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

#### Documented in NormalVaRFigure

```#' Figure of normal VaR and pdf against L/P
#'
#' Gives figure showing the VaR and probability distribution function against L/P of a portfolio assuming P/L are normally 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 3
#'  or 4. In case there 3 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
#'
#'  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.
#'
#' @author Dinesh Acharya
#' @examples
#'
#'    # Plots normal VaR and pdf against L/P data for given returns data
#'    data <- runif(5, min = 0, max = .2)
#'    NormalVaRFigure(returns = data, cl = .95, hp = 90)
#'
#'    # Plots normal VaR and pdf against L/P data with given parameters
#'    NormalVaRFigure(mu = .012, sigma = .03, cl = .95, hp = 90)
#'
#'
#' @export
NormalVaRFigure <- function(...){
# Determine if there are three or four arguments and ensure that arguments are
if (nargs() < 3) {
stop("Too few arguments")
}
if (nargs() > 4) {
stop("Too many arguments")
}
args <- list(...)
if (nargs() == 4) {
mu <- args\$mu
cl <- args\$cl
sigma <- args\$sigma
hp <- args\$hp
}
if (nargs() == 3) {
mu <- mean(args\$returns)
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 scalar or 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 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 (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) %*% qnorm(1 - cl, 0, 1)  - mu[1,1] * hp %*% matrix(1,cl.row,cl.col) # VaR

# 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 <- dlnorm(x, - mu, sigma)
plot(x, p, type = "l", xlim = c(x.min, x.max), ylim = c(0, max(p)*1.1), xlab = "Loss (+) / Profit (-)", ylab = "Probability", main = "Normal VaR")
u <- c(VaR, VaR)
v <- c(0, .6*max(p))
lines(0,0,2,.6,type="l")
lines(u, v, type = "l", col = "blue")
cl.for.label <- 100*cl
text(1,.95*max(p), pos = 1, 'Input parameters', cex=.75, font = 2)
text(1, .875*max(p),pos = 1, paste('Daily mean L/P = ', round(mu,2)), cex=.75)
text(1, .8*max(p),pos = 1, paste('St. dev. of daily L/P = ',round(sigma,2)), cex=.75)
text(1, .725*max(p),pos = 1, paste('Holding period = ', hp,' day(s)'), cex=.75)
text(VaR, .7*max(p),pos = 2, paste('VaR at ', cl.for.label,'% CL'), cex=.75)
text(VaR, .64 * max(p),pos = 2, paste('= ',VaR), cex=.75)
}
```

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