[Returnanalytics-commits] r3950 - pkg/Dowd/R

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

Author: dacharya
Date: 2015-08-13 11:59:29 +0200 (Thu, 13 Aug 2015)
New Revision: 3950

Added:
   pkg/Dowd/R/NormalESHotspots.R
Log:
Function NormalESHotspot.R added.

Added: pkg/Dowd/R/NormalESHotspots.R
===================================================================
--- pkg/Dowd/R/NormalESHotspots.R	                        (rev 0)
+++ pkg/Dowd/R/NormalESHotspots.R	2015-08-13 09:59:29 UTC (rev 3950)
@@ -0,0 +1,97 @@
+#' @title Hotspots for normal ES
+#' 
+#' @description Estimates the ES hotspots (or vector of incremental ESs) for a 
+#' portfolio assuming individual asset returns are normally distributed, for 
+#' specified confidence level and holding period.
+#' 
+#' @param vc.matrix Variance covariance matrix for returns
+#' @param mu Vector of expected position returns
+#' @param positions Vector of positions
+#' @param cl Confidence level and is scalar
+#' @param hp Holding period and is scalar
+#' @return Hotspots for normal ES
+#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
+#' 
+#' @author Dinesh Acharya
+#' 
+#' @examples
+#' 
+#'    # Hotspots for ES for randomly generated portfolio
+#'    vc.matrix <- matrix(rnorm(16),4,4)
+#'    mu <- rnorm(4,.08,.04)
+#'    skew <- .5
+#'    kurtosis <- 1.2
+#'    positions <- c(5,2,6,10)
+#'    cl <- .95
+#'    hp <- 280
+#'    AdjustedNormalESHotspots(vc.matrix, mu, skew, kurtosis, positions, cl, hp)
+#' 
+#' @export
+NormalESHotspots <- function(vc.matrix, mu, skew, kurtosis, positions,
+                                    cl, hp){
+  
+  # Check that positions vector read as a scalar or row vector
+  positions <- as.matrix(positions)
+  if (dim(positions)[1] > dim(positions)[2]){
+    positions <- t(positions)
+  }
+  
+  # Check that expected returns vector is read as a scalar or row vector
+  mu <- as.matrix(mu)
+  if (dim(mu)[1] > dim(mu)[2]){
+    mu <- t(mu)
+  }
+  
+  # Check that dimensions are correct
+  if (max(dim(mu)) != max(dim(positions))){
+    stop("Positions vector and expected returns vector must have same size")
+  }
+  if (max(dim(vc.matrix)) != max(dim(positions))){
+    stop("Positions vector and expected returns vector must have same size")
+  }
+  
+  # Check that inputs obey sign and value restrictions
+  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("Holding period must be greater than 0");
+  }
+  
+  VaR <- - mu %*% t(positions) * hp - qnorm(1 - cl, 0, 1) * 
+    (positions %*% vc.matrix %*% t(positions)) * sqrt(hp) # VaR
+  n <- 1000 # Number of slives into which tail is divided
+  cl0 <- cl # Initial confidence level
+  term <- VaR
+  delta.cl <- (1 - cl) / n # Increment to confidence level
+  for (k in 1:(n - 1)) {
+    cl <- cl0 + k * delta.cl # Revised cl
+    term <- term - mu %*% t(positions) * hp - qnorm(1 - cl, 0, 1) * 
+      (positions %*% vc.matrix %*% t(positions)) * sqrt(hp)
+  }
+  portfolio.ES <- term/n
+  
+  # Portfolio ES
+  es <- double(length(positions))
+  ies <- double(length(positions))
+  for (j in 1:length(positions)) {
+    x <- positions
+    x[j] <- 0
+    term[j] <- - mu %*% t(x) * hp - qnorm(1-cl, 0, 1) * x %*% 
+      vc.matrix %*% t(x) * sqrt(hp)
+    
+    for (k in 1:(n - 1)){
+      cl <- cl0 + k * delta.cl # Revised cl
+      term[j] <- term[j] - mu %*% t(x) * hp - qnorm(1-cl, 0, 1) * x %*% 
+        vc.matrix %*% t(x) * sqrt(hp)
+    }
+    es[j] <- term[j]/n # ES on portfolio minus position j
+    ies [j] <- portfolio.ES - es[j] # Incremental ES
+    
+  }
+  y <- ies
+  return(ies)
+}