[Returnanalytics-commits] r2957 - in pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm: R vignettes

noreply at r-forge.r-project.org noreply at r-forge.r-project.org
Sat Aug 31 23:38:47 CEST 2013 

Author: shubhanm
Date: 2013-08-31 23:38:47 +0200 (Sat, 31 Aug 2013)
New Revision: 2957

Added:
   pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/vignettes/NormCalmar.pdf
   pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/vignettes/NormCalmar.rnw
   pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/vignettes/OkunevWhite.Rnw
   pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/vignettes/OkunevWhite.pdf
Modified:
   pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/AcarSim.R
Log:
./ Further Addition of clean build vignettes 

Modified: pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/AcarSim.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/AcarSim.R	2013-08-31 21:27:27 UTC (rev 2956)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/AcarSim.R	2013-08-31 21:38:47 UTC (rev 2957)
@@ -40,7 +40,7 @@
 T= 36
 j=1
 dt=1/T
-nsim=30;
+nsim=3;
 thres=4;
 r=matrix(0,nsim,T+1)
 monthly = 0

Added: pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/vignettes/NormCalmar.pdf
===================================================================
(Binary files differ)


Property changes on: pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/vignettes/NormCalmar.pdf
___________________________________________________________________
Added: svn:mime-type
   + application/octet-stream

Added: pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/vignettes/NormCalmar.rnw
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/vignettes/NormCalmar.rnw	                        (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/vignettes/NormCalmar.rnw	2013-08-31 21:38:47 UTC (rev 2957)
@@ -0,0 +1,111 @@
+%% 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{Normalized Calmar and Sterling Ratio}
+\author{R Project for Statistical Computing}
+
+\begin{document}
+\SweaveOpts{concordance=TRUE}
+
+\maketitle
+
+
+\begin{abstract}
+ Both the Calmar and the Sterling ratio are the ratio of annualized returnmover the absolute value of the maximum drawdown of an investment. The Sterling ratio adds an excess risk measure to the maximum drawdown,  traditionally and defaulting to 10\%.It is also traditional to use a three year return series for these
+ calculations, although the functions included here make no effort to
+ determine the length of your series. However, Malik Magdon-Ismail devised a scaling law in which can be used to compare Calmar/Sterling ratio's with different 
+$\mu$ ,$\sigma$ and T.
+\end{abstract}
+
+<<echo=FALSE >>=
+library(PerformanceAnalytics)
+data(edhec)
+@
+
+<<echo=FALSE>>=
+source("C:/Users/shubhankit/Desktop/Again/pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/CalmarRatio.Norm.R")
+source("C:/Users/shubhankit/Desktop/Again/pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/SterlingRatio.Norm.R")
+source("C:/Users/shubhankit/Desktop/Again/pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/QP.Norm.R")
+@
+
+\section{Background}
+Given a sample of historical returns \((R_1,R_2, . . .,R_T)\),the Calmar and Sterling Ratio's are defined as :
+
+%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}
+ Calmar Ratio  =  \frac{Return [0,T]}{max Drawdown  [0,T]} \\
+\end{equation}
+
+\begin{equation}
+ Sterling Ratio  =  \frac{Return [0,T]}{max Drawdown  [0,T] - 10\%} \\
+\end{equation}
+
+\section{Scaling Law}
+Malik Magdon-Ismail  impmemented a sclaing law for different $\mu$ ,$\sigma$ and T.Defined as :
+
+
+\begin{equation}
+Calmar_{\tau}  =  \gamma(_{\tau , Sharpe_{1}})Calmar_{T_{1}}  \\
+\end{equation}
+
+Where : 
+  \begin{equation}
+\gamma(_{\tau , Sharpe_{1}})  =  \frac{\frac{Q_p(T_1/2Sharpe^2_{1})}{T_1}}{\frac{Q_p(T_2/2Sharpe^2_{1})}{\tau}} \\
+\end{equation}
+
+ And , when T tends to  Infinity
+\begin{equation}
+Q_p(T/2Sharpe^2)  =  .63519 + log (Sharpe)  + 0.5 log T\\
+\end{equation}
+
+Same methodolgy goes to Sterling Ratio.
+\section{Usage}
+
+In this example we use edhec database, to compute Calmar and Sterling Ratio.
+
+<<echo=T>>=
+library(PerformanceAnalytics)
+data(edhec)
+CalmarRatio.Norm(edhec,1)
+SterlingRatio.Norm(edhec,1)
+@
+
+We can see as we shrunk the period the Ratio's decrease because the Max Drawdown does not change much over reduction of time period, but returns are approximately scaled according to  the time length. 
+
+\end{document}
\ No newline at end of file

Added: pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/vignettes/OkunevWhite.Rnw
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/vignettes/OkunevWhite.Rnw	                        (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/vignettes/OkunevWhite.Rnw	2013-08-31 21:38:47 UTC (rev 2957)
@@ -0,0 +1,135 @@
+%% 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{Okunev White Return Model}
+\author{R Project for Statistical Computing}
+
+\begin{document}
+\SweaveOpts{concordance=TRUE}
+
+\maketitle
+
+
+\begin{abstract}
+The fact that many hedge fund returns exhibit extraordinary levels of serial correlation is now well-known and generally accepted as fact.Because hedge fund strategies have exceptionally high autocorrelations in reported returns and this is taken as evidence of return smoothing, we first develop a method to completely eliminate any order of serial correlation across a wide array of time series processes.Once this is complete, we can determine the underlying risk factors to the "true" hedge fund returns and examine the incremental benefit attained from using nonlinear payoffs relative to the more traditional linear factors.
+\end{abstract}
+
+<<echo=FALSE >>=
+library(PerformanceAnalytics)
+data(edhec)
+@
+
+<<echo=FALSE,eval=TRUE,results=verbatim >>=
+source("C:/Users/shubhankit/Desktop/Again/pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/R/Return.Okunev.R")
+@
+
+\section{Methodology}
+Given a sample of historical returns \((R_1,R_2, . . .,R_T)\),the method assumes the fund manager smooths returns in the following manner:
+
+%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}
+ r_{0,t}  =  \sum_{i}^{} \beta_{i}r_{0,t-i} + (1- \alpha)r_{m,t} \\
+\end{equation}
+
+
+\begin{equation}
+where :  \sum_{i}^{} \beta_{i} = (1- \alpha) \\
+\end{equation}
+
+\(r_{0,t}\) : is the observed (reported) return at time t (with 0 adjustments' to reported returns), \\
+\(r_{m,t}\) : is the true underlying (unreported) return at time t (determined by making m adjustments to reported returns). \\
+
+The objective is to determine the true underlying return by removing the
+autocorrelation structure in the original return series without making any assumptions regarding the actual time series properties of the underlying process. We are implicitly assuming by this approach that the autocorrelations that arise in reported returns are entirely due to the smoothing behavior funds engage in when reporting results. In fact, the method may be adopted to produce any desired level of autocorrelation at any lag and is not limited to simply eliminating all autocorrelations.
+
+\section{To Remove Up to m Orders of Autocorrelation}
+To remove the first m orders of autocorrelation from a given return series we would proceed in a manner very similar to that detailed in \textbf{Geltner Return}. We would initially remove the first order autocorrelation, then proceed to eliminate the second order autocorrelation through the iteration process. In general, to remove any order, m, autocorrelations from a given return series we would make the following transformation to returns:
+
+\begin{equation}
+r_{m,t}=\frac{r_{m-1,t}-c_{m}r_{m-1,t-m}}{1-c_{m}}
+\end{equation}
+
+Where  \(r_{m-1,t}\) is the series return with the first (m-1) order autocorrelation coefficient's removed.The general form for all the autocorrelations given by the process is : 
+\begin{equation}
+a_{m,n}=\frac{a_{m-1,n}(1+c_{m}^2)-c_{m}(1+a_{m-1,2m})}{1+c_{m}^2 -2c_{m}a_{m-1,n}}
+\end{equation}
+
+Once a solution is found for \(c_{m}\) to create \(r_{m,t}\) , one will need to iterate back to remove the first m ??? 1  autocorrelations again. One will then need to once again remove the mth autocorrelation using the adjustment in equation (3). It would continue the process until the first m autocorrelations are sufficiently close to zero.
+
+\section{Usage}
+
+In this example we use edhec database, to compute true Hedge Fund Returns.
+
+<<Graph10,echo=T,fig=T>>=
+library(PerformanceAnalytics)
+data(edhec)
+Returns = Return.Okunev(edhec[,1])
+skewness(edhec[,1])
+skewness(Returns)
+# Right Shift of Returns Ditribution for a negative skewed distribution 
+kurtosis(edhec[,1])
+kurtosis(Returns)
+# Reduction in "peakedness" around the mean
+layout(rbind(c(1, 2), c(3, 4)))
+ chart.Histogram(Returns, main = "Plain", methods = NULL)
+ chart.Histogram(Returns, main = "Density", breaks = 40,
+ methods = c("add.density", "add.normal"))
+ chart.Histogram(Returns, main = "Skew and Kurt",
+ methods = c("add.centered", "add.rug"))
+chart.Histogram(Returns, main = "Risk Measures",
+ methods = c("add.risk"))
+@
+
+The above figure shows the behaviour of the distribution tending to a normal IID distribution.For comparitive purpose, one can observe the change in the charateristics of return as compared to the orignal.
+<<echo=T,fig=T>>=
+library(PerformanceAnalytics)
+data(edhec)
+Returns = Return.Okunev(edhec[,1])
+layout(rbind(c(1, 2), c(3, 4)))
+ chart.Histogram(edhec[,1], main = "Plain", methods = NULL)
+ chart.Histogram(edhec[,1], main = "Density", breaks = 40,
+ methods = c("add.density", "add.normal"))
+ chart.Histogram(edhec[,1], main = "Skew and Kurt",
+ methods = c("add.centered", "add.rug"))
+chart.Histogram(edhec[,1], main = "Risk Measures",
+ methods = c("add.risk"))
+
+@
+
+\end{document}
\ No newline at end of file

Added: pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/vignettes/OkunevWhite.pdf
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/vignettes/OkunevWhite.pdf	                        (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Shubhankit/noniid.sm/vignettes/OkunevWhite.pdf	2013-08-31 21:38:47 UTC (rev 2957)
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[TRUNCATED]

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