sandbox/Shubhankit/sandbox/vignettes/AcarSim.R

In cloudcello/PerformanceAnalytics: Econometric Tools for Performance and Risk Analysis

#' @title Acar-Shane Maximum Loss Plot 
#' 
#'@description To get some insight on the relationships between maximum drawdown per unit of volatility 
#'and mean return divided by volatility, we have proceeded to Monte-Carlo simulations.
#' We have simulated cash flows over a period of 36 monthly returns and measured maximum 
#'drawdown for varied levels of annualised return divided by volatility varying from minus
#' \emph{two to two} by step of \emph{0.1} . The process has been repeated \bold{six thousand times}.
#' @details  Unfortunately, there is no \bold{analytical formulae} to establish the maximum drawdown properties under 
#' the random walk assumption. We should note first that due to its definition, the maximum drawdown 
#' divided by volatility can be interpreted as the only function of the ratio mean divided by volatility.
#' \deqn{MD/[\sigma]= Min (\sum[X(j)])/\sigma = F(\mu/\sigma)}
#' Where j varies from 1 to n ,which is the number of drawdown's in simulation 
#' @param R an xts, vector, matrix, data frame, timeSeries or zoo object of
#' asset returns
#' @param nsim number of simulations input
#' @author Shubhankit Mohan
#' @references Maximum Loss and Maximum Drawdown in Financial Markets,\emph{International Conference Sponsored by BNP and Imperial College on: 
#' Forecasting Financial Markets, London, United Kingdom, May 1997} \url{http://www.intelligenthedgefundinvesting.com/pubs/easj.pdf}
#' @keywords Maximum Loss Simulated Drawdown
#' @examples
#' library(PerformanceAnalytics)
#' AcarSim(R)
#' @rdname AcarSim
#' @export 
AcarSim <-
  function(R,nsim=1)
  {
       library(PerformanceAnalytics)

    data(edhec)
    
    R = checkData(R, method="xts")
    # Get dimensions and labels
    # simulated parameters using edhec data
mu=mean(Return.annualized(R))
monthly=(1+mu)^(1/12)-1
    vol = as.numeric(StdDev.annualized(R));
    ret=as.numeric(Return.annualized(R))
    drawdown =as.numeric(maxDrawdown(R))
    sig=mean(StdDev.annualized(R));
T= 36
j=1
dt=1/T
thres=4;
r=matrix(0,nsim,T+1)
monthly = 0
r[,1]=monthly;
# Sigma 'monthly volatiltiy' will be the varying term
ratio= seq(-2, 2, by=.1);
len = length(ratio)
ddown=array(0, dim=c(nsim,len,thres))
fddown=array(0, dim=c(len,thres))
Z <- array(0, c(len))
for(i in 1:len)
{
  monthly = sig*ratio[i];

  for(j in 1:nsim)
{
    dz=rnorm(T)
    
    
      r[j,2:37]=monthly+(sig*dz*sqrt(3*dt))
    
    ddown[j,i,1]= ES((r[j,]),.99, method="modified")
    ddown[j,i,1][is.na(ddown[j,i,1])] <- 0
    fddown[i,1]=fddown[i,1]+ddown[j,i,1]
    ddown[j,i,2]= ES((r[j,]),.95, method="modified")
    ddown[j,i,2][is.na(ddown[j,i,2])] <- 0
    fddown[i,2]=fddown[i,2]+ddown[j,i,2]
    ddown[j,i,3]= ES((r[j,]),.90, method="modified")
    ddown[j,i,3][is.na(ddown[j,i,3])] <- 0
    fddown[i,3]=fddown[i,3]+ddown[j,i,3]
    ddown[j,i,4]= ES((r[j,]),.85, method="modified")
    ddown[j,i,4][is.na(ddown[j,i,4])] <- 0
    fddown[i,4]=fddown[i,4]+ddown[j,i,4]
    assign("last.warning", NULL, envir = baseenv())
}
}
plot(((fddown[,1])/(sig*nsim)),xlab="Annualised Return/Volatility from [-2,2]",ylab="Maximum Drawdown/Volatility",type='o',col="blue")
lines(((fddown[,2])/(sig*nsim)),type='o',col="pink")
lines(((fddown[,3])/(sig*nsim)),type='o',col="green")
lines(((fddown[,4])/(sig*nsim)),type='o',col="red")
    points((ret/vol), (-drawdown/vol), col = "black", pch=10)
    legend(32,-4, c("%99", "%95", "%90","%85","Fund"), col = c("blue","pink","green","red","black"), text.col= "black",
       lty = c(2, -1, 1,2), pch = c(-1, 3, 4,10), merge = TRUE, bg='gray90')
    
title("Maximum Drawdown/Volatility as a function of Return/Volatility 
36 monthly returns simulated 6,000 times") 
       edhec=NULL
}

###############################################################################
# R (http://r-project.org/) Econometrics for Performance and Risk Analysis
#
# Copyright (c) 2004-2012 Peter Carl and Brian G. Peterson
#
# This R package is distributed under the terms of the GNU Public License (GPL)
# for full details see the file COPYING
#
# $Id: AcarSim.R 2163 2012-07-16 00:30:19Z braverock $
#
###############################################################################