[Returnanalytics-commits] r3910 - pkg/Dowd/R

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

Author: dacharya
Date: 2015-08-05 07:23:09 +0200 (Wed, 05 Aug 2015)
New Revision: 3910

Added:
   pkg/Dowd/R/tESPlot2DHP.R
Log:
Function tESPlot2DHP added

Added: pkg/Dowd/R/tESPlot2DHP.R
===================================================================
--- pkg/Dowd/R/tESPlot2DHP.R	                        (rev 0)
+++ pkg/Dowd/R/tESPlot2DHP.R	2015-08-05 05:23:09 UTC (rev 3910)
@@ -0,0 +1,142 @@
+#' Plots t ES against holding period
+#' 
+#' Plots the ES of a portfolio against holding period assuming that L/P is t distributed, for specified confidence level and holding periods.
+#' 
+#' @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 P/L data
+#' 
+#'  mu Mean of daily P/L data
+#' 
+#'  sigma Standard deviation of daily P/L data
+#' 
+#'  df Number of degrees of freedom in the t distribution
+#' 
+#'  cl ES confidence level and must be a scalar
+#' 
+#'  hp ES holding period and must be a vector
+#'  
+#' @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)
+#'    tESPlot2DHP(returns = data, df = 6, cl = .95, hp = 60:90)
+#'    
+#'    # Computes v given mean and standard deviation of return data
+#'    tESPlot2DHP(mu = .012, sigma = .03, df = 6, cl = .99, hp = 40:80)
+#'
+#' @export
+tESPlot2DHP <- function(...){
+  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 (max(cl.row, cl.col) > 1) {
+    stop("Confidence level 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 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")
+  }
+  # Check that hp is read as row vector
+  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")
+  }
+  # VaR estimation
+  VaR <- (-sigma[1,1] * sqrt(t(hp)) %*% sqrt((df - 2) / df) %*% qt(1 - cl, df)) + (- mu[1,1] * t(hp)) # 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(t(hp)) %*% sqrt((df - 2) / df) %*% qt(1 - cl, df)) + (- mu[1,1] * t(hp) %*% matrix(1, cl.row, cl.col))
+  }
+  v <- v/n
+  
+  # Plotting
+  plot(hp, v, type = "l", xlab = "Holding Period", ylab = "ES")
+  title("t ES against holding period")
+  xmin <-min(hp)+.25*(max(hp)-min(hp))
+  cl.label <- cl0 * 100
+  text(xmin,max(v)-.5*(max(v)-min(v)),
+       'Input parameters', cex=.75, font = 2)
+  text(xmin,max(v)-.55*(max(v)-min(v)),
+       paste('Daily mean L/P data = ', round(mu[1,1], 3)),cex=.75)
+  text(xmin,max(v)-.6*(max(v)-min(v)),
+       paste('Stdev. of daily L/P data = ',round(sigma[1,1],3)),cex=.75)
+  text(xmin,max(v)-.65*(max(v)-min(v)),
+       paste('Degrees of freedom = ',df),cex=.75)
+  text(xmin,max(v)-.7*(max(v)-min(v)),
+       paste('Confidence level = ',cl.label,'%'),cex=.75)
+}
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