sandbox/Shubhankit/noniid.sm/R/table.EMaxDDGBM.R
In naturalsmen/PerformanceAnalytics: Econometric Tools for Performance and Risk Analysis
#' @title Summary of Expected Drawdown using Brownian Motion Assumptions and Return-Volatility
#'
#' @description Works on the model specified by Maddon-Ismail which investigates the behavior of this statistic for a Brownian motion
#' with drift.
#' @details If X(t) is a random process on [0, T ], the maximum drawdown at time T , D(T), is defined by
#' where \deqn{D(T) = sup [X(s) - X(t)]} where s belongs to [0,t] and s belongs to [0,T]
#'Informally, this is the largest drop from a peak to a bottom. In this paper, we investigate the
#'behavior of this statistic for a Brownian motion with drift. In particular, we give an infinite
#'series representation of its distribution, and consider its expected value. When the drift is zero,
#'we give an analytic expression for the expected value, and for non-zero drift, we give an infinite
#'series representation. For all cases, we compute the limiting \bold{(\eqn{T tends to \infty})} behavior, which can be
#'logarithmic (\eqn{\mu} > 0), square root (\eqn{\mu} = 0), or linear (\eqn{\mu} < 0).
#' @param R an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns
#' @param digits significant number
#' @author Shubhankit Mohan
#' @keywords Expected Drawdown Using Brownian Motion Assumptions
#' @references Magdon-Ismail, M., Atiya, A., Pratap, A., and Yaser S. Abu-Mostafa: On the Maximum Drawdown of a Browninan Motion, Journal of Applied Probability 41, pp. 147-161, 2004 \url{http://alumnus.caltech.edu/~amir/drawdown-jrnl.pdf}
#' @keywords Drawdown models Brownian Motion Assumptions
#' @examples
#'
#'library(PerformanceAnalytics)
#' data(edhec)
#' table.EMaxDDGBM(edhec)
#' @rdname table.EMaxDDGBM
#' @export
table.EMaxDDGBM <-
function (R,digits =4)
{# @author
# DESCRIPTION:
# Downside Risk Summary: Statistics and Stylized Facts
# Inputs:
# R: a regular timeseries of returns (rather than prices)
# Output: Table of Estimated Drawdowns
y = checkData(R, method = "xts")
columns = ncol(y)
rows = nrow(y)
columnnames = colnames(y)
rownames = rownames(y)
T= nyears(y);
# for each column, do the following:
for(column in 1:columns) {
x = y[,column]
mu = Return.annualized(x, scale = NA, geometric = TRUE)
sig=StdDev(x)
gamma<-sqrt(pi/8)
if(mu==0){
Ed<-2*gamma*sig*sqrt(T)
}
else{
alpha<-mu*sqrt(T/(2*sig^2))
x<-alpha^2
if(mu>0){
mQp<-matrix(c(
0.0005, 0.0010, 0.0015, 0.0020, 0.0025, 0.0050, 0.0075, 0.0100, 0.0125,
0.0150, 0.0175, 0.0200, 0.0225, 0.0250, 0.0275, 0.0300, 0.0325, 0.0350,
0.0375, 0.0400, 0.0425, 0.0450, 0.0500, 0.0600, 0.0700, 0.0800, 0.0900,
0.1000, 0.2000, 0.3000, 0.4000, 0.5000, 1.5000, 2.5000, 3.5000, 4.5000,
10, 20, 30, 40, 50, 150, 250, 350, 450, 1000, 2000, 3000, 4000, 5000, 0.019690,
0.027694, 0.033789, 0.038896, 0.043372, 0.060721, 0.073808, 0.084693, 0.094171,
0.102651, 0.110375, 0.117503, 0.124142, 0.130374, 0.136259, 0.141842, 0.147162,
0.152249, 0.157127, 0.161817, 0.166337, 0.170702, 0.179015, 0.194248, 0.207999,
0.220581, 0.232212, 0.243050, 0.325071, 0.382016, 0.426452, 0.463159, 0.668992,
0.775976, 0.849298, 0.905305, 1.088998, 1.253794, 1.351794, 1.421860, 1.476457,
1.747485, 1.874323, 1.958037, 2.020630, 2.219765, 2.392826, 2.494109, 2.565985,
2.621743),ncol=2)
if(x<0.0005){
Qp<-gamma*sqrt(2*x)
}
if(x>0.0005 & x<5000){
Qp<-spline(log(mQp[,1]),mQp[,2],n=1,xmin=log(x),xmax=log(x))$y
}
if(x>5000){
Qp<-0.25*log(x)+0.49088
}
Ed<-(2*sig^2/mu)*Qp
}
if(mu<0){
mQn<-matrix(c(
0.0005, 0.0010, 0.0015, 0.0020, 0.0025, 0.0050, 0.0075, 0.0100, 0.0125, 0.0150,
0.0175, 0.0200, 0.0225, 0.0250, 0.0275, 0.0300, 0.0325, 0.0350, 0.0375, 0.0400,
0.0425, 0.0450, 0.0475, 0.0500, 0.0550, 0.0600, 0.0650, 0.0700, 0.0750, 0.0800,
0.0850, 0.0900, 0.0950, 0.1000, 0.1500, 0.2000, 0.2500, 0.3000, 0.3500, 0.4000,
0.5000, 1.0000, 1.5000, 2.0000, 2.5000, 3.0000, 3.5000, 4.0000, 4.5000, 5.0000,
0.019965, 0.028394, 0.034874, 0.040369, 0.045256, 0.064633, 0.079746, 0.092708,
0.104259, 0.114814, 0.124608, 0.133772, 0.142429, 0.150739, 0.158565, 0.166229,
0.173756, 0.180793, 0.187739, 0.194489, 0.201094, 0.207572, 0.213877, 0.220056,
0.231797, 0.243374, 0.254585, 0.265472, 0.276070, 0.286406, 0.296507, 0.306393,
0.316066, 0.325586, 0.413136, 0.491599, 0.564333, 0.633007, 0.698849, 0.762455,
0.884593, 1.445520, 1.970740, 2.483960, 2.990940, 3.492520, 3.995190, 4.492380,
4.990430, 5.498820),ncol=2)
if(x<0.0005){
Qn<-gamma*sqrt(2*x)
}
if(x>0.0005 & x<5000){
Qn<-spline(mQn[,1],mQn[,2],n=1,xmin=x,xmax=x)$y
}
if(x>5000){
Qn<-x+0.50
}
Ed<-(2*sig^2/mu)*(-Qn)
}
}
# return(Ed)
z = c((mu*100),
(sig*100),
(Ed*100))
znames = c(
"Annual Returns in %",
"Std Devetions in %",
"Expected Drawdown in %"
)
if(column == 1) {
resultingtable = data.frame(Value = z, row.names = znames)
}
else {
nextcolumn = data.frame(Value = z, row.names = znames)
resultingtable = cbind(resultingtable, nextcolumn)
}
}
colnames(resultingtable) = columnnames
ans = base::round(resultingtable, digits)
ans
}
###############################################################################
################################################################################
# R (http://r-project.org/) Econometrics for Performance and Risk Analysis
#
# Copyright (c) 2004-2014 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: EmaxDDGBM.R 2271 2012-09-02 01:56:23Z braverock $
#
###############################################################################
naturalsmen/PerformanceAnalytics documentation built on May 23, 2019, 12:20 p.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
#' @title Summary of Expected Drawdown using Brownian Motion Assumptions and Return-Volatility
#'
#' @description Works on the model specified by Maddon-Ismail which investigates the behavior of this statistic for a Brownian motion
#' with drift.
#' @details If X(t) is a random process on [0, T ], the maximum drawdown at time T , D(T), is defined by
#' where \deqn{D(T) = sup [X(s) - X(t)]} where s belongs to [0,t] and s belongs to [0,T]
#'Informally, this is the largest drop from a peak to a bottom. In this paper, we investigate the
#'behavior of this statistic for a Brownian motion with drift. In particular, we give an infinite
#'series representation of its distribution, and consider its expected value. When the drift is zero,
#'we give an analytic expression for the expected value, and for non-zero drift, we give an infinite
#'series representation. For all cases, we compute the limiting \bold{(\eqn{T tends to \infty})} behavior, which can be
#'logarithmic (\eqn{\mu} > 0), square root (\eqn{\mu} = 0), or linear (\eqn{\mu} < 0).
#' @param R an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns
#' @param digits significant number
#' @author Shubhankit Mohan
#' @keywords Expected Drawdown Using Brownian Motion Assumptions
#' @references Magdon-Ismail, M., Atiya, A., Pratap, A., and Yaser S. Abu-Mostafa: On the Maximum Drawdown of a Browninan Motion, Journal of Applied Probability 41, pp. 147-161, 2004 \url{http://alumnus.caltech.edu/~amir/drawdown-jrnl.pdf}
#' @keywords Drawdown models Brownian Motion Assumptions
#' @examples
#'
#'library(PerformanceAnalytics)
#' data(edhec)
#' table.EMaxDDGBM(edhec)
#' @rdname table.EMaxDDGBM
#' @export
table.EMaxDDGBM <-
function (R,digits =4)
{# @author
# DESCRIPTION:
# Downside Risk Summary: Statistics and Stylized Facts
# Inputs:
# R: a regular timeseries of returns (rather than prices)
# Output: Table of Estimated Drawdowns
y = checkData(R, method = "xts")
columns = ncol(y)
rows = nrow(y)
columnnames = colnames(y)
rownames = rownames(y)
T= nyears(y);
# for each column, do the following:
for(column in 1:columns) {
x = y[,column]
mu = Return.annualized(x, scale = NA, geometric = TRUE)
sig=StdDev(x)
gamma<-sqrt(pi/8)
if(mu==0){
Ed<-2*gamma*sig*sqrt(T)
}
else{
alpha<-mu*sqrt(T/(2*sig^2))
x<-alpha^2
if(mu>0){
mQp<-matrix(c(
0.0005, 0.0010, 0.0015, 0.0020, 0.0025, 0.0050, 0.0075, 0.0100, 0.0125,
0.0150, 0.0175, 0.0200, 0.0225, 0.0250, 0.0275, 0.0300, 0.0325, 0.0350,
0.0375, 0.0400, 0.0425, 0.0450, 0.0500, 0.0600, 0.0700, 0.0800, 0.0900,
0.1000, 0.2000, 0.3000, 0.4000, 0.5000, 1.5000, 2.5000, 3.5000, 4.5000,
10, 20, 30, 40, 50, 150, 250, 350, 450, 1000, 2000, 3000, 4000, 5000, 0.019690,
0.027694, 0.033789, 0.038896, 0.043372, 0.060721, 0.073808, 0.084693, 0.094171,
0.102651, 0.110375, 0.117503, 0.124142, 0.130374, 0.136259, 0.141842, 0.147162,
0.152249, 0.157127, 0.161817, 0.166337, 0.170702, 0.179015, 0.194248, 0.207999,
0.220581, 0.232212, 0.243050, 0.325071, 0.382016, 0.426452, 0.463159, 0.668992,
0.775976, 0.849298, 0.905305, 1.088998, 1.253794, 1.351794, 1.421860, 1.476457,
1.747485, 1.874323, 1.958037, 2.020630, 2.219765, 2.392826, 2.494109, 2.565985,
2.621743),ncol=2)
if(x<0.0005){
Qp<-gamma*sqrt(2*x)
}
if(x>0.0005 & x<5000){
Qp<-spline(log(mQp[,1]),mQp[,2],n=1,xmin=log(x),xmax=log(x))$y
}
if(x>5000){
Qp<-0.25*log(x)+0.49088
}
Ed<-(2*sig^2/mu)*Qp
}
if(mu<0){
mQn<-matrix(c(
0.0005, 0.0010, 0.0015, 0.0020, 0.0025, 0.0050, 0.0075, 0.0100, 0.0125, 0.0150,
0.0175, 0.0200, 0.0225, 0.0250, 0.0275, 0.0300, 0.0325, 0.0350, 0.0375, 0.0400,
0.0425, 0.0450, 0.0475, 0.0500, 0.0550, 0.0600, 0.0650, 0.0700, 0.0750, 0.0800,
0.0850, 0.0900, 0.0950, 0.1000, 0.1500, 0.2000, 0.2500, 0.3000, 0.3500, 0.4000,
0.5000, 1.0000, 1.5000, 2.0000, 2.5000, 3.0000, 3.5000, 4.0000, 4.5000, 5.0000,
0.019965, 0.028394, 0.034874, 0.040369, 0.045256, 0.064633, 0.079746, 0.092708,
0.104259, 0.114814, 0.124608, 0.133772, 0.142429, 0.150739, 0.158565, 0.166229,
0.173756, 0.180793, 0.187739, 0.194489, 0.201094, 0.207572, 0.213877, 0.220056,
0.231797, 0.243374, 0.254585, 0.265472, 0.276070, 0.286406, 0.296507, 0.306393,
0.316066, 0.325586, 0.413136, 0.491599, 0.564333, 0.633007, 0.698849, 0.762455,
0.884593, 1.445520, 1.970740, 2.483960, 2.990940, 3.492520, 3.995190, 4.492380,
4.990430, 5.498820),ncol=2)
if(x<0.0005){
Qn<-gamma*sqrt(2*x)
}
if(x>0.0005 & x<5000){
Qn<-spline(mQn[,1],mQn[,2],n=1,xmin=x,xmax=x)$y
}
if(x>5000){
Qn<-x+0.50
}
Ed<-(2*sig^2/mu)*(-Qn)
}
}
# return(Ed)
z = c((mu*100),
(sig*100),
(Ed*100))
znames = c(
"Annual Returns in %",
"Std Devetions in %",
"Expected Drawdown in %"
)
if(column == 1) {
resultingtable = data.frame(Value = z, row.names = znames)
}
else {
nextcolumn = data.frame(Value = z, row.names = znames)
resultingtable = cbind(resultingtable, nextcolumn)
}
}
colnames(resultingtable) = columnnames
ans = base::round(resultingtable, digits)
ans
}
###############################################################################
################################################################################
# R (http://r-project.org/) Econometrics for Performance and Risk Analysis
#
# Copyright (c) 2004-2014 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: EmaxDDGBM.R 2271 2012-09-02 01:56:23Z braverock $
#
###############################################################################
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We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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