[Returnanalytics-commits] r2818 - in pkg/PerformanceAnalytics/sandbox/pulkit: . R man
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Sun Aug 18 15:19:59 CEST 2013
Author: pulkit
Date: 2013-08-18 15:19:58 +0200 (Sun, 18 Aug 2013)
New Revision: 2818
Modified:
pkg/PerformanceAnalytics/sandbox/pulkit/NAMESPACE
pkg/PerformanceAnalytics/sandbox/pulkit/R/DrawdownBeta.R
pkg/PerformanceAnalytics/sandbox/pulkit/R/DrawdownBetaMulti.R
pkg/PerformanceAnalytics/sandbox/pulkit/R/ExtremeDrawdown.R
pkg/PerformanceAnalytics/sandbox/pulkit/R/GoldenSection.R
pkg/PerformanceAnalytics/sandbox/pulkit/R/MaxDD.R
pkg/PerformanceAnalytics/sandbox/pulkit/R/MinTRL.R
pkg/PerformanceAnalytics/sandbox/pulkit/R/MonteSimulTriplePenance.R
pkg/PerformanceAnalytics/sandbox/pulkit/R/PSRopt.R
pkg/PerformanceAnalytics/sandbox/pulkit/R/ProbSharpeRatio.R
pkg/PerformanceAnalytics/sandbox/pulkit/R/TuW.R
pkg/PerformanceAnalytics/sandbox/pulkit/R/table.PSR.R
pkg/PerformanceAnalytics/sandbox/pulkit/R/table.Penance.R
pkg/PerformanceAnalytics/sandbox/pulkit/man/BetaDrawdown.Rd
pkg/PerformanceAnalytics/sandbox/pulkit/man/EconomicDrawdown.Rd
pkg/PerformanceAnalytics/sandbox/pulkit/man/MaxDD.Rd
pkg/PerformanceAnalytics/sandbox/pulkit/man/MinTrackRecord.Rd
pkg/PerformanceAnalytics/sandbox/pulkit/man/ProbSharpeRatio.Rd
pkg/PerformanceAnalytics/sandbox/pulkit/man/PsrPortfolio.Rd
pkg/PerformanceAnalytics/sandbox/pulkit/man/TuW.Rd
Log:
some modifications
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/NAMESPACE
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/NAMESPACE 2013-08-18 12:39:18 UTC (rev 2817)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/NAMESPACE 2013-08-18 13:19:58 UTC (rev 2818)
@@ -1,21 +1,21 @@
export(AlphaDrawdown)
export(BenchmarkSR)
+export(CdarMultiPath)
export(chart.BenchmarkSR)
+export(chart.Penance)
export(chart.SRIndifference)
+export(DrawdownGPD)
export(EconomicDrawdown)
export(EDDCOPS)
+export(golden_section)
export(MinTrackRecord)
+export(MonteSimulTriplePenance)
+export(MultiBetaDrawdown)
+export(ProbSharpeRatio)
+export(PsrPortfolio)
export(REDDCOPS)
export(rollDrawdown)
export(rollEconomicMax)
-export(CDaR)
-export(CdarMultiPath)
-export(chart.Penance)
-export(chart.REDD)
-export(chart.SharpeEfficientFrontier)
-export(BetaDrawdown)
-export(MultiBetaDrawdown)
-export(EDDCOPS)
-export(DrawdownGPD)
-export(golden_section)
-export(MaxDD)
+export(table.Penance)
+export(table.PSR)
+export(TuW)
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/R/DrawdownBeta.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/R/DrawdownBeta.R 2013-08-18 12:39:18 UTC (rev 2817)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/R/DrawdownBeta.R 2013-08-18 13:19:58 UTC (rev 2818)
@@ -40,8 +40,7 @@
#'of Florida,September 2012.
#'
#'@examples
-#'
-#'BetaDrawdown(edhec[,1],edhec[,2]) #expected value 0.5390431
+#'BetaDrawdown(edhec[,1],edhec[,2])
BetaDrawdown<-function(R,Rm,h=0,p=0.95,weights=NULL,geometric=TRUE,type=c("alpha","average","max"),...){
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/R/DrawdownBetaMulti.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/R/DrawdownBetaMulti.R 2013-08-18 12:39:18 UTC (rev 2817)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/R/DrawdownBetaMulti.R 2013-08-18 13:19:58 UTC (rev 2818)
@@ -37,6 +37,7 @@
#'@examples
#'MultiBetaDrawdown(cbind(edhec,edhec),cbind(edhec[,2],edhec[,2]),sample = 2,ps=c(0.4,0.6))
#'BetaDrawdown(edhec[,1],edhec[,2]) #expected value 0.5390431
+#'@export
MultiBetaDrawdown<-function(R,Rm,sample,ps,h=0,p=0.95,weights=NULL,geometric=TRUE,type=c("alpha","average","max"),...){
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/R/ExtremeDrawdown.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/R/ExtremeDrawdown.R 2013-08-18 12:39:18 UTC (rev 2817)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/R/ExtremeDrawdown.R 2013-08-18 13:19:58 UTC (rev 2818)
@@ -34,7 +34,7 @@
#'Mendes, Beatriz V.M. and Leal, Ricardo P.C., Maximum Drawdown: Models and Applications (November 2003). Coppead Working Paper Series No. 359.
#'Available at SSRN: http://ssrn.com/abstract=477322 or http://dx.doi.org/10.2139/ssrn.477322.
#'
-#'
+#'@export
DrawdownGPD<-function(R,type=c("gpd","pd","weibull"),threshold=0.90){
x = checkData(R)
columns = ncol(R)
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/R/GoldenSection.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/R/GoldenSection.R 2013-08-18 12:39:18 UTC (rev 2817)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/R/GoldenSection.R 2013-08-18 13:19:58 UTC (rev 2818)
@@ -14,14 +14,13 @@
#' in which \eqn{x_2} is chosen. If \eqn{f(x_2)>f(x_1)} then the new three points would be \eqn{x_l \textless x_2 \textless x_1} else if
#' \eqn{f(x_2)<f(x_1)} then the three new points are \eqn{x_2<x_1<x_u}. This process is continued until the distance between the outer point
#' is sufficiently small.
-
-#' @references Bailey, David H. and Lopez de Prado, Marcos, Drawdown-Based Stop-Outs and the ‘Triple Penance’ Rule(January 1, 2013).
-#'
#'@param a initial point
#'@param b final point
#'@param minimum TRUE to calculate the minimum and FALSE to calculate the Maximum
#'@param function_name The name of the function
-
+#' @references Bailey, David H. and Lopez de Prado, Marcos, Drawdown-Based Stop-Outs and the ‘Triple Penance’ Rule(January 1, 2013).
+#'
+#'@export
golden_section<-function(a,b,minimum = TRUE,function_name,...){
# DESCRIPTION
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/R/MaxDD.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/R/MaxDD.R 2013-08-18 12:39:18 UTC (rev 2817)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/R/MaxDD.R 2013-08-18 13:19:58 UTC (rev 2818)
@@ -13,14 +13,12 @@
#'
#' The time at which the Maximum Drawdown occurs is given by
#' \deqn{t^\ast=\biggl(\frac{Z_{\alpha}\sigma}{2\mu}\biggr)^2}
-#' Here $Z_{\alpha}$ is the critical value of the Standard Normal Distribution
-#' associated with a probability $\alpha$.$\sigma$ and $\mu$ are the Standard
-#' Distribution and the mean respectively.
+#' Here \eqn{Z_{\alpha}} is the critical value of the Standard Normal Distribution associated with a probability \eqn{\alpha}.\eqn{\sigma} and \eqn{\mu} are the Standard Distribution and the mean respectively.
#' When the distribution is non-normal and time dependent, Autoregressive process.
#'
#' \deqn{Q_{\alpha,t}=\frac{\phi^{(t+1)}-\phi}{\phi-1}(\triangle\pi_0-\mu)+{\mu}t+Z_{\alpha}\frac{\sigma}{|\phi-1|}\biggl(\frac{\phi^{2(t+1)}-1}{\phi^2-1}-2\frac{\phi^(t+1)-1}{\phi-1}+t+1\biggr)^{1/2}}
#'
-#' $\phi$ is estimated as
+#' \eqn{\phi} is estimated as
#'
#' \deqn{\hat{\phi} = Cov_0[\triangle\pi_\tau,\triangle\pi_{\tau-1}](Cov_0[\triangle\pi_{\tau-1},\triangle\pi_{\tau-1}])^{-1}}
#'
@@ -34,8 +32,7 @@
#'
#'The random shocks are iid distributed \eqn{\epsilon_{\tau}~N(0,1)}. These random shocks follow an independent and
#'identically distributed Gaussian Process, however \eqn{\triangle{\pi_\tau}} is neither an independent nor an
-#'identically distributed Gaussian Process. This is due to the parameter \eqn{\phi}, which incorporates a first-order
-#'serial-correlation effect of auto-regressive form.
+#'identically distributed Gaussian Process. This is due to the parameter \eqn{\phi}, which incorporates a first-order serial-correlation effect of auto-regressive form.
#'
#' Golden Section Algorithm is used to calculate the Minimum of the function Q.
#'
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/R/MinTRL.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/R/MinTRL.R 2013-08-18 12:39:18 UTC (rev 2817)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/R/MinTRL.R 2013-08-18 13:19:58 UTC (rev 2818)
@@ -12,7 +12,7 @@
#'
#'\deqn{MinTRL = n^\ast = 1+\biggl[1-\hat{\gamma_3}\hat{SR}+\frac{\hat{\gamma_4}}{4}\hat{SR^2}\biggr]\biggl(\frac{Z_\alpha}{\hat{SR}-SR^\ast}\biggr)^2}
#'
-#'$\gamma{_3}$ and $\gamma{_4}$ are the skewness and kurtosis respectively.
+#'\eqn{\gamma{_3}} and \eqn{\gamma{_4}} are the skewness and kurtosis respectively.
#'It is important to note that MinTRL is expressed in terms of number of observations,
#'not annual or calendar terms.
#'
@@ -118,4 +118,4 @@
#
# $Id: MinTRL.R $
#
-##############################################################################
\ No newline at end of file
+##############################################################################
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/R/MonteSimulTriplePenance.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/R/MonteSimulTriplePenance.R 2013-08-18 12:39:18 UTC (rev 2817)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/R/MonteSimulTriplePenance.R 2013-08-18 13:19:58 UTC (rev 2818)
@@ -25,7 +25,8 @@
#'
#' @examples
#' MonteSimulTriplePenance(10^6,0.5,1,2,1,25,0.95) # Expected Value Quantile (Exact) = 6.781592
-#'
+#'
+#'@export
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/R/PSRopt.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/R/PSRopt.R 2013-08-18 12:39:18 UTC (rev 2817)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/R/PSRopt.R 2013-08-18 13:19:58 UTC (rev 2818)
@@ -3,14 +3,14 @@
#'Maximizing for PSR leads to better diversified and more balanced hedge fund allocations compared to the concentrated
#'outcomes of Sharpe ratio maximization.We would like to find the vector of weights that maximize the expression
#'
-#'\deqn{\hat{PSR}(SR^\ast) = Z\biggl[\frac{(\hat{SR}-SR^\ast)\sqrt{n-1}}{\sqrt{1-\hat{\gamma_3}SR^\ast + \frac{\hat{\gamma_4}-1}{4}\hat{SR^2}}}\biggr]}
+#'\deqn{\hat{PSR}(SR^\**) = Z\biggl[\frac{(\hat{SR}-SR^\**)\sqrt{n-1}}{\sqrt{1-\hat{\gamma_3}SR^\** + \frac{\hat{\gamma_4}-1}{4}\hat{SR^2}}}\biggr]}
#'
#'where \eqn{\sigma = \sqrt{E[(r-\mu)^2]}} ,its standard deviation.\eqn{\gamma_3=\frac{E\biggl[(r-\mu)^3\biggr]}{\sigma^3}} its skewness,
#'\eqn{\gamma_4=\frac{E\biggl[(r-\mu)^4\biggr]}{\sigma^4}} its kurtosis and \eqn{SR = \frac{\mu}{\sigma}} its Sharpe Ratio.
-#'Because \eqn{\hat{PSR}(SR^\ast)=Z[\hat{Z^\ast}]} is a monotonic increasing function of
-#'\eqn{\hat{Z^\ast}} ,it suffices to compute the vector that maximizes \eqn{\hat{Z^\ast}}
+#'Because \eqn{\hat{PSR}(SR^\**)=Z[\hat{Z^\**}]} is a monotonic increasing function of
+#'\eqn{\hat{Z^\**}} ,it suffices to compute the vector that maximizes \eqn{\hat{Z^\**}}
#'
-#'This optimal vector is invariant of the value adopted by the parameter $SR^\ast$.
+#'This optimal vector is invariant of the value adopted by the parameter \eqn{SR^\**}.
#'Gradient Ascent Logic is used to compute the weights using the Function PsrPortfolio
@@ -32,6 +32,7 @@
#'
#'data(edhec)
#'PsrPortfolio(edhec)
+#'@export
PsrPortfolio<-function(R,refSR=0,bounds=NULL,MaxIter = 1000,delta = 0.005){
# DESCRIPTION:
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/R/ProbSharpeRatio.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/R/ProbSharpeRatio.R 2013-08-18 12:39:18 UTC (rev 2817)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/R/ProbSharpeRatio.R 2013-08-18 13:19:58 UTC (rev 2818)
@@ -10,9 +10,9 @@
#'
#' \deqn{\hat{PSR}(SR^\ast) = Z\biggl[\frac{(\hat{SR}-SR^\ast)\sqrt{n-1}}{\sqrt{1-\hat{\gamma_3}SR^\ast + \frac{\hat{\gamma_4}-1}{4}\hat{SR^2}}}\biggr]}
-#' Here $n$ is the track record length or the number of data points. It can be daily,weekly or yearly depending on the input given
+#' Here \eqn{n} is the track record length or the number of data points. It can be daily,weekly or yearly depending on the input given
-#' $\hat{\gamma{_3}}$ and $\hat{\gamma{_4}}$ are the skewness and kurtosis respectively.
+#' \eqn{\hat{\gamma{_3}}} and \eqn{\hat{\gamma{_4}}} are the skewness and kurtosis respectively.
#'
#'
#' @aliases ProbSharpeRatio
@@ -43,6 +43,7 @@
#' ProbSharpeRatio(edhec[,1],refSR = 0.23)
#' ProbSharpeRatio(refSR = 1/12^0.5,Rf = 0,p=0.95,sr = 2/12^0.5,sk=-0.72,kr=5.78,n=59)
#' ProbSharpeRatio(edhec[,1:2],refSR = c(0.28,0.24))
+#'@export
ProbSharpeRatio<-
function(R = NULL, refSR,Rf=0,p = 0.95, weights = NULL,n = NULL,sr = NULL,sk = NULL, kr = NULL, ...){
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/R/TuW.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/R/TuW.R 2013-08-18 12:39:18 UTC (rev 2817)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/R/TuW.R 2013-08-18 13:19:58 UTC (rev 2818)
@@ -5,8 +5,8 @@
#' \code{TriplePenance} calculates the maximum
#' Maximum Time under water for a particular confidence interval is given by
#'
-#' For a particular sequence $\left\{\pi_t\right\}$, the time under water $(TuW)$
-#' is the minimum number of observations, $t>0$, such that $\pi_{t-1}<0$ and $\pi_t>0$.
+#' For a particular sequence \eqn{\left\{\pi_t\right\}}, the time under water \eqn{(TuW)}
+#' is the minimum number of observations, \eqn{t>0}, such that \eqn{\pi_{t-1}<0} and \eqn{\pi_t>0}.
#'
#' For a normal distribution Maximum Time Under Water is given by the following expression.
#' \deqn{MaxTuW_\alpha=\biggl(\frac{Z_\alpha{\sigma}}{\mu}\biggr)^2}
@@ -32,6 +32,7 @@
#' @examples
#' TuW(edhec,0.95,"ar")
#' TuW(edhec[,1],0.95,"normal") # expected value 103.2573
+#'@export
TuW<-function(R,confidence,type=c("ar","normal"),...){
x = checkData(R)
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/R/table.PSR.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/R/table.PSR.R 2013-08-18 12:39:18 UTC (rev 2817)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/R/table.PSR.R 2013-08-18 13:19:58 UTC (rev 2818)
@@ -21,6 +21,7 @@
#'data(edhec)
#'table.PSR(edhec[,1],0.20)
#'
+#'@export
table.PSR<-function(R=NULL,refSR,Rf=0,p=0.95,weights = NULL,...){
if(!is.null(R)){
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/R/table.Penance.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/R/table.Penance.R 2013-08-18 12:39:18 UTC (rev 2817)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/R/table.Penance.R 2013-08-18 13:19:58 UTC (rev 2818)
@@ -8,6 +8,7 @@
#' @param confidence the confidence interval
#'
#' @references Bailey, David H. and Lopez de Prado, Marcos, Drawdown-Based Stop-Outs and the ‘Triple Penance’ Rule(January 1, 2013).
+#' @export
table.Penance<-function(R,confidence){
# DESCRIPTION:
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/man/BetaDrawdown.Rd
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/man/BetaDrawdown.Rd 2013-08-18 12:39:18 UTC (rev 2817)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/man/BetaDrawdown.Rd 2013-08-18 13:19:58 UTC (rev 2818)
@@ -65,7 +65,7 @@
the market performs well.
}
\examples{
-BetaDrawdown(edhec[,1],edhec[,2]) #expected value 0.5390431
+BetaDrawdown(edhec[,1],edhec[,2])
}
\references{
Zabarankin, M., Pavlikov, K., and S. Uryasev. Capital
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/man/EconomicDrawdown.Rd
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/man/EconomicDrawdown.Rd 2013-08-18 12:39:18 UTC (rev 2817)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/man/EconomicDrawdown.Rd 2013-08-18 13:19:58 UTC (rev 2818)
@@ -3,8 +3,6 @@
\title{Calculate the Economic Drawdown}
\usage{
EconomicDrawdown(R, Rf, geometric = TRUE, ...)
-
- EconomicDrawdown(R, Rf, geometric = TRUE, ...)
}
\arguments{
\item{R}{an xts, vector, matrix, data frame, timeseries,
@@ -18,18 +16,6 @@
default is TRUE}
\item{\dots}{any other variable}
-
- \item{R}{an xts, vector, matrix, data frame, timeseries,
- or zoo object of asset return.}
-
- \item{Rf}{risk free rate can be vector such as government
- security rate of return}
-
- \item{geometric}{utilize geometric chaining (TRUE) or
- simple/arithmetic chaining(FALSE) to aggregate returns,
- default is TRUE}
-
- \item{\dots}{any other variable}
}
\description{
\code{EconomicDrawdown} calculates the Economic
@@ -44,31 +30,13 @@
Here EM stands for Economic Max and is the code
\code{\link{EconomicMax}}
-
- \code{EconomicDrawdown} calculates the Economic
- Drawdown(EDD) for a return series.To calculate the
- economic drawdown cumulative return and economic max is
- calculated for each point. The risk free return(rf) is
- taken as the input.
-
- Economic Drawdown is given by the equation
-
- \deqn{EDD(t)=1-\frac{W_t}/{EM(t)}}
-
- Here EM stands for Economic Max and is the code
- \code{\link{EconomicMax}}
}
\examples{
EconomicDrawdown(edhec,0.08,100)
-EconomicDrawdown(edhec,0.08,100)
}
\references{
Yang, Z. George and Zhong, Liang, Optimal Portfolio
Strategy to Control Maximum Drawdown - The Case of Risk
Based Dynamic Asset Allocation (February 25, 2012)
-
- Yang, Z. George and Zhong, Liang, Optimal Portfolio
- Strategy to Control Maximum Drawdown - The Case of Risk
- Based Dynamic Asset Allocation (February 25, 2012)
}
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/man/MaxDD.Rd
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/man/MaxDD.Rd 2013-08-18 12:39:18 UTC (rev 2817)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/man/MaxDD.Rd 2013-08-18 13:19:58 UTC (rev 2818)
@@ -21,19 +21,20 @@
autoregressive. For a normal process Maximum Drawdown is
given by the formula When the distibution is normal
- \deqn{MaxDD_{\alpha}=max\left\{0,\frac{(z_{\alpha}\sigma)^2}{4\mu}\right\}}
+ \deqn{MaxDD_\alpha=max\left\{0,\frac{(z_\alpha\sigma)^2}{4\mu}\right\}}
The time at which the Maximum Drawdown occurs is given by
\deqn{t^\ast=\biggl(\frac{Z_{\alpha}\sigma}{2\mu}\biggr)^2}
- Here $Z_{\alpha}$ is the critical value of the Standard
- Normal Distribution associated with a probability
- $\alpha$.$\sigma$ and $\mu$ are the Standard Distribution
- and the mean respectively. When the distribution is
- non-normal and time dependent, Autoregressive process.
+ Here \eqn{Z_{\alpha}} is the critical value of the
+ Standard Normal Distribution associated with a
+ probability \eqn{\alpha}.\eqn{\sigma} and \eqn{\mu} are
+ the Standard Distribution and the mean respectively. When
+ the distribution is non-normal and time dependent,
+ Autoregressive process.
\deqn{Q_{\alpha,t}=\frac{\phi^{(t+1)}-\phi}{\phi-1}(\triangle\pi_0-\mu)+{\mu}t+Z_{\alpha}\frac{\sigma}{|\phi-1|}\biggl(\frac{\phi^{2(t+1)}-1}{\phi^2-1}-2\frac{\phi^(t+1)-1}{\phi-1}+t+1\biggr)^{1/2}}
- $\phi$ is estimated as
+ \eqn{\phi} is estimated as
\deqn{\hat{\phi} =
Cov_0[\triangle\pi_\tau,\triangle\pi_{\tau-1}](Cov_0[\triangle\pi_{\tau-1},\triangle\pi_{\tau-1}])^{-1}}
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/man/MinTrackRecord.Rd
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/man/MinTrackRecord.Rd 2013-08-18 12:39:18 UTC (rev 2817)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/man/MinTrackRecord.Rd 2013-08-18 13:19:58 UTC (rev 2818)
@@ -48,8 +48,8 @@
\deqn{MinTRL = n^\ast =
1+\biggl[1-\hat{\gamma_3}\hat{SR}+\frac{\hat{\gamma_4}}{4}\hat{SR^2}\biggr]\biggl(\frac{Z_\alpha}{\hat{SR}-SR^\ast}\biggr)^2}
- $\gamma{_3}$ and $\gamma{_4}$ are the skewness and
- kurtosis respectively. It is important to note that
+ \eqn{\gamma{_3}} and \eqn{\gamma{_4}} are the skewness
+ and kurtosis respectively. It is important to note that
MinTRL is expressed in terms of number of observations,
not annual or calendar terms.
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/man/ProbSharpeRatio.Rd
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/man/ProbSharpeRatio.Rd 2013-08-18 12:39:18 UTC (rev 2817)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/man/ProbSharpeRatio.Rd 2013-08-18 13:19:58 UTC (rev 2818)
@@ -47,11 +47,12 @@
\deqn{\hat{PSR}(SR^\ast) =
Z\biggl[\frac{(\hat{SR}-SR^\ast)\sqrt{n-1}}{\sqrt{1-\hat{\gamma_3}SR^\ast
- + \frac{\hat{\gamma_4}-1}{4}\hat{SR^2}}}\biggr]} Here $n$
- is the track record length or the number of data points.
- It can be daily,weekly or yearly depending on the input
- given $\hat{\gamma{_3}}$ and $\hat{\gamma{_4}}$ are the
- skewness and kurtosis respectively.
+ + \frac{\hat{\gamma_4}-1}{4}\hat{SR^2}}}\biggr]} Here
+ \eqn{n} is the track record length or the number of data
+ points. It can be daily,weekly or yearly depending on the
+ input given \eqn{\hat{\gamma{_3}}} and
+ \eqn{\hat{\gamma{_4}}} are the skewness and kurtosis
+ respectively.
}
\examples{
data(edhec)
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/man/PsrPortfolio.Rd
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/man/PsrPortfolio.Rd 2013-08-18 12:39:18 UTC (rev 2817)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/man/PsrPortfolio.Rd 2013-08-18 13:19:58 UTC (rev 2818)
@@ -23,8 +23,8 @@
would like to find the vector of weights that maximize
the expression
- \deqn{\hat{PSR}(SR^\ast) =
- Z\biggl[\frac{(\hat{SR}-SR^\ast)\sqrt{n-1}}{\sqrt{1-\hat{\gamma_3}SR^\ast
+ \deqn{\hat{PSR}(SR^\**) =
+ Z\biggl[\frac{(\hat{SR}-SR^\**)\sqrt{n-1}}{\sqrt{1-\hat{\gamma_3}SR^\**
+ \frac{\hat{\gamma_4}-1}{4}\hat{SR^2}}}\biggr]}
where \eqn{\sigma = \sqrt{E[(r-\mu)^2]}} ,its standard
@@ -32,14 +32,14 @@
its skewness,
\eqn{\gamma_4=\frac{E\biggl[(r-\mu)^4\biggr]}{\sigma^4}}
its kurtosis and \eqn{SR = \frac{\mu}{\sigma}} its Sharpe
- Ratio. Because \eqn{\hat{PSR}(SR^\ast)=Z[\hat{Z^\ast}]}
- is a monotonic increasing function of \eqn{\hat{Z^\ast}}
- ,it suffices to compute the vector that maximizes
- \eqn{\hat{Z^\ast}}
+ Ratio. Because \eqn{\hat{PSR}(SR^\**)=Z[\hat{Z^\**}]} is
+ a monotonic increasing function of \eqn{\hat{Z^\**}} ,it
+ suffices to compute the vector that maximizes
+ \eqn{\hat{Z^\**}}
This optimal vector is invariant of the value adopted by
- the parameter $SR^\ast$. Gradient Ascent Logic is used to
- compute the weights using the Function PsrPortfolio
+ the parameter \eqn{SR^\**}. Gradient Ascent Logic is used
+ to compute the weights using the Function PsrPortfolio
}
\examples{
data(edhec)
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/man/TuW.Rd
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/man/TuW.Rd 2013-08-18 12:39:18 UTC (rev 2817)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/man/TuW.Rd 2013-08-18 13:19:58 UTC (rev 2818)
@@ -17,10 +17,10 @@
under water for a particular confidence interval is given
by
- For a particular sequence $\left\{\pi_t\right\}$, the
- time under water $(TuW)$ is the minimum number of
- observations, $t>0$, such that $\pi_{t-1}<0$ and
- $\pi_t>0$.
+ For a particular sequence \eqn{\left\{\pi_t\right\}}, the
+ time under water \eqn{(TuW)} is the minimum number of
+ observations, \eqn{t>0}, such that \eqn{\pi_{t-1}<0} and
+ \eqn{\pi_t>0}.
For a normal distribution Maximum Time Under Water is
given by the following expression.
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