[Returnanalytics-commits] r3936 - pkg/Dowd/R

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

Author: dacharya
Date: 2015-08-11 09:40:00 +0200 (Tue, 11 Aug 2015)
New Revision: 3936

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

Added: pkg/Dowd/R/VarianceCovarianceES.R
===================================================================
--- pkg/Dowd/R/VarianceCovarianceES.R	                        (rev 0)
+++ pkg/Dowd/R/VarianceCovarianceES.R	2015-08-11 07:40:00 UTC (rev 3936)
@@ -0,0 +1,103 @@
+#' @title Variance-covariance ES for normally distributed returns
+#' 
+#' @description Estimates the variance-covariance VaR of 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
+#' 
+#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
+#' 
+#' @author Dinesh Acharya
+#' 
+#' @examples
+#' 
+#'    # Variance-covariance ES for randomly generated portfolio
+#'    vc.matrix <- matrix(rnorm(16), 4, 4)
+#'    mu <- rnorm(4)
+#'    positions <- c(5, 2, 6, 10)
+#'    cl <- .95
+#'    hp <- 280
+#'    VarianceCovarianceES(vc.matrix, mu, positions, cl, hp)
+#' 
+#' @export
+VarianceCovarianceES <- function(vc.matrix, mu, positions, cl, hp){
+  
+  # Check that cl is read as a row vector
+  cl <- as.matrix(cl)
+  if (dim(cl)[1] > dim(cl)[2]) {
+    cl <- t(cl)
+  }
+  
+  # Check that hp is read as a column vector
+  hp <- as.matrix(hp)
+  if (dim(hp)[1] < dim(hp)[2]) {
+    hp <- t(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 and ES estimation
+  VaR <- matrix(0, length(cl), length(hp))
+  term <- matrix(0, length(cl), length(hp))
+  es <- matrix(0, length(cl), length(hp))
+  cl0 <- double(length(cl))
+  delta.cl <- double(length(cl))
+  for (i in 1:length(cl)) {
+    for (j in 1:length(hp)) {
+      VaR[i,j] <- - mu %*% t(positions) * hp[j] - qnorm(1-cl[i],0,1) * 
+        (positions%*%vc.matrix%*%t(positions))*sqrt(hp[j]) # VaR
+      # ES Estimation
+      n <- 1000 # Number of slives into which tail is divided
+      cl0[i] <- cl[i] # Initial confidence level
+      term[i, j] <- VaR[i, j]
+      delta.cl[i] <- (1 - cl[i]) / n # Increment to confidence level as each 
+      # slice is taken
+      
+      for (k in 1:(n - 1)) {
+        
+        cl[i] <- cl0[i] + k * delta.cl[i] # Revised cl
+        term[i, j] <- term[i, j] - mu %*% t(positions) * hp[j] - 
+          (qnorm(1-cl[i],0,1)) * (positions%*%vc.matrix%*%t(positions))*sqrt(hp[j])
+      }
+      es[i, j] <- term[i, j]/n
+      
+    }
+  }
+  y <- t(es)
+  return(y)
+  
+}