[Returnanalytics-commits] r3908 - pkg/Dowd/R

[noreply at r-forge.r-project.org]

Author: dacharya
Date: 2015-08-05 07:22:35 +0200 (Wed, 05 Aug 2015)
New Revision: 3908

Added:
   pkg/Dowd/R/tESPlot2DCL.R
Log:
Function tESPlot2DCL added

Added: pkg/Dowd/R/tESPlot2DCL.R
===================================================================
--- pkg/Dowd/R/tESPlot2DCL.R	                        (rev 0)
+++ pkg/Dowd/R/tESPlot2DCL.R	2015-08-05 05:22:35 UTC (rev 3908)
@@ -0,0 +1,144 @@
+#' Plots t- ES against confidence level
+#' 
+#' Plots the ES of a portfolio against confidence level, assuming that L/P 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 in the t distribution
+#' 
+#'  cl ES confidence level and must be a vector
+#' 
+#'  hp ES holding period and must be a 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
+#' 
+#'    # Computes ES given geometric return data
+#'    data <- runif(5, min = 0, max = .2)
+#'    tESPlot2DCL(returns = data, df = 6, cl = seq(.9,.99,.01), hp = 60)
+#'    
+#'    # Computes v given mean and standard deviation of return data
+#'    tESPlot2DCL(mu = .012, sigma = .03, df = 6, cl = seq(.9,.99,.01), hp = 40)
+#'
+#'
+#' @export
+tESPlot2DCL <- function(...){
+  # Determine if there are five or six 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$mu
+    df <- args$df
+    cl <- args$cl
+    sigma <- args$sigma
+    hp <- args$hp
+  }
+  if (nargs() == 4) {
+    mu <- mean(args$returns)
+    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")
+  }
+  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')
+  }
+  # Check that hp 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 (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")
+  }
+  # VaR estimation  
+  cl.row <- dim(cl)[1]
+  cl.col <- dim(cl)[2]
+  VaR <-  (-sigma[1,1] * sqrt(hp[1,1]) * sqrt((df - 2) / df) %*% qt(1 - cl, df)) + (- mu[1,1] * hp[1,1] * matrix(1, cl.row, cl.col)) # VaR
+  # ES etimation
+  n <- 1000 # Number of slices into which tail is divided
+  cl0 <- cl # Initial confidence level
+  delta.cl <- (1 - cl) / n # Increment to confidence level as each slice is taken
+  v <- VaR
+  for (i in 1:(n-1)) {
+    cl <- cl0 + i * delta.cl # Revised cl
+    v <- v + (-sigma[1,1] * sqrt(hp[1,1]) * sqrt((df - 2) / df) %*% qt(1 - cl, df)) + (- mu[1,1] * hp[1,1] * matrix(1, cl.row, cl.col))
+  }
+  v <- v/n
+  
+  # Plotting
+  plot(cl0, v, type = "l", xlab = "Holding Period", ylab = "ES")
+  title("t ES against confidence level")
+  xmin <-min(cl0)+.25*(max(cl0)-min(cl0))
+  text(xmin,max(v)-.1*(max(v)-min(v)),
+       'Input parameters', cex=.75, font = 2)
+  text(xmin,max(v)-.15*(max(v)-min(v)),
+       paste('Daily mean L/P = ',round(mu[1,1],3)),cex=.75)
+  text(xmin,max(v)-.2*(max(v)-min(v)),
+       paste('Stdev. of daily L/P = ',round(sigma[1,1],3)),cex=.75)
+  text(xmin,max(v)-.25*(max(v)-min(v)),
+       paste('Degrees of freedom = ',df),cex=.75)
+  text(xmin,max(v)-.3*(max(v)-min(v)),
+       paste('Holding Period = ',hp),cex=.75)
+}
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