R/tESFigure.R

In Dowd: Functions Ported from 'MMR2' Toolbox Offered in Kevin Dowd's Book Measuring Market Risk

#' 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)
  
}