[Returnanalytics-commits] r3814 - in pkg/Dowd: R man

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

Author: dacharya
Date: 2015-07-13 14:03:55 +0200 (Mon, 13 Jul 2015)
New Revision: 3814

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

Added: pkg/Dowd/R/LogNormalES.R
===================================================================
--- pkg/Dowd/R/LogNormalES.R	                        (rev 0)
+++ pkg/Dowd/R/LogNormalES.R	2015-07-13 12:03:55 UTC (rev 3814)
@@ -0,0 +1,125 @@
+#' ES for normally distributed geometric returns
+#' 
+#' Estimates the ES of a portfolio assuming that geometric returns are 
+#' normally distributed, for specified confidence level and holding period.
+#' 
+#' @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 investment Size of investment
+#' @param cl VaR confidence level
+#' @param hp VaR holding period in days
+#' @return Matrix of ES 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.
+#'  
+#'  @note 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.
+#'  
+#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
+#'
+#' @author Dinesh Acharya
+#' @examples
+#' 
+#'    # Computes ES given geometric return data
+#'    data <- runif(5, min = 0, max = .2)
+#'    LogNormalES(returns = data, investment = 5, cl = .95, hp = 90)
+#'    
+#'    # Computes ES given mean and standard deviation of return data
+#'    LogNormalES(mu = .012, sigma = .03, investment = 5, cl = .95, hp = 90)
+#'
+#'
+#' @export
+LogNormalES <- function(...){
+  # Determine if there are four or fice 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$mu
+    investment <- args$investment
+    cl <- args$cl
+    sigma <- args$sigma
+    hp <- args$hp
+  }
+  if (nargs() == 4) {
+    mu <- mean(args$returns)
+    investment <- args$investment
+    cl <- args$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")
+  }
+  
+  # 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 (max(cl) >= 1){
+    stop("Confidence levels must be less than 1")
+  }
+  if (min(cl) <= 0){
+    stop("Confidence levels must be greater than 0")
+  }
+  if (min(hp) <= 0){
+    stop("Holding periods must be greater than 0")
+  }
+  # VaR estimation
+  cl.row <- dim(cl)[1]
+  cl.col <- dim(cl)[2]
+  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
+  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/LogNormalES.Rd
===================================================================
--- pkg/Dowd/man/LogNormalES.Rd	                        (rev 0)
+++ pkg/Dowd/man/LogNormalES.Rd	2015-07-13 12:03:55 UTC (rev 3814)
@@ -0,0 +1,53 @@
+% Generated by roxygen2 (4.1.1): do not edit by hand
+% Please edit documentation in R/LogNormalES.R
+\name{LogNormalES}
+\alias{LogNormalES}
+\title{ES for normally distributed geometric returns}
+\usage{
+LogNormalES(...)
+}
+\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{investment}{Size of investment}
+
+\item{cl}{VaR confidence level}
+
+\item{hp}{VaR holding period in days}
+}
+\value{
+Matrix of ES 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.
+}
+\description{
+Estimates the ES of a portfolio assuming that geometric returns are
+normally distributed, for specified confidence level and holding period.
+}
+\note{
+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.
+}
+\examples{
+# Computes ES given geometric return data
+   data <- runif(5, min = 0, max = .2)
+   LogNormalES(returns = data, investment = 5, cl = .95, hp = 90)
+
+   # Computes ES given mean and standard deviation of return data
+   LogNormalES(mu = .012, sigma = .03, investment = 5, cl = .95, hp = 90)
+}
+\author{
+Dinesh Acharya
+}
+\references{
+Dowd, K. Measuring Market Risk, Wiley, 2007.
+}
+