[Returnanalytics-commits] r3923 - pkg/Dowd/R

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

Author: dacharya
Date: 2015-08-07 10:18:58 +0200 (Fri, 07 Aug 2015)
New Revision: 3923

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

Added: pkg/Dowd/R/tVaRDFPerc.R
===================================================================
--- pkg/Dowd/R/tVaRDFPerc.R	                        (rev 0)
+++ pkg/Dowd/R/tVaRDFPerc.R	2015-08-07 08:18:58 UTC (rev 3923)
@@ -0,0 +1,172 @@
+#' Percentiles of VaR distribution function
+#' 
+#' Plots the VaR of a portfolio against confidence level assuming that P/L 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 5 
+#' or 7. In case there 6 input arguments, the mean, standard deviation and 
+#' number of observations of the 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
+#' 
+#'  n Sample size
+#' 
+#'  perc Desired percentile
+#' 
+#'  df Number of degrees of freedom in the t distribution
+#' 
+#'  cl VaR confidence level and must be a scalar
+#' 
+#'  hp VaR holding period and must be a a scalar
+#' 
+#'  Percentiles of VaR distribution function
+#'  
+#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
+#'
+#' @author Dinesh Acharya
+#' @examples
+#' 
+#'    # Estimates Percentiles of VaR distribution
+#'    data <- runif(5, min = 0, max = .2)
+#'    tVaRDFPerc(returns = data, perc = .7, 
+#'                  df = 6, cl = .95, hp = 60)
+#'    
+#'    # Computes v given mean and standard deviation of return data
+#'    tVaRDFPerc(mu = .012, sigma = .03, n= 10, 
+#'                  perc = .8, df = 6, cl = .99, hp = 40)
+#'
+#'
+#' @export
+tVaRDFPerc <- function(...){
+  # Determine if there are five or seven arguments, and ensure that arguments are read as intended
+  if (nargs() < 5) {
+    stop("Too few arguments")
+  }
+  if (nargs() == 6) {
+    stop("Incorrect number of arguments")
+  }
+  if (nargs() > 7) {
+    stop("Too many arguments")
+  }
+  args <- list(...)
+  if (nargs() == 7) {
+    mu <- args$mu
+    df <- args$df
+    cl <- args$cl
+    perc <- args$perc
+    n <- args$n
+    sigma <- args$sigma
+    hp <- args$hp
+  }
+  if (nargs() == 5) {
+    mu <- mean(args$returns)
+    df <- args$df
+    n <- max(dim(as.matrix(args$returns)))
+    perc <- args$perc
+    cl <- args$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")
+  }
+  n <- as.matrix(n)
+  n.row <- dim(n)[1]
+  n.col <- dim(n)[2]
+  if (max(n.row, n.col) > 1) {
+    stop("Number of observations in a sample must be an integer")
+  }
+  perc <- as.matrix(perc)
+  perc.row <- dim(perc)[1]
+  perc.col <- dim(perc)[2]
+  if (max(perc.row, perc.col) > 1) {
+    stop("Chosen percentile of the distribution 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 (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 inputs obey sign and value restrictions
+  if (sigma < 0) {
+    stop("Standard deviation must be non-negative")
+  }
+  if (n < 0) {
+    stop("Number of observations must be non-negative")
+  }
+  if (perc > 1){
+    stop("Chosen percentile must not exceed 1")
+  }
+  if (perc <= 0){
+    stop("Chosen percentile must be positive")
+  }
+  if (cl >= 1){
+    stop("Confidence level(s) must be less than 1")
+  }
+  if (cl <= 0){
+    stop("Confidence level(s) must be greater than 0")
+  }
+  if (hp <= 0){
+    stop("Honding period(s) must be greater than 0")
+  }
+  if (df < 3) {
+    stop("Number of degrees of freedom must be at least 3 for first two moments of distribution to be defined")
+  }
+  
+  # Derive order statistic and ensure it is an integer
+  w <- n * cl # Derive r-th order statistic
+  r <- round(w) # Round r to nearest integer
+  # Bisection routine
+  a <- 0
+  fa <- -Inf
+  b <- 1
+  fb <- Inf
+  eps <- .Machine$double.eps
+  while (b - a > eps * b) {
+    x <- (a + b) / 2
+    fx <- 1 - pbinom(r - 1, n, x) - perc
+    if (sign(fx) == sign(fa)){
+      a <- x
+      fa <- fx
+    } else {
+      b <- x
+      fb <- fx
+    }
+  }
+  # VaR estimation
+  y <- -mu %*% hp + sigma %*% sqrt(hp) %*% sqrt((df - 2) / df) %*% qt(x, df)# VaR
+  
+  return(y)
+}