl is read as row vector
if (cl.row > cl.col) {
cl <- t(cl)
}
# Check that hp is read as column vector
if (hp.col > hp.row) {
hp <- t(hp)
}

# Check that inputs obey sign and value restrictions
if (sigma < 0) {
stop("Standard deviation must be non-negative")
}
if (max(cl) >= 1){
stop("Confidence levels must be less than 1")
}
if (min(cl) <= 0){
stop("Confidence levels must be greater than 0")
}
if (min(hp) <= 0){
stop("Holding periods must be greater than 0")
}

# VaR estimation
cl.row <- dim(cl)[1]
cl.col <- dim(cl)[2]
VaR <- investment - exp( sigma[1,1] * sqrt(hp) %*% qnorm(1 - cl, 0, 1)  + mu[1,1] * hp %*% matrix(1,cl.row,cl.col) + log(investment)) # VaR
# Plotting
persp(x=cl, y=hp, t(VaR), xlab = "Confidence Level",
ylab = "Holding Period", zlab = "VaR", border=NA,
theta = -45, phi = 35, shade = .75, ltheta = 90, cex.axis=.85, cex.lab=.85,
col = "lightgray", ticktype = "detailed", nticks = 5,
main = "Log Normal VaR against CL and HP")
}
```

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