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#' VaR for t distributed geometric returns
#'
#' Estimates the VaR of a portfolio 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
#'
#' hp VaR holding period
#'
#' @return Matrix of VaRs whose dimension depends on dimension of hp and cl. If
#' cl and hp are both scalars, the matrix is 1 by 1. If cl is a vector and hp is
#' a scalar, the matrix is row matrix, if cl is a scalar and hp is a vector,
#' the matrix is column matrix and if both cl and hp are vectors, the matrix
#' has dimension length of cl * length of hp.
#'
#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
#'
#' @author Dinesh Acharya
#' @examples
#'
#' # Computes VaR given geometric return data
#' data <- runif(5, min = 0, max = .2)
#' LogtVaR(returns = data, investment = 5, df = 6, cl = .95, hp = 90)
#'
#' # Computes VaR given mean and standard deviation of return data
#' LogtVaR(mu = .012, sigma = .03, investment = 5, df = 6, cl = .95, hp = 90)
#'
#'
#' @export
LogtVaR <- 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 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")
}
# VaR estimation
y <- investment - exp(((df - 2) / 2) * sigma %*% sqrt(t(hp)) %*% qt(1 - cl, df)
+ mu * t(hp) %*% matrix(1, cl.row, cl.col) + log(investment)) # VaR
return (y)
}
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