[Returnanalytics-commits] r3020 - in pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm: . R man vignettes
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Sat Sep 7 16:58:14 CEST 2013
Author: shubhanm
Date: 2013-09-07 16:58:14 +0200 (Sat, 07 Sep 2013)
New Revision: 3020
Added:
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/R/table.Sharpe.R
pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/man/LoSharpe.Rd
pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/man/se.LoSharpe.Rd
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/vignettes/LoSharpe.pdf
Log:
3 Sharpe Ratio function : correction of bugs, addition of examples in documentation using managers data to Clean R CMD Build
Modified: pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/DESCRIPTION
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/DESCRIPTION 2013-09-07 13:42:33 UTC (rev 3019)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/DESCRIPTION 2013-09-07 14:58:14 UTC (rev 3020)
@@ -33,3 +33,6 @@
'table.EMaxDDGBM.R'
'table.UnsmoothReturn.R'
'UnsmoothReturn.R'
+ 'LoSharpe.R'
+ 'se.LoSharpe.R'
+ 'table.Sharpe.R'
Modified: pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/NAMESPACE
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/NAMESPACE 2013-09-07 13:42:33 UTC (rev 3019)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/NAMESPACE 2013-09-07 14:58:14 UTC (rev 3020)
@@ -5,11 +5,14 @@
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)
export(UnsmoothReturn)
Added: pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/LoSharpe.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/LoSharpe.R (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/LoSharpe.R 2013-09-07 14:58:14 UTC (rev 3020)
@@ -0,0 +1,101 @@
+#'@title Andrew Lo Sharpe Ratio
+#'@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
+#' @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.
+#' \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(managers)
+#' LoSharpe(managers,0,3)
+#' @rdname LoSharpe
+#' @export
+LoSharpe <-
+ function (Ra,Rf = 0,q = 3, ...)
+ { # @author Brian G. Peterson, Peter Carl
+
+
+ # Function:
+ R = checkData(Ra, method="xts")
+ # Get dimensions and labels
+ columns.a = ncol(R)
+ columnnames.a = colnames(R)
+ # Time used for daily Return manipulations
+ Time= 252*nyears(R)
+ clean.lo <- function(column.R,q) {
+ # compute the lagged return series
+ gamma.k =matrix(0,q)
+ mu = sum(column.R)/(Time)
+ Rf= Rf/(Time)
+ for(i in 1:q){
+ lagR = lag(column.R, k=i)
+ # compute the Momentum Lagged Values
+ gamma.k[i]= (sum(((column.R-mu)*(lagR-mu)),na.rm=TRUE))
+ }
+ return(gamma.k)
+ }
+ neta.lo <- function(pho.k,q) {
+ # compute the lagged return series
+ sumq = 0
+ for(j in 1:q){
+ sumq = sumq+ (q-j)*pho.k[j]
+ }
+ return(q/(sqrt(q+2*sumq)))
+ }
+ column.lo=NULL
+ lo=NULL
+ for(column.a in 1:columns.a) { # for each asset passed in as R
+ # clean the data and get rid of NAs
+ clean.ret=na.omit(R[,column.a])
+ mu = sum(clean.ret)/(Time)
+ sig=sqrt(((clean.ret-mu)^2/(Time)))
+ pho.k = na.omit(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 = as.numeric(SharpeRatio.annualized(R[,column.a]))[1]*netaq
+ # if(column.a == 1) { lo = column.lo }
+ # else { lo = cbind (lo, column.lo)
+ # colnames(lo) = columnnames.a
+ # }
+
+ lo=cbind(lo,column.lo)
+ }
+ colnames(lo) = columnnames.a
+ rownames(lo)= paste("Lo Sharpe Ratio")
+ return(lo)
+
+
+ # RESULTS:
+
+ }
Added: pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/se.LoSharpe.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/se.LoSharpe.R (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/se.LoSharpe.R 2013-09-07 14:58:14 UTC (rev 3020)
@@ -0,0 +1,104 @@
+#'@title Andrew Lo Sharpe Ratio Statistics
+#'@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 which 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
+#' 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 Shubhankit Mohan
+#' @references Andrew Lo,\emph{ The Statistics of Sharpe Ratio.}2002, AIMR.
+#' \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(managers)
+#' se.LoSharpe(managers,0,3)
+#' @rdname se.LoSharpe
+#' @export
+se.LoSharpe <-
+ function (Ra,Rf = 0,q = 3, ...)
+ { # @author Brian G. Peterson, Peter Carl
+
+
+ # Function:
+ R = checkData(Ra, method="xts")
+ # Get dimensions and labels
+ columns.a = ncol(R)
+ columnnames.a = colnames(R)
+ # Time used for daily Return manipulations
+ Time= 252*nyears(R)
+ clean.lo <- function(column.R,q) {
+ # compute the lagged return series
+ gamma.k =matrix(0,q)
+ mu = sum(column.R)/(Time)
+ Rf= Rf/(Time)
+ for(i in 1:q){
+ lagR = lag(column.R, k=i)
+ # compute the Momentum Lagged Values
+ gamma.k[i]= (sum(((column.R-mu)*(lagR-mu)),na.rm=TRUE))
+ }
+ return(gamma.k)
+ }
+ neta.lo <- function(pho.k,q) {
+ # compute the lagged return series
+ sumq = 0
+ for(j in 1:q){
+ sumq = sumq+ (q-j)*pho.k[j]
+ }
+ return(q/(sqrt(q+2*sumq)))
+ }
+ column.lo=NULL
+ lo=NULL
+
+ 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]))
+ netaq=neta.lo(pho.k,q)
+ column.lo = (netaq*((mu-Rf)/as.numeric(sig[1])))
+ column.lo= 1.96*sqrt((1+(column.lo*column.lo/2))/(Time))
+ lo=cbind(lo,column.lo)
+ }
+
+ colnames(lo) = columnnames.a
+ rownames(lo)= paste("Standard Error of Sharpe Ratio Estimates(95% Confidence)")
+ return(lo)
+
+#colnames(lo) = columnnames.a
+#rownames(lo)= paste("Lo Sharpe Ratio")
+#return(lo)
+
+
+ # RESULTS:
+
+ }
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 2013-09-07 14:58:14 UTC (rev 3020)
@@ -0,0 +1,96 @@
+#'@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 digits Round off Numerical Value
+#' @param \dots any other pass thru parameters
+#' @author Shubhankit Mohan
+#' @references Andrew Lo,\emph{ The Statistics of Sharpe Ratio.}2002, AIMR.
+#' \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(managers)
+#' table.Sharpe(managers,0,3)
+#' @rdname table.Sharpe
+#' @export
+table.Sharpe <-
+ function (Ra,Rf = 0,q = 3,digits=4, ...)
+ { 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(as.numeric(SharpeRatio.annualized(x)),
+ as.numeric(LoSharpe(x)),
+ as.numeric(Return.annualized(x)),as.numeric(StdDev.annualized(x)),as.numeric(se.LoSharpe(x)))
+
+ znames = c(
+ "William 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
+
+
+ }
Added: pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/man/LoSharpe.Rd
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/man/LoSharpe.Rd (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/man/LoSharpe.Rd 2013-09-07 14:58:14 UTC (rev 3020)
@@ -0,0 +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 SR(q) :
+ Estimated Lo Sharpe Ratio SR : Theoretical William Sharpe
+ Ratio
+}
+\examples{
+data(managers)
+LoSharpe(managers,0,3)
+}
+\author{
+ Shubhankit Mohan
+}
+\references{
+ Andrew Lo,\emph{ The Statistics of Sharpe Ratio.}2002,
+ AIMR.
+ \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}
+
Added: pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/man/se.LoSharpe.Rd
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/man/se.LoSharpe.Rd (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/man/se.LoSharpe.Rd 2013-09-07 14:58:14 UTC (rev 3020)
@@ -0,0 +1,74 @@
+\name{se.LoSharpe}
+\alias{se.LoSharpe}
+\title{Andrew Lo Sharpe Ratio Statistics}
+\usage{
+ se.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 which 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 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(managers)
+se.LoSharpe(managers,0,3)
+}
+\author{
+ Shubhankit Mohan
+}
+\references{
+ Andrew Lo,\emph{ The Statistics of Sharpe Ratio.}2002,
+ AIMR.
+ \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}
+
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 2013-09-07 14:58:14 UTC (rev 3020)
@@ -0,0 +1,88 @@
+\name{table.Sharpe}
+\alias{table.Sharpe}
+\title{Sharpe Ratio Statistics Summary}
+\usage{
+ table.Sharpe(Ra, Rf = 0, q = 3, digits = 4, ...)
+}
+\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{digits}{Round off Numerical Value}
+
+ \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(managers)
+table.Sharpe(managers,0,3)
+}
+\author{
+ Shubhankit Mohan
+}
+\references{
+ Andrew Lo,\emph{ The Statistics of Sharpe Ratio.}2002,
+ AIMR.
+ \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/vignettes/LoSharpe.pdf
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