[Returnanalytics-commits] r3004 - in pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm: . R man
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Thu Sep 5 23:29:27 CEST 2013
Author: shubhanm
Date: 2013-09-05 23:29:26 +0200 (Thu, 05 Sep 2013)
New Revision: 3004
Added:
pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/inst/
pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/man/
pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/table.Sharpe.R
pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/inst/
pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/man/table.Sharpe.Rd
Modified:
pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/DESCRIPTION
pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/NAMESPACE
pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/LoSharpe.R
pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/se.LoSharpe.R
pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/man/LoSharpe.Rd
pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/man/se.LoSharpe.Rd
Log:
Lo Sharpe final documentation + additon of table summary of all Sharpe Ratio functions
Modified: pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/DESCRIPTION
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/DESCRIPTION 2013-09-05 19:33:22 UTC (rev 3003)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/DESCRIPTION 2013-09-05 21:29:26 UTC (rev 3004)
@@ -1,38 +1,39 @@
-Package: noniid.sm
-Type: Package
-Title: Non-i.i.d. GSoC 2013 Shubhankit
-Version: 0.1
-Date: $Date: 2013-05-13 14:30:22 -0500 (Mon, 13 May 2013) $
-Author: Shubhankit Mohan <shubhankit1 at gmail.com>
-Contributors: Peter Carl, Brian G. Peterson
-Depends:
- xts,
- PerformanceAnalytics,
- tseries,
- stats
-Maintainer: Brian G. Peterson <brian at braverock.com>
-Description: GSoC 2013 project to replicate literature on drawdowns and
- non-i.i.d assumptions in finance.
-License: GPL-3
-ByteCompile: TRUE
-Collate:
- 'AcarSim.R'
- 'ACStdDev.annualized.R'
- 'CalmarRatio.Norm.R'
- 'CDrawdown.R'
- 'chart.AcarSim.R'
- 'chart.Autocorrelation.R'
- 'EmaxDDGBM.R'
- 'GLMSmoothIndex.R'
- 'LoSharpe.R'
- 'na.skip.R'
- 'noniid.sm-internal.R'
- 'QP.Norm.R'
- 'Return.GLM.R'
- 'Return.Okunev.R'
- 'se.LoSharpe.R'
- 'SterlingRatio.Norm.R'
- 'table.ComparitiveReturn.GLM.R'
- 'table.EMaxDDGBM.R'
- 'table.UnsmoothReturn.R'
- 'UnsmoothReturn.R'
+Package: noniid.sm
+Type: Package
+Title: Non-i.i.d. GSoC 2013 Shubhankit
+Version: 0.1
+Date: $Date: 2013-05-13 14:30:22 -0500 (Mon, 13 May 2013) $
+Author: Shubhankit Mohan <shubhankit1 at gmail.com>
+Contributors: Peter Carl, Brian G. Peterson
+Depends:
+ xts,
+ PerformanceAnalytics,
+ tseries,
+ stats
+Maintainer: Brian G. Peterson <brian at braverock.com>
+Description: GSoC 2013 project to replicate literature on drawdowns and
+ non-i.i.d assumptions in finance.
+License: GPL-3
+ByteCompile: TRUE
+Collate:
+ 'AcarSim.R'
+ 'ACStdDev.annualized.R'
+ 'CalmarRatio.Norm.R'
+ 'CDrawdown.R'
+ 'chart.AcarSim.R'
+ 'chart.Autocorrelation.R'
+ 'EmaxDDGBM.R'
+ 'GLMSmoothIndex.R'
+ 'LoSharpe.R'
+ 'na.skip.R'
+ 'noniid.sm-internal.R'
+ 'QP.Norm.R'
+ 'Return.GLM.R'
+ 'Return.Okunev.R'
+ 'se.LoSharpe.R'
+ 'SterlingRatio.Norm.R'
+ 'table.ComparitiveReturn.GLM.R'
+ 'table.EMaxDDGBM.R'
+ 'table.UnsmoothReturn.R'
+ 'UnsmoothReturn.R'
+ 'table.Sharpe.R'
Modified: pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/NAMESPACE
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/NAMESPACE 2013-09-05 19:33:22 UTC (rev 3003)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/NAMESPACE 2013-09-05 21:29:26 UTC (rev 3004)
@@ -1,17 +1,18 @@
-export(AcarSim)
-export(ACStdDev.annualized)
-export(CalmarRatio.Norm)
-export(CDrawdown)
-export(chart.AcarSim)
-export(chart.Autocorrelation)
-export(EMaxDDGBM)
-export(GLMSmoothIndex)
-export(LoSharpe)
-export(QP.Norm)
-export(Return.GLM)
-export(Return.Okunev)
-export(se.LoSharpe)
-export(SterlingRatio.Norm)
-export(table.ComparitiveReturn.GLM)
-export(table.EMaxDDGBM)
-export(table.UnsmoothReturn)
+export(AcarSim)
+export(ACStdDev.annualized)
+export(CalmarRatio.Norm)
+export(CDrawdown)
+export(chart.AcarSim)
+export(chart.Autocorrelation)
+export(EMaxDDGBM)
+export(GLMSmoothIndex)
+export(LoSharpe)
+export(QP.Norm)
+export(Return.GLM)
+export(Return.Okunev)
+export(se.LoSharpe)
+export(SterlingRatio.Norm)
+export(table.ComparitiveReturn.GLM)
+export(table.EMaxDDGBM)
+export(table.Sharpe)
+export(table.UnsmoothReturn)
Modified: pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/LoSharpe.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/LoSharpe.R 2013-09-05 19:33:22 UTC (rev 3003)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/LoSharpe.R 2013-09-05 21:29:26 UTC (rev 3004)
@@ -20,21 +20,27 @@
#'\deqn{SR(q) = \eta(q) }
#'Where :
#' \deqn{ }{\eta(q) = [q]/[\sqrt(q\sigma^2) + 2\sigma^2 \sum(q-k)\rho(k)] }
-#' Where k belongs to 0 to q-1
+#' Where, k belongs to 0 to q-1
+#' SR(q) : Estimated Lo Sharpe Ratio
+#' SR : Theoretical William Sharpe Ratio
#' @param Ra an xts, vector, matrix, data frame, timeSeries or zoo object of
#' daily asset returns
#' @param Rf an xts, vector, matrix, data frame, timeSeries or zoo object of
#' annualized Risk Free Rate
#' @param q Number of autocorrelated lag periods. Taken as 3 (Default)
#' @param \dots any other pass thru parameters
-#' @author Brian G. Peterson, Peter Carl, Shubhankit Mohan
-#' @references Getmansky, Mila, Lo, Andrew W. and Makarov, Igor,\emph{ An Econometric Model of Serial Correlation and Illiquidity in Hedge Fund Returns} (March 1, 2003). MIT Sloan Working Paper No. 4288-03; MIT Laboratory for Financial Engineering Working Paper No. LFE-1041A-03; EFMA 2003 Helsinki Meetings.
-#' \url{http://ssrn.com/abstract=384700}
+#' @author Shubhankit Mohan
+#' @references Andrew Lo,\emph{ The Statistics of Sharpe Ratio.}2002, AIMR.
+#'\code{\link[stats]{}} \cr
+#' \url{http://papers.ssrn.com/sol3/papers.cfm?abstract_id=377260}
+#'
+#' Andrew Lo,\emph{Sharpe Ratio may be Overstated}
+#' \url{http://www.risk.net/risk-magazine/feature/1506463/lo-sharpe-ratios-overstated}
#' @keywords ts multivariate distribution models non-iid
#' @examples
#'
#' data(edhec)
-#' head(LoSharpe(edhec,0,3))
+#' LoSharpe(edhec,0,3)
#' @rdname LoSharpe
#' @export
LoSharpe <-
@@ -48,7 +54,7 @@
columns.a = ncol(R)
columnnames.a = colnames(R)
# Time used for daily Return manipulations
- Time= 252*nyears(R)
+ Time= 252*nyears(edhec)
clean.lo <- function(column.R,q) {
# compute the lagged return series
gamma.k =matrix(0,q)
@@ -71,12 +77,13 @@
}
for(column.a in 1:columns.a) { # for each asset passed in as R
# clean the data and get rid of NAs
- mu = sum(R[,column.a])/(Time)
- sig=sqrt(((R[,column.a]-mu)^2/(Time)))
- pho.k = clean.lo(R[,column.a],q)/(as.numeric(sig[1]))
+ clean.ret=na.omit(R[,column.a])
+ mu = sum(clean.ret)/(Time)
+ sig=sqrt(((clean.ret-mu)^2/(Time)))
+ pho.k = clean.lo(clean.ret,q)/(as.numeric(sig[1]))
netaq=neta.lo(pho.k,q)
- column.lo = (netaq*((mu-Rf)/as.numeric(sig[1])))
-
+ #column.lo = (netaq*((mu-Rf)/as.numeric(sig[1])))
+ column.lo = as.numeric(SharpeRatio.annualized(R[,column.a]))[1]*netaq
if(column.a == 1) { lo = column.lo }
else { lo = cbind (lo, column.lo) }
@@ -85,7 +92,7 @@
rownames(lo)= paste("Lo Sharpe Ratio")
return(lo)
- edhec=NULL
+
# RESULTS:
}
Modified: pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/se.LoSharpe.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/se.LoSharpe.R 2013-09-05 19:33:22 UTC (rev 3003)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/se.LoSharpe.R 2013-09-05 21:29:26 UTC (rev 3004)
@@ -21,15 +21,23 @@
#'Where :
#' \deqn{ }{\eta(q) = [q]/[\sqrt(q\sigma^2) + 2\sigma^2 \sum(q-k)\rho(k)] }
#' Where k belongs to 0 to q-1
+#' Under the assumption of assumption of asymptotic variance of SR(q), the standard error for the Sharpe Ratio Esitmator can be computed as:
+#' \deqn{SE(SR(q)) = \sqrt((1+SR^2/2)/T)}
+#' SR(q) : Estimated Lo Sharpe Ratio
+#' SR : Theoretical William Sharpe Ratio
#' @param Ra an xts, vector, matrix, data frame, timeSeries or zoo object of
#' daily asset returns
#' @param Rf an xts, vector, matrix, data frame, timeSeries or zoo object of
#' annualized Risk Free Rate
#' @param q Number of autocorrelated lag periods. Taken as 3 (Default)
#' @param \dots any other pass thru parameters
-#' @author Brian G. Peterson, Peter Carl, Shubhankit Mohan
-#' @references Getmansky, Mila, Lo, Andrew W. and Makarov, Igor,\emph{ An Econometric Model of Serial Correlation and Illiquidity in Hedge Fund Returns} (March 1, 2003). MIT Sloan Working Paper No. 4288-03; MIT Laboratory for Financial Engineering Working Paper No. LFE-1041A-03; EFMA 2003 Helsinki Meetings.
-#' \url{http://ssrn.com/abstract=384700}
+#' @author Shubhankit Mohan
+#' @references Andrew Lo,\emph{ The Statistics of Sharpe Ratio.}2002, AIMR.
+#'\code{\link[stats]{}} \cr
+#' \url{http://papers.ssrn.com/sol3/papers.cfm?abstract_id=377260}
+#'
+#' Andrew Lo,\emph{Sharpe Ratio may be Overstated}
+#' \url{http://www.risk.net/risk-magazine/feature/1506463/lo-sharpe-ratios-overstated}
#' @keywords ts multivariate distribution models non-iid
#' @examples
#'
@@ -48,7 +56,7 @@
columns.a = ncol(R)
columnnames.a = colnames(R)
# Time used for daily Return manipulations
- Time= 252*nyears(R)
+ Time= 252*nyears(edhec)
clean.lo <- function(column.R,q) {
# compute the lagged return series
gamma.k =matrix(0,q)
Added: pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/table.Sharpe.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/table.Sharpe.R (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/table.Sharpe.R 2013-09-05 21:29:26 UTC (rev 3004)
@@ -0,0 +1,98 @@
+#'@title Sharpe Ratio Statistics Summary
+#'@description
+#' The Sharpe ratio is simply the return per unit of risk (represented by
+#' variability). In the classic case, the unit of risk is the standard
+#' deviation of the returns.
+#'
+#' \deqn{\frac{\overline{(R_{a}-R_{f})}}{\sqrt{\sigma_{(R_{a}-R_{f})}}}}
+#'
+#' William Sharpe now recommends \code{\link{InformationRatio}} preferentially
+#' to the original Sharpe Ratio.
+#'
+#' The higher the Sharpe ratio, the better the combined performance of "risk"
+#' and return.
+#'
+#' As noted, the traditional Sharpe Ratio is a risk-adjusted measure of return
+#' that uses standard deviation to represent risk.
+
+#' Although the Sharpe ratio has become part of the canon of modern financial
+#' analysis, its applications typically do not account for the fact that it is an
+#' estimated quantity, subject to estimation errors that can be substantial in
+#' some cases.
+#'
+#' Many studies have documented various violations of the assumption of
+#' IID returns for financial securities.
+#'
+#' Under the assumption of stationarity,a version of the Central Limit Theorem can
+#' still be applied to the estimator .
+#' @details
+#' The relationship between SR and SR(q) is somewhat more involved for non-
+#'IID returns because the variance of Rt(q) is not just the sum of the variances of component returns but also includes all the covariances. Specifically, under
+#' the assumption that returns \eqn{R_t} are stationary,
+#' \deqn{ Var[(R_t)] = \sum \sum Cov(R(t-i),R(t-j)) = q{\sigma^2} + 2{\sigma^2} \sum (q-k)\rho(k) }
+#' Where \eqn{ \rho(k) = Cov(R(t),R(t-k))/Var[(R_t)]} is the \eqn{k^{th}} order autocorrelation coefficient of the series of returns.This yields the following relationship between SR and SR(q):
+#' and i,j belongs to 0 to q-1
+#'\deqn{SR(q) = \eta(q) }
+#'Where :
+#' \deqn{ }{\eta(q) = [q]/[\sqrt(q\sigma^2) + 2\sigma^2 \sum(q-k)\rho(k)] }
+#' Where, k belongs to 0 to q-1
+#' SR(q) : Estimated Lo Sharpe Ratio
+#' SR : Theoretical William Sharpe Ratio
+#' @param Ra an xts, vector, matrix, data frame, timeSeries or zoo object of
+#' daily asset returns
+#' @param Rf an xts, vector, matrix, data frame, timeSeries or zoo object of
+#' annualized Risk Free Rate
+#' @param q Number of autocorrelated lag periods. Taken as 3 (Default)
+#' @param \dots any other pass thru parameters
+#' @author Shubhankit Mohan
+#' @references Andrew Lo,\emph{ The Statistics of Sharpe Ratio.}2002, AIMR.
+#'\code{\link[stats]{}} \cr
+#' \url{http://papers.ssrn.com/sol3/papers.cfm?abstract_id=377260}
+#'
+#' Andrew Lo,\emph{Sharpe Ratio may be Overstated}
+#' \url{http://www.risk.net/risk-magazine/feature/1506463/lo-sharpe-ratios-overstated}
+#' @keywords ts multivariate distribution models non-iid
+#' @examples
+#'
+#' data(edhec)
+#' table.Sharpe(edhec,0,3)
+#' @rdname table.Sharpe
+#' @export
+table.Sharpe <-
+ function (Ra,Rf = 0,q = 3, ...)
+ { y = checkData(Ra, method = "xts")
+ columns = ncol(y)
+ rows = nrow(y)
+ columnnames = colnames(y)
+ rownames = rownames(y)
+
+ # for each column, do the following:
+ for(column in 1:columns) {
+ x = y[,column]
+
+ z = c(SharpeRatio.annualized(x),
+ SharpeRatio.modified(x),
+ LoSharpe(x),
+ Return.annualized(x),StdDev.annualized(x),se.Losharpe(x))
+
+ znames = c(
+ "William Sharpe Ratio",
+ "Modified Sharpe Ratio",
+ "Andrew Lo Sharpe Ratio",
+ "Annualized Return",
+ "Annualized Standard Deviation","Sharpe Ratio Standard Error(95%)"
+ )
+ 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
+
+
+ }
Modified: pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/man/LoSharpe.Rd
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/man/LoSharpe.Rd 2013-09-05 19:33:22 UTC (rev 3003)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/man/LoSharpe.Rd 2013-09-05 21:29:26 UTC (rev 3004)
@@ -1,70 +1,71 @@
-\name{LoSharpe}
-\alias{LoSharpe}
-\title{Andrew Lo Sharpe Ratio}
-\usage{
- LoSharpe(Ra, Rf = 0, q = 3, ...)
-}
-\arguments{
- \item{Ra}{an xts, vector, matrix, data frame, timeSeries
- or zoo object of daily asset returns}
-
- \item{Rf}{an xts, vector, matrix, data frame, timeSeries
- or zoo object of annualized Risk Free Rate}
-
- \item{q}{Number of autocorrelated lag periods. Taken as 3
- (Default)}
-
- \item{\dots}{any other pass thru parameters}
-}
-\description{
- Although the Sharpe ratio has become part of the canon of
- modern financial analysis, its applications typically do
- not account for the fact that it is an estimated
- quantity, subject to estimation errors that can be
- substantial in some cases.
-
- Many studies have documented various violations of the
- assumption of IID returns for financial securities.
-
- Under the assumption of stationarity,a version of the
- Central Limit Theorem can still be applied to the
- estimator .
-}
-\details{
- The relationship between SR and SR(q) is somewhat more
- involved for non- IID returns because the variance of
- Rt(q) is not just the sum of the variances of component
- returns but also includes all the covariances.
- Specifically, under the assumption that returns \eqn{R_t}
- are stationary, \deqn{ Var[(R_t)] = \sum \sum
- Cov(R(t-i),R(t-j)) = q{\sigma^2} + 2{\sigma^2} \sum
- (q-k)\rho(k) } Where \eqn{ \rho(k) =
- Cov(R(t),R(t-k))/Var[(R_t)]} is the \eqn{k^{th}} order
- autocorrelation coefficient of the series of returns.This
- yields the following relationship between SR and SR(q):
- and i,j belongs to 0 to q-1 \deqn{SR(q) = \eta(q) } Where
- : \deqn{ }{\eta(q) = [q]/[\sqrt(q\sigma^2) + 2\sigma^2
- \sum(q-k)\rho(k)] } Where k belongs to 0 to q-1
-}
-\examples{
-data(edhec)
-head(LoSharpe(edhec,0,3))
-}
-\author{
- Brian G. Peterson, Peter Carl, Shubhankit Mohan
-}
-\references{
- Getmansky, Mila, Lo, Andrew W. and Makarov, Igor,\emph{
- An Econometric Model of Serial Correlation and
- Illiquidity in Hedge Fund Returns} (March 1, 2003). MIT
- Sloan Working Paper No. 4288-03; MIT Laboratory for
- Financial Engineering Working Paper No. LFE-1041A-03;
- EFMA 2003 Helsinki Meetings.
- \url{http://ssrn.com/abstract=384700}
-}
-\keyword{distribution}
-\keyword{models}
-\keyword{multivariate}
-\keyword{non-iid}
-\keyword{ts}
-
+\name{LoSharpe}
+\alias{LoSharpe}
+\title{Andrew Lo Sharpe Ratio}
+\usage{
+ LoSharpe(Ra, Rf = 0, q = 3, ...)
+}
+\arguments{
+ \item{Ra}{an xts, vector, matrix, data frame, timeSeries
+ or zoo object of daily asset returns}
+
+ \item{Rf}{an xts, vector, matrix, data frame, timeSeries
+ or zoo object of annualized Risk Free Rate}
+
+ \item{q}{Number of autocorrelated lag periods. Taken as 3
+ (Default)}
+
+ \item{\dots}{any other pass thru parameters}
+}
+\description{
+ Although the Sharpe ratio has become part of the canon of
+ modern financial analysis, its applications typically do
+ not account for the fact that it is an estimated
+ quantity, subject to estimation errors that can be
+ substantial in some cases.
+
+ Many studies have documented various violations of the
+ assumption of IID returns for financial securities.
+
+ Under the assumption of stationarity,a version of the
+ Central Limit Theorem can still be applied to the
+ estimator .
+}
+\details{
+ The relationship between SR and SR(q) is somewhat more
+ involved for non- IID returns because the variance of
+ Rt(q) is not just the sum of the variances of component
+ returns but also includes all the covariances.
+ Specifically, under the assumption that returns \eqn{R_t}
+ are stationary, \deqn{ Var[(R_t)] = \sum \sum
+ Cov(R(t-i),R(t-j)) = q{\sigma^2} + 2{\sigma^2} \sum
+ (q-k)\rho(k) } Where \eqn{ \rho(k) =
+ Cov(R(t),R(t-k))/Var[(R_t)]} is the \eqn{k^{th}} order
+ autocorrelation coefficient of the series of returns.This
+ yields the following relationship between SR and SR(q):
+ and i,j belongs to 0 to q-1 \deqn{SR(q) = \eta(q) } Where
+ : \deqn{ }{\eta(q) = [q]/[\sqrt(q\sigma^2) + 2\sigma^2
+ \sum(q-k)\rho(k)] } Where, k belongs to 0 to q-1 SR(q) :
+ Estimated Lo Sharpe Ratio SR : Theoretical William Sharpe
+ Ratio
+}
+\examples{
+data(edhec)
+LoSharpe(edhec,0,3)
+}
+\author{
+ Shubhankit Mohan
+}
+\references{
+ Andrew Lo,\emph{ The Statistics of Sharpe Ratio.}2002,
+ AIMR. \code{\link[stats]{}} \cr
+ \url{http://papers.ssrn.com/sol3/papers.cfm?abstract_id=377260}
+
+ Andrew Lo,\emph{Sharpe Ratio may be Overstated}
+ \url{http://www.risk.net/risk-magazine/feature/1506463/lo-sharpe-ratios-overstated}
+}
+\keyword{distribution}
+\keyword{models}
+\keyword{multivariate}
+\keyword{non-iid}
+\keyword{ts}
+
Modified: pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/man/se.LoSharpe.Rd
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/man/se.LoSharpe.Rd 2013-09-05 19:33:22 UTC (rev 3003)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/man/se.LoSharpe.Rd 2013-09-05 21:29:26 UTC (rev 3004)
@@ -44,23 +44,27 @@
yields the following relationship between SR and SR(q):
and i,j belongs to 0 to q-1 \deqn{SR(q) = \eta(q) } Where
: \deqn{ }{\eta(q) = [q]/[\sqrt(q\sigma^2) + 2\sigma^2
- \sum(q-k)\rho(k)] } Where k belongs to 0 to q-1
+ \sum(q-k)\rho(k)] } Where k belongs to 0 to q-1 Under the
+ assumption of assumption of asymptotic variance of SR(q),
+ the standard error for the Sharpe Ratio Esitmator can be
+ computed as: \deqn{SE(SR(q)) = \sqrt((1+SR^2/2)/T)} SR(q)
+ : Estimated Lo Sharpe Ratio SR : Theoretical William
+ Sharpe Ratio
}
\examples{
data(edhec)
se.LoSharpe(edhec,0,3)
}
\author{
- Brian G. Peterson, Peter Carl, Shubhankit Mohan
+ Shubhankit Mohan
}
\references{
- Getmansky, Mila, Lo, Andrew W. and Makarov, Igor,\emph{
- An Econometric Model of Serial Correlation and
- Illiquidity in Hedge Fund Returns} (March 1, 2003). MIT
- Sloan Working Paper No. 4288-03; MIT Laboratory for
- Financial Engineering Working Paper No. LFE-1041A-03;
- EFMA 2003 Helsinki Meetings.
- \url{http://ssrn.com/abstract=384700}
+ Andrew Lo,\emph{ The Statistics of Sharpe Ratio.}2002,
+ AIMR. \code{\link[stats]{}} \cr
+ \url{http://papers.ssrn.com/sol3/papers.cfm?abstract_id=377260}
+
+ Andrew Lo,\emph{Sharpe Ratio may be Overstated}
+ \url{http://www.risk.net/risk-magazine/feature/1506463/lo-sharpe-ratios-overstated}
}
\keyword{distribution}
\keyword{models}
Added: pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/man/table.Sharpe.Rd
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/man/table.Sharpe.Rd (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/man/table.Sharpe.Rd 2013-09-05 21:29:26 UTC (rev 3004)
@@ -0,0 +1,86 @@
+\name{table.Sharpe}
+\alias{table.Sharpe}
+\title{Sharpe Ratio Statistics Summary}
+\usage{
+ table.Sharpe(Ra, Rf = 0, q = 3, ...)
+}
+\arguments{
+ \item{Ra}{an xts, vector, matrix, data frame, timeSeries
+ or zoo object of daily asset returns}
+
+ \item{Rf}{an xts, vector, matrix, data frame, timeSeries
+ or zoo object of annualized Risk Free Rate}
+
+ \item{q}{Number of autocorrelated lag periods. Taken as 3
+ (Default)}
+
+ \item{\dots}{any other pass thru parameters}
+}
+\description{
+ The Sharpe ratio is simply the return per unit of risk
+ (represented by variability). In the classic case, the
+ unit of risk is the standard deviation of the returns.
+
+ \deqn{\frac{\overline{(R_{a}-R_{f})}}{\sqrt{\sigma_{(R_{a}-R_{f})}}}}
+
+ William Sharpe now recommends
+ \code{\link{InformationRatio}} preferentially to the
+ original Sharpe Ratio.
+
+ The higher the Sharpe ratio, the better the combined
+ performance of "risk" and return.
+
+ As noted, the traditional Sharpe Ratio is a risk-adjusted
+ measure of return that uses standard deviation to
+ represent risk. Although the Sharpe ratio has become part
+ of the canon of modern financial analysis, its
+ applications typically do not account for the fact that
+ it is an estimated quantity, subject to estimation errors
+ that can be substantial in some cases.
+
+ Many studies have documented various violations of the
+ assumption of IID returns for financial securities.
+
+ Under the assumption of stationarity,a version of the
+ Central Limit Theorem can still be applied to the
+ estimator .
+}
+\details{
+ The relationship between SR and SR(q) is somewhat more
+ involved for non- IID returns because the variance of
+ Rt(q) is not just the sum of the variances of component
+ returns but also includes all the covariances.
+ Specifically, under the assumption that returns \eqn{R_t}
+ are stationary, \deqn{ Var[(R_t)] = \sum \sum
+ Cov(R(t-i),R(t-j)) = q{\sigma^2} + 2{\sigma^2} \sum
+ (q-k)\rho(k) } Where \eqn{ \rho(k) =
+ Cov(R(t),R(t-k))/Var[(R_t)]} is the \eqn{k^{th}} order
+ autocorrelation coefficient of the series of returns.This
+ yields the following relationship between SR and SR(q):
+ and i,j belongs to 0 to q-1 \deqn{SR(q) = \eta(q) } Where
+ : \deqn{ }{\eta(q) = [q]/[\sqrt(q\sigma^2) + 2\sigma^2
+ \sum(q-k)\rho(k)] } Where, k belongs to 0 to q-1 SR(q) :
+ Estimated Lo Sharpe Ratio SR : Theoretical William Sharpe
+ Ratio
+}
+\examples{
+data(edhec)
+table.Sharpe(edhec,0,3)
+}
+\author{
+ Shubhankit Mohan
+}
+\references{
+ Andrew Lo,\emph{ The Statistics of Sharpe Ratio.}2002,
+ AIMR. \code{\link[stats]{}} \cr
+ \url{http://papers.ssrn.com/sol3/papers.cfm?abstract_id=377260}
+
+ Andrew Lo,\emph{Sharpe Ratio may be Overstated}
+ \url{http://www.risk.net/risk-magazine/feature/1506463/lo-sharpe-ratios-overstated}
+}
+\keyword{distribution}
+\keyword{models}
+\keyword{multivariate}
+\keyword{non-iid}
+\keyword{ts}
+
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