[Returnanalytics-commits] r3917 - pkg/Dowd/R

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

Author: dacharya
Date: 2015-08-05 22:37:07 +0200 (Wed, 05 Aug 2015)
New Revision: 3917

Added:
   pkg/Dowd/R/tVaRESPlot2DCL.R
Log:
Function tVaRESPlot2DCL added

Added: pkg/Dowd/R/tVaRESPlot2DCL.R
===================================================================
--- pkg/Dowd/R/tVaRESPlot2DCL.R	                        (rev 0)
+++ pkg/Dowd/R/tVaRESPlot2DCL.R	2015-08-05 20:37:07 UTC (rev 3917)
@@ -0,0 +1,155 @@
+#' Plots t VaR and ES against confidence level
+#' 
+#' Plots the VaR and ES of a portfolio against confidence level assuming that P/L
+#' data are 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 are 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
+#' 
+#'  cl VaR confidence level and must be a vector
+#' 
+#'  hp VaR holding period and must be a scalar
+#'  
+#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
+#'
+#' @author Dinesh Acharya
+#' @examples
+#' 
+#'    # Plots VaR and ETL against confidene level given P/L data
+#'    data <- runif(5, min = 0, max = .2)
+#'    tVaRESPlot2DCL(returns = data, df = 7, cl = seq(.85,.99,.01), hp = 60)
+#'    
+#'    # Computes VaR against confidence level given mean and standard deviation of P/L data
+#'    tVaRESPlot2DCL(mu = .012, sigma = .03, df = 7, cl = seq(.85,.99,.01), hp = 40)
+#'
+#'
+#' @export
+tVaRESPlot2DCL<- 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
+    sigma <- args$sigma
+    hp <- args$hp
+    df <- args$df
+  }
+  if (nargs() == 4) {
+    mu <- mean(args$returns)
+    cl <- args$cl
+    sigma <- sd(args$returns)
+    hp <- args$hp
+    df <- args$df
+  }
+  
+  # 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 cl 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 must be greater than 0")
+  }
+  # VaR estimation  
+  cl.row <- dim(cl)[1]
+  cl.col <- dim(cl)[2]
+  VaR <- (-sigma[1,1] * sqrt(t(hp)) %*% sqrt((df - 2) / df) %*% qt(1 - cl, df)) + (- mu[1,1] * t(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
+  v <- 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 # Revised cl
+    v <- v + (-sigma[1,1] * sqrt(t(hp)) %*% sqrt((df - 2) / df) %*% qt(1 - cl, df)) + (- mu[1,1] * t(hp) %*% matrix(1, cl.row, cl.col))
+  }
+  v <- v/n # ES
+    
+  # Plotting
+  ymin <- min(VaR, v)
+  ymax <- max(VaR, v)
+  xmin <- min(cl0)
+  xmax <- max(cl0)
+  plot(cl0, VaR, type = "l", xlim = c(xmin, xmax), ylim = c(ymin, ymax), xlab = "Confidence level", ylab = "VaR/ETL")
+  par(new=TRUE)
+  plot(cl0, v, type = "l", xlim = c(xmin, xmax), ylim = c(ymin, ymax), xlab = "Confidence level", ylab = "VaR/ETL")
+  
+  title("t VaR and ETL against confidence level")
+  xmin <- min(cl0)+.3*(max(cl0)-min(cl0))
+  text(xmin,max(VaR)-.1*(max(VaR)-min(VaR)),
+       'Input parameters', cex=.75, font = 2)
+  text(xmin,max(VaR)-.175*(max(VaR)-min(VaR)),
+       paste('Daily mean L/P = ',round(mu[1,1],3)),cex=.75)
+  text(xmin,max(VaR)-.25*(max(VaR)-min(VaR)),
+       paste('Stdev. of daily L/P = ',round(sigma[1,1],3)),cex=.75)
+  text(xmin,max(VaR)-.325*(max(VaR)-min(VaR)),
+       paste('Degrees of freedom = ',df),cex=.75)
+  text(xmin,max(VaR)-.4*(max(VaR)-min(VaR)),
+       paste('Holding period = ',hp,'days'),cex=.75)
+  # VaR and ETL labels
+  text(max(cl0)-.4*(max(cl0)-min(cl0)),min(VaR)+.3*(max(VaR)-min(VaR)),'Upper line - ETL',cex=.75);
+  text(max(cl0)-.4*(max(cl0)-min(cl0)),min(VaR)+.2*(max(VaR)-min(VaR)),'Lower line - VaR',cex=.75);
+
+}