sandbox/R/nonparametricIncrementalES.R

In R-Finance/FactorAnalytics: factor analysis

#' Compute incremental ES given bootstrap data and portfolio weights.
#' 
#' Compute incremental ES given bootstrap data and portfolio weights.
#' Incremental ES is defined as the change in portfolio ES that occurs when an
#' asset is removed from the portfolio and allocation is spread equally among
#' remaining assets. VaR used in ES computation is computed as the sample
#' quantile.
#' 
#' 
#' @param bootData B x N matrix of B bootstrap returns on n assets in
#' portfolio.
#' @param w N x 1 vector of portfolio weights
#' @param tail.prob scalar tail probability.
#' @param i1,i2 if ff object is used, the ffapply functions do apply an
#' EXPRession and provide two indices FROM="i1" and TO="i2", which mark
#' beginning and end of the batch and can be used in the applied expression.
#' @return n x 1 matrix of incremental ES values for each asset.
#' @author Eric Zivot and Yi-An Chen.
#' @references Jorian, P. (2007). Value-at-Risk, pg. 168.
#' @examples
#' 
#' data(managers.df)
#' ret.assets = managers.df[,(1:6)]
#' nonparametricIncrementalES(ret.assets[,1:3],w=c(1/3,1/3,1/3),tail.prob = 0.05)
#' 
nonparametricIncrementalES <-
function(bootData, w, tail.prob = 0.01, i1,i2) {
## Compute incremental ES given bootstrap data and portfolio weights.
## Incremental ES is defined as the change in portfolio ES that occurs
## when an asset is removed from the portfolio and allocation is spread equally
## among remaining assets. VaR used in ES computation is computed either as the 
## sample quantile or as an estimated quantile using the Cornish-Fisher expansion
## inputs:
## bootData   B x n matrix of B bootstrap returns on n assets in portfolio
## w          n x 1 vector of portfolio weights
## tail.prob  scalar tail probability
## i1,i2       if ff object is used,  the ffapply functions do apply an EXPRession and 
##                provide two indices FROM="i1" and TO="i2", which mark beginning and end 
##                of the batch and can be used in the applied expression.  
## output:
## iES        n x 1 matrix of incremental ES values for each asset
## References:
## Jorian, P. (2007). Value-at-Risk, pg. 168.
## 
  require(PerformanceAnalytics)
  require(ff)
  if (!is.ff(bootData))
    bootData = as.matrix(bootData)
  w = as.matrix(w)
  if ( ncol(bootData) != nrow(w) )
    stop("Columns of bootData and rows of w do not match")
  if ( tail.prob < 0 || tail.prob > 1)
    stop("tail.prob must be between 0 and 1")
  
  if (ncol(bootData) == 1) {
  ## EZ: Added 12/2/2009
  ## one asset portfolio so iES = 0 by construction
    iES = 0
  } else { 
      
  n.w = nrow(w)
  ## portfolio VaR with all assets
  if (is.ff(bootData)) {
  ## use on disk ff object
    r.p = ffrowapply( bootData[i1:i2, ]%*%w, X=bootData, RETURN=TRUE, RETCOL=1)
  } else {
  ## use in RAM object
    r.p = bootData %*% w
  }
  
  ## use empirical quantile to compute VaR
    pVaR = quantile(r.p[], prob=tail.prob)
    idx = which(r.p[] <= pVaR)
    pES = -mean(r.p[idx]) 
    temp.w = w
    iES = matrix(0, n.w, 1)
    rownames(iES) = colnames(bootData)
    colnames(iES) = "i.ES"
    for (i in 1:n.w) {
    ## set weight for asset i to zero and renormalize
      temp.w[i,1] = 0
      temp.w = temp.w/sum(temp.w)
      if (is.ff(bootData)) {
        temp.r.p = ffrowapply( bootData[i1:i2, ]%*%temp.w, X=bootData, RETURN=TRUE, RETCOL=1)
      } else {
        temp.r.p = bootData %*% temp.w
      }
      pVaR.new = quantile(temp.r.p[], prob=tail.prob)    
      idx = which(temp.r.p[] <= pVaR.new)
      pES.new = -mean(temp.r.p[idx])
      iES[i,1] = pES.new - pES
    ## reset weight
      temp.w = w
  }
  return(iES)
}
}