[Returnanalytics-commits] r3914 - pkg/Dowd/R

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

Author: dacharya
Date: 2015-08-05 22:34:43 +0200 (Wed, 05 Aug 2015)
New Revision: 3914

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

Added: pkg/Dowd/R/tVaR.R
===================================================================
--- pkg/Dowd/R/tVaR.R	                        (rev 0)
+++ pkg/Dowd/R/tVaR.R	2015-08-05 20:34:43 UTC (rev 3914)
@@ -0,0 +1,137 @@
+#' VaR for t distributed P/L
+#' 
+#' Estimates the VaR of a portfolio 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 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 VaR confidence level
+#' 
+#'  hp VaR holding period
+#'  
+#' @return Matrix of VaRs whose dimension depends on dimension of hp and cl. If 
+#' cl and hp are both scalars, the matrix is 1 by 1. If cl is a vector and hp is
+#'  a scalar, the matrix is row matrix, if cl is a scalar and hp is a vector, 
+#'  the matrix is column matrix and if both cl and hp are vectors, the matrix 
+#'  has dimension length of cl * length of hp.
+#'  
+#' @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 VaR given P/L data
+#'    data <- runif(5, min = 0, max = .2)
+#'    tVaR(returns = data, df = 6, cl = .95, hp = 90)
+#'    
+#'    # Computes VaR given mean and standard deviation of P/L data
+#'    tVaR(mu = .012, sigma = .03, df = 6, cl = .95, hp = 90)
+#'
+#'
+#' @export
+tVaR <- 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$mu
+    df <- args$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 scalar or a vector")
+  }
+  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")
+  }
+  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 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")
+  }
+  
+  
+  cl.row <- dim(cl)[1]
+  cl.col <- dim(cl)[2]
+  # VaR estimation
+  y <- (-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
+  return (y)
+}