[Returnanalytics-commits] r3815 - in pkg/Dowd: R man

noreply at r-forge.r-project.org noreply at r-forge.r-project.org
Mon Jul 13 14:04:29 CEST 2015


Author: dacharya
Date: 2015-07-13 14:04:29 +0200 (Mon, 13 Jul 2015)
New Revision: 3815

Added:
   pkg/Dowd/R/LogNormalESDFPerc.R
   pkg/Dowd/man/LogNormalESDFPerc.Rd
Log:
Function LogNormalESDFPerc added.

Added: pkg/Dowd/R/LogNormalESDFPerc.R
===================================================================
--- pkg/Dowd/R/LogNormalESDFPerc.R	                        (rev 0)
+++ pkg/Dowd/R/LogNormalESDFPerc.R	2015-07-13 12:04:29 UTC (rev 3815)
@@ -0,0 +1,165 @@
+#' Percentiles of ES distribution function for normally distributed geometric returns
+#' 
+#' Estimates the percentiles of ES distribution for normally distributed geometric returns, for specified confidence level and holding period using the theory of order statistics.
+#' 
+#' @param returns Vector of daily geometric return data
+#' @param mu Mean of daily geometric return data
+#' @param sigma Standard deviation of daily geometric return data
+#' @param n Sample size
+#' @param investment Size of investment
+#' @param perc Desired percentile
+#' @param cl ES confidence level and must be a scalar
+#' @param hp ES holding period and must be a a scalar
+#' @return Percentiles of ES distribution function
+#' @note 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 5 input arguments, the mean, standard deviation and number of 
+#' samples is computed from return data. See examples for details.
+#'  
+#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
+#'
+#' @author Dinesh Acharya
+#' @examples
+#' 
+#'    # Estimates Percentiles of ES distribution
+#'    data <- runif(5, min = 0, max = .2)
+#'    LogNormalESDFPerc(returns = data, investment = 5, perc = .7, cl = .95, hp = 60)
+#'    
+#'    # Estimates Percentiles given mean, standard deviation and number of sambles of return data
+#'    LogNormalESDFPerc(mu = .012, sigma = .03, n= 10, investment = 5, perc = .8, cl = .99, hp = 40)
+#'
+#'
+#' @export
+LogNormalESDFPerc <- 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$mu
+    investment <- args$investment
+    cl <- args$cl
+    perc <- args$sigma
+    n <- args$n
+    sigma <- args$sigma
+    hp <- args$hp
+  }
+  if (nargs() == 5) {
+    mu <- mean(args$returns)
+    investment <- args$investment
+    n <- max(dim(as.matrix(args$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 a scalar")
+  }
+  if (n %% 1 != 0) {
+    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")
+  }
+  
+  # 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 must be less than 1")
+  }
+  if (cl <= 0){
+    stop("Confidence level must be greater than 0")
+  }
+  if (hp <= 0){
+    stop("Honding period must be greater than 0")
+  }
+  
+  # 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
+  VaR <- investment - exp( sigma[1,1] * sqrt(hp) %*% qnorm(1 - cl, 0, 1)  + mu[1,1] * hp %*% matrix(1,cl.row,cl.col) + log(investment)) # VaR
+  
+  # ES estimation
+  cl <- x
+  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
+  term <- VaR
+  for (i in 1:(n-1)) {
+    cl <- cl0 + i * delta.cl # Revised cl
+    term <- term + investment - exp(sigma[1,1] * sqrt(hp) %*% qnorm(1 - cl, 0, 1)  + mu[1,1] * hp %*% matrix(1,cl.row,cl.col) + log(investment))
+  }
+  y <- term/n
+  return(y)
+  
+}
\ No newline at end of file

Added: pkg/Dowd/man/LogNormalESDFPerc.Rd
===================================================================
--- pkg/Dowd/man/LogNormalESDFPerc.Rd	                        (rev 0)
+++ pkg/Dowd/man/LogNormalESDFPerc.Rd	2015-07-13 12:04:29 UTC (rev 3815)
@@ -0,0 +1,52 @@
+% Generated by roxygen2 (4.1.1): do not edit by hand
+% Please edit documentation in R/LogNormalESDFPerc.R
+\name{LogNormalESDFPerc}
+\alias{LogNormalESDFPerc}
+\title{Percentiles of ES distribution function for normally distributed geometric returns}
+\usage{
+LogNormalESDFPerc(...)
+}
+\arguments{
+\item{returns}{Vector of daily geometric return data}
+
+\item{mu}{Mean of daily geometric return data}
+
+\item{sigma}{Standard deviation of daily geometric return data}
+
+\item{n}{Sample size}
+
+\item{investment}{Size of investment}
+
+\item{perc}{Desired percentile}
+
+\item{cl}{ES confidence level and must be a scalar}
+
+\item{hp}{ES holding period and must be a a scalar}
+}
+\value{
+Percentiles of ES distribution function
+}
+\description{
+Estimates the percentiles of ES distribution for normally distributed geometric returns, for specified confidence level and holding period using the theory of order statistics.
+}
+\note{
+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 5 input arguments, the mean, standard deviation and number of
+samples is computed from return data. See examples for details.
+}
+\examples{
+# Estimates Percentiles of ES distribution
+   data <- runif(5, min = 0, max = .2)
+   LogNormalESDFPerc(returns = data, investment = 5, perc = .7, cl = .95, hp = 60)
+
+   # Estimates Percentiles given mean, standard deviation and number of sambles of return data
+   LogNormalESDFPerc(mu = .012, sigma = .03, n= 10, investment = 5, perc = .8, cl = .99, hp = 40)
+}
+\author{
+Dinesh Acharya
+}
+\references{
+Dowd, K. Measuring Market Risk, Wiley, 2007.
+}
+



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