[Returnanalytics-commits] r2651 - in pkg/PerformanceAnalytics/sandbox/Shubhankit: Week1 Week1/Code Week1/Vignette Week4/Code Week5/Code
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Sat Jul 27 12:10:07 CEST 2013
Author: shubhanm
Date: 2013-07-27 12:10:07 +0200 (Sat, 27 Jul 2013)
New Revision: 2651
Added:
pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Return.Okunev.R
pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/GLMSmoothIndex.Rnw
pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/GLMSmoothIndex.pdf
pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/GLMSmoothIndex.tex
pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/LoSharpeRatio-concordance.tex
pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/LoSharpeRatio.Rnw
pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/LoSharpeRatio.log
pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/LoSharpeRatio.pdf
pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/OkunevWhite-Graph1.pdf
pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/OkunevWhite-Graph10.pdf
pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/OkunevWhite-concordance.tex
pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/OkunevWhite.Rnw
pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/OkunevWhite.log
pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/OkunevWhite.pdf
pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/OkunevWhite.tex
pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/Rplots.pdf
Modified:
pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Code/LoSharpe.R
pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Code/Return.Okunev.R
pkg/PerformanceAnalytics/sandbox/Shubhankit/Week4/Code/AcarSim.R.R
pkg/PerformanceAnalytics/sandbox/Shubhankit/Week5/Code/CDrawdown.R
Log:
Modified : Week 5 and Week 1 Code
Final Vignette : Week 1
Modified: pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Code/LoSharpe.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Code/LoSharpe.R 2013-07-26 19:45:12 UTC (rev 2650)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Code/LoSharpe.R 2013-07-27 10:10:07 UTC (rev 2651)
@@ -1,31 +1,31 @@
-#'@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 .
-#' @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 passthru parameters
-#' @author R
-#' @references "The Statistics of Sharpe Ratios" Andrew. W. Lo
-#'
-#' @keywords ts multivariate distribution models non-iid
-#' @examples
-#'
-#' data(edhec)
-#' head(LoSharpe(edhec,0,3)
-#'
-#' @export
+##'@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 .
+##' @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 passthru parameters
+##' @author R
+##' @references "The Statistics of Sharpe Ratios" Andrew. W. Lo
+##'
+##' @keywords ts multivariate distribution models non-iid
+##' @examples
+##'
+##' data(edhec)
+##' head(LoSharpe(edhec,0,3)
+##'
+##' @export
LoSharpe <-
function (Ra,Rf = 0,q = 3, ...)
{ # @author Brian G. Peterson, Peter Carl
Modified: pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Code/Return.Okunev.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Code/Return.Okunev.R 2013-07-26 19:45:12 UTC (rev 2650)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Code/Return.Okunev.R 2013-07-27 10:10:07 UTC (rev 2651)
@@ -1,12 +1,3 @@
-quad <- function(R,d)
-{
- coeff = as.numeric(acf(as.numeric(edhec[,1]), plot = FALSE)[1:2][[1]])
-b=-(1+coeff[2]-2*d*coeff[1])
-c=(coeff[1]-d)
- ans= (-b-sqrt(b*b-4*c*c))/(2*c)
- a <- a[!is.na(a)]
- return(c(ans))
-}
Return.Okunev<-function(R,q=3)
{
column.okunev=R
@@ -18,3 +9,13 @@
}
return(c(column.okunev))
}
+
+quad <- function(R,d)
+{
+ coeff = as.numeric(acf(as.numeric(edhec[,1]), plot = FALSE)[1:2][[1]])
+b=-(1+coeff[2]-2*d*coeff[1])
+c=(coeff[1]-d)
+ ans= (-b-sqrt(b*b-4*c*c))/(2*c)
+ #a <- a[!is.na(a)]
+ return(c(ans))
+}
Added: pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Return.Okunev.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Return.Okunev.R (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Return.Okunev.R 2013-07-27 10:10:07 UTC (rev 2651)
@@ -0,0 +1,20 @@
+quad <- function(R,d)
+{
+ coeff = as.numeric(acf(as.numeric(edhec[,1]), plot = FALSE)[1:2][[1]])
+b=-(1+coeff[2]-2*d*coeff[1])
+c=(coeff[1]-d)
+ ans= (-b-sqrt(b*b-4*c*c))/(2*c)
+ a <- a[!is.na(a)]
+ return(c(ans))
+}
+Return.Okunev<-function(R,q=3)
+{
+ column.okunev=R
+ column.okunev <- column.okunev[!is.na(column.okunev)]
+ for(i in 1:q)
+ {
+ lagR = lag(column.okunev, k=i)
+ column.okunev= (column.okunev-(lagR*quad(lagR,0)))/(1-quad(lagR,0))
+ }
+ return(c(column.okunev))
+}
Added: pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/GLMSmoothIndex.Rnw
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/GLMSmoothIndex.Rnw (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/GLMSmoothIndex.Rnw 2013-07-27 10:10:07 UTC (rev 2651)
@@ -0,0 +1,107 @@
+%% no need for \DeclareGraphicsExtensions{.pdf,.eps}
+
+\documentclass[12pt,letterpaper,english]{article}
+\usepackage{times}
+\usepackage[T1]{fontenc}
+\IfFileExists{url.sty}{\usepackage{url}}
+ {\newcommand{\url}{\texttt}}
+
+\usepackage{babel}
+%\usepackage{noweb}
+\usepackage{Rd}
+
+\usepackage{Sweave}
+\SweaveOpts{engine=R,eps=FALSE}
+%\VignetteIndexEntry{Performance Attribution from Bacon}
+%\VignetteDepends{PerformanceAnalytics}
+%\VignetteKeywords{returns, performance, risk, benchmark, portfolio}
+%\VignettePackage{PerformanceAnalytics}
+
+%\documentclass[a4paper]{article}
+%\usepackage[noae]{Sweave}
+%\usepackage{ucs}
+%\usepackage[utf8x]{inputenc}
+%\usepackage{amsmath, amsthm, latexsym}
+%\usepackage[top=3cm, bottom=3cm, left=2.5cm]{geometry}
+%\usepackage{graphicx}
+%\usepackage{graphicx, verbatim}
+%\usepackage{ucs}
+%\usepackage[utf8x]{inputenc}
+%\usepackage{amsmath, amsthm, latexsym}
+%\usepackage{graphicx}
+
+\title{GLM Smoothing Index}
+\author{R Project for Statistical Computing}
+
+\begin{document}
+\SweaveOpts{concordance=TRUE}
+
+\maketitle
+
+
+\begin{abstract}
+The returns to hedge funds and other alternative investments are often highly serially correlated.Gemanstsy,Lo and Markov propose an econometric model of return smoothingand develop estimators for the smoothing profile.The magnitude of impact is measured by the smoothing index, which is a measure of concentration of weight in lagged terms.
+\end{abstract}
+
+<<echo=FALSE >>=
+library(PerformanceAnalytics)
+data(edhec)
+@
+
+<<echo=FALSE>>=
+source("../code/GLMSmoothIndex.R")
+@
+
+\section{Background}
+To quantify the impact of all of these possible sources of serial correlation, denote by \(R_t\),the true economic return of a hedge fund in period t; and let \(R_t\) satisfy the following linear single-factor model:
+
+\begin{equation}
+ R_t = \\ {\mu} + {\beta}{{\delta}}_t+ \xi_t
+\end{equation}
+
+Where $\xi_t, \sim N(0,1)$
+and Var[\(R_t\)] = $\sigma$\ \(^2\)
+
+True returns represent the flow of information that would determine the equilibrium value of the fund's securities in a frictionless market. However, true economic returns are not observed. Instead, \(R_t^0\) denotes the reported or observed return in period t; and let
+%$Z = \sin(X)$. $\sqrt{X}$.
+
+%$\hat{\mu}$ = $\displaystyle\frac{22}{7}$
+%e^{2 \mu} = 1
+%\begin{equation}
+%\left(\sum_{t=1}^{T} R_t/T\right) = \hat{\mu} \\
+%\end{equation}
+\begin{equation}
+ R_t^0 = \theta _0R_{t} + \theta _1R_{t-1}+\theta _2R_{t-2} + \cdots + \theta _kR_{t-k}\\
+\end{equation}
+\begin{equation}
+\theta _j \epsilon [0,1] where : j = 0,1, \cdots , k \\
+\end{equation}
+
+and
+%\left(\mu \right) = \sum_{t=1}^{T} \(Ri)/T\ \\
+\begin{equation}
+\theta _1 + \theta _2 + \theta _3 \cdots + \theta _k = 1 \\
+\end{equation}
+
+which is a weighted average of the fund's true returns over the most recent k + 1
+periods, including the current period.
+
+\section{Smoothing Index}
+A useful summary statistic for measuringthe concentration of weights is :
+\begin{equation}
+\xi = \sum_{j=0}^{k} \theta _j^2 \\
+\end{equation}
+
+This measure is well known in the industrial organization literature as the Herfindahl index, a measure of the concentration of firms in a given industry where $\theta$\(_j\) represents the market share of firm j. Becaus $\xi_t$\ is confined to the unit interval, and is minimized when all the $\theta$\(_j\) 's are identical, which implies a value of 1/k+1 for $\xi_i$\ ; and is maximized when one coefficient is 1 and the rest are 0. In the context of smoothed returns, a lower value of implies more smoothing, and the upper bound of 1 implies no smoothing, hence we shall refer to $\theta$\(_j\) as a ''\textbf{smoothingindex}''.
+
+\section{Usage}
+
+In this example we use edhec database, to compute Smoothing Index for Hedge Fund Returns.
+<<>>=
+library(PerformanceAnalytics)
+data(edhec)
+GLMSmoothIndex(edhec)
+@
+
+
+\end{document}
\ No newline at end of file
Added: pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/GLMSmoothIndex.pdf
===================================================================
(Binary files differ)
Property changes on: pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/GLMSmoothIndex.pdf
___________________________________________________________________
Added: svn:mime-type
+ application/octet-stream
Added: pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/GLMSmoothIndex.tex
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/GLMSmoothIndex.tex (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/GLMSmoothIndex.tex 2013-07-27 10:10:07 UTC (rev 2651)
@@ -0,0 +1,112 @@
+%% no need for \DeclareGraphicsExtensions{.pdf,.eps}
+
+\documentclass[12pt,letterpaper,english]{article}
+\usepackage{times}
+\usepackage[T1]{fontenc}
+\IfFileExists{url.sty}{\usepackage{url}}
+ {\newcommand{\url}{\texttt}}
+
+\usepackage{babel}
+%\usepackage{noweb}
+\usepackage{Rd}
+
+\usepackage{Sweave}
+
+%\VignetteIndexEntry{Performance Attribution from Bacon}
+%\VignetteDepends{PerformanceAnalytics}
+%\VignetteKeywords{returns, performance, risk, benchmark, portfolio}
+%\VignettePackage{PerformanceAnalytics}
+
+%\documentclass[a4paper]{article}
+%\usepackage[noae]{Sweave}
+%\usepackage{ucs}
+%\usepackage[utf8x]{inputenc}
+%\usepackage{amsmath, amsthm, latexsym}
+%\usepackage[top=3cm, bottom=3cm, left=2.5cm]{geometry}
+%\usepackage{graphicx}
+%\usepackage{graphicx, verbatim}
+%\usepackage{ucs}
+%\usepackage[utf8x]{inputenc}
+%\usepackage{amsmath, amsthm, latexsym}
+%\usepackage{graphicx}
+
+\title{GLM Smoothing Index}
+\author{R Project for Statistical Computing}
+
+\begin{document}
+\input{GLMSmoothIndex-concordance}
+
+\maketitle
+
+
+\begin{abstract}
+The returns to hedge funds and other alternative investments are often highly serially correlated.Gemanstsy,Lo and Markov propose an econometric model of return smoothingand develop estimators for the smoothing profile.The magnitude of impact is measured by the smoothing index, which is a measure of concentration of weight in lagged terms.
+\end{abstract}
+
+
+
+\section{Background}
+To quantify the impact of all of these possible sources of serial correlation, denote by \(R_t\),the true economic return of a hedge fund in period t; and let \(R_t\) satisfy the following linear single-factor model:
+
+\begin{equation}
+ R_t = \\ {\mu} + {\beta}{{\delta}}_t+ \xi_t
+\end{equation}
+
+Where $\xi_t, \sim N(0,1)$
+and Var[\(R_t\)] = $\sigma$\ \(^2\)
+
+True returns represent the flow of information that would determine the equilibrium value of the fund's securities in a frictionless market. However, true economic returns are not observed. Instead, \(R_t^0\) denotes the reported or observed return in period t; and let
+%$Z = \sin(X)$. $\sqrt{X}$.
+
+%$\hat{\mu}$ = $\displaystyle\frac{22}{7}$
+%e^{2 \mu} = 1
+%\begin{equation}
+%\left(\sum_{t=1}^{T} R_t/T\right) = \hat{\mu} \\
+%\end{equation}
+\begin{equation}
+ R_t^0 = \theta _0R_{t} + \theta _1R_{t-1}+\theta _2R_{t-2} + \cdots + \theta _kR_{t-k}\\
+\end{equation}
+\begin{equation}
+\theta _j \epsilon [0,1] where : j = 0,1, \cdots , k \\
+\end{equation}
+
+and
+%\left(\mu \right) = \sum_{t=1}^{T} \(Ri)/T\ \\
+\begin{equation}
+\theta _1 + \theta _2 + \theta _3 \cdots + \theta _k = 1 \\
+\end{equation}
+
+which is a weighted average of the fund's true returns over the most recent k + 1
+periods, including the current period.
+
+\section{Smoothing Index}
+A useful summary statistic for measuringthe concentration of weights is :
+\begin{equation}
+\xi = \sum_{j=0}^{k} \theta _j^2 \\
+\end{equation}
+
+This measure is well known in the industrial organization literature as the Herfindahl index, a measure of the concentration of firms in a given industry where $\theta$\(_j\) represents the market share of firm j. Becaus $\xi_t$\ is confined to the unit interval, and is minimized when all the $\theta$\(_j\) 's are identical, which implies a value of 1/k+1 for $\xi_i$\ ; and is maximized when one coefficient is 1 and the rest are 0. In the context of smoothed returns, a lower value of implies more smoothing, and the upper bound of 1 implies no smoothing, hence we shall refer to $\theta$\(_j\) as a ''\textbf{smoothingindex}''.
+
+\section{Usage}
+
+In this example we use edhec database, to compute Smoothing Index for Hedge Fund Returns.
+\begin{Schunk}
+\begin{Sinput}
+> library(PerformanceAnalytics)
+> data(edhec)
+> GLMSmoothIndex(edhec)
+\end{Sinput}
+\begin{Soutput}
+ Convertible Arbitrage CTA Global Distressed Securities
+GLM Smooth Index 0.3487825 0.1866095 0.3187229
+ Emerging Markets Equity Market Neutral Event Driven
+GLM Smooth Index 0.3022908 0.2046973 0.3580198
+ Fixed Income Arbitrage Global Macro Long/Short Equity
+GLM Smooth Index 0.3090088 0.252546 0.277132
+ Merger Arbitrage Relative Value Short Selling Funds of Funds
+GLM Smooth Index 0.2292355 0.2917355 0.2348319 0.2873716
+\end{Soutput}
+\end{Schunk}
+
+
+\end{document}
Added: pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/LoSharpeRatio-concordance.tex
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/LoSharpeRatio-concordance.tex (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/LoSharpeRatio-concordance.tex 2013-07-27 10:10:07 UTC (rev 2651)
@@ -0,0 +1,2 @@
+\Sconcordance{concordance:LoSharpeRatio.tex:LoSharpeRatio.Rnw:%
+1 50 1 1 5 1 4 50 1 1 2 1 0 2 1 13 0 1 2 2 1}
Added: pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/LoSharpeRatio.Rnw
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/LoSharpeRatio.Rnw (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/LoSharpeRatio.Rnw 2013-07-27 10:10:07 UTC (rev 2651)
@@ -0,0 +1,118 @@
+%% no need for \DeclareGraphicsExtensions{.pdf,.eps}
+
+\documentclass[12pt,letterpaper,english]{article}
+\usepackage{times}
+\usepackage[T1]{fontenc}
+\IfFileExists{url.sty}{\usepackage{url}}
+ {\newcommand{\url}{\texttt}}
+
+\usepackage{babel}
+%\usepackage{noweb}
+\usepackage{Rd}
+
+\usepackage{Sweave}
+\SweaveOpts{engine=R,eps=FALSE}
+%\VignetteIndexEntry{Performance Attribution from Bacon}
+%\VignetteDepends{PerformanceAnalytics}
+%\VignetteKeywords{returns, performance, risk, benchmark, portfolio}
+%\VignettePackage{PerformanceAnalytics}
+
+%\documentclass[a4paper]{article}
+%\usepackage[noae]{Sweave}
+%\usepackage{ucs}
+%\usepackage[utf8x]{inputenc}
+%\usepackage{amsmath, amsthm, latexsym}
+%\usepackage[top=3cm, bottom=3cm, left=2.5cm]{geometry}
+%\usepackage{graphicx}
+%\usepackage{graphicx, verbatim}
+%\usepackage{ucs}
+%\usepackage[utf8x]{inputenc}
+%\usepackage{amsmath, amsthm, latexsym}
+%\usepackage{graphicx}
+
+\title{Lo Sharpe Ratio}
+\author{R Project for Statistical Computing}
+
+\begin{document}
+\SweaveOpts{concordance=TRUE}
+
+\maketitle
+
+
+\begin{abstract}
+The building blocks of the Sharpe ratio-expected returns and volatilities-
+are unknown quantities that must be estimated statistically and are,
+therefore, subject to estimation error.In an illustrative
+empirical example of mutual funds and hedge funds, Andrew Lo finds that the annual Sharpe ratio for a hedge fund can be overstated by as much as 65 percent
+because of the presence of serial correlation in monthly returns, and once
+this serial correlation is properly taken into account, the rankings of hedge
+funds based on Sharpe ratios can change dramatically.
+\end{abstract}
+
+<<echo=FALSE >>=
+library(PerformanceAnalytics)
+data(edhec)
+@
+
+<<echo=FALSE>>=
+source("../code/LoSharpe.R")
+@
+
+\section{Background}
+Given a sample of historical returns \((R_1,R_2, . . .,R_T)\), the standard estimators for these moments are the sample mean and variance:
+
+%Let $X \sim N(0,1)$ and $Y \sim \textrm{Exponential}(\mu)$. Let
+%$Z = \sin(X)$. $\sqrt{X}$.
+
+%$\hat{\mu}$ = $\displaystyle\frac{22}{7}$
+%e^{2 \mu} = 1
+%\begin{equation}
+%\left(\sum_{t=1}^{T} R_t/T\right) = \hat{\mu} \\
+%\end{equation}
+\begin{equation}
+ \hat{\mu} = \sum_{t=1}^{T} (R_t)/T\\
+\end{equation}
+\begin{equation}
+\hat{\sigma^2} = \sum_{t=1}^{T} (R_t-\hat{\mu})^2/T\\
+\end{equation}
+
+From which the estimator of the Sharpe ratio $\hat{SR}$ follows immediately:
+%\left(\mu \right) = \sum_{t=1}^{T} \(Ri)/T\ \\
+\begin{equation}
+\hat{SR} = (\hat{\mu}- R_f)/\hat{\sigma} \\
+\end{equation}
+
+Using a set of techniques collectively known as "large-sample'' or "asymptotic'' statistical theory in which the Central Limit Theorem is applied to
+estimators such as and , the distribution of and other nonlinear functions of and can be easily derived.
+
+\section{Non-IID Returns}
+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 \(R_t\) are stationary,
+\begin{equation}
+Var[(R_t)] = \sum_{i=0}^{q-1} \sum_{j=1}^{q-1} Cov(R(t-i),R(t-j)) = q\hat{\sigma^2} + 2\hat{\sigma^2} \sum_{k=1}^{q-1} (q-k)\rho_k \\
+\end{equation}
+
+Where $\rho$\(_k\) = Cov(\(R(t)\),\(R(t-k\)))/Var[\(R_t\)] is the \(k^{th}\) order autocorrelation coefficient of the series of returns.This yields the following relationship between SR and SR(q):
+
+\begin{equation}
+\hat{SR}(q) = \eta(q) \\
+\end{equation}
+
+Where :
+
+\begin{equation}
+\eta(q) = \frac{q}{\sqrt{(q\hat{\sigma^2} + 2\hat{\sigma^2} \sum_{k=1}^{q-1} (q-k)\rho_k)}} \\
+\end{equation}
+
+\section{Usage}
+
+In this example we use edhec database, to compute Sharpe Ratio for Hedge Fund Returns.
+<<>>=
+library(PerformanceAnalytics)
+data(edhec)
+LoSharpe(edhec)
+@
+
+
+\end{document}
\ No newline at end of file
Added: pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/LoSharpeRatio.log
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/LoSharpeRatio.log (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/Week1/Vignette/LoSharpeRatio.log 2013-07-27 10:10:07 UTC (rev 2651)
@@ -0,0 +1,354 @@
+This is pdfTeX, Version 3.1415926-2.4-1.40.13 (MiKTeX 2.9) (preloaded format=pdflatex 2013.7.14) 26 JUL 2013 23:22
+entering extended mode
+**LoSharpeRatio.tex
+
+("C:\Users\shubhankit\Desktop\New folder\pkg\PerformanceAnalytics\sandbox\Shubh
+ankit\Week1\Vignette\LoSharpeRatio.tex"
+LaTeX2e <2011/06/27>
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[TRUNCATED]
To get the complete diff run:
svnlook diff /svnroot/returnanalytics -r 2651
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