% $Id$

\documentclass[10pt,usletter]{beamer}

% may need full path to find these .sty files outside of R environment
\usepackage{Sweave}
% \usepackage{/usr/lib/R/share/texmf/Sweave}

\SweaveOpts{engine=R,eps=TRUE}
%\VignetteIndexEntry{PerformanceAnalytics Data Mining Presentation - UseR - 2007}
%\VignetteDepends{PerformanceAnalytics}
%\VignetteKeywords{returns, performance, risk, benchmark, portfolio}
%\VignettePackage{PerformanceAnalytics}

% Contents Copyright 2007 Peter Carl and Brian G. Peterson
%
% This file can be redistributed and/or modified under
% the terms of the GNU Public License, version 2.

\mode<presentation>
{
   \usetheme{default}
}

\makeatletter
%%%
\usepackage{subfigure}

\usepackage[english]{babel}
\makeatother

\usepackage[latin1]{inputenc}

\usepackage{times}
\usepackage[T1]{fontenc}

\title[PerformanceAnalytics] % (optional, use only with long paper titles)
{Exploratory Data Analysis in Finance Using PerformanceAnalytics}

% \subtitle

\author[Brian Peterson \& Peter Carl]
{Brian~G.~Peterson \& Peter~Carl}

\institute[Braverock] 
{
\inst{1}
  Diamond Management \& Technology Consultants \\
  Chicago, IL \\
  brian@braverock.com
  \and
\inst{2}
  Guidance Capital\\
  Chicago, IL\\
  peter@braverock.com
}

\date[July 2007] 
{UseR! International User and Developer Conference, Ames, Iowa, 8-10 Aug 2007}

\subject{Data Mining using PerformanceAnalytics}

%%%
\begin{document}
% this has to be after \begin{document} to work
\setkeys{Gin}{width=2.5in}

\begin{frame}
\titlepage
\end{frame}


<<LoadLibrary,echo=F,results=hide>>=
library('PerformanceAnalytics')
data(managers)
data(edhec)
@

<<CalcDataDimensions,echo=F>>=
managers.length = dim(managers)[1]
manager.col = 1
peers.cols = c(2,3,4,5,6)
indexes.cols = c(7,8)
Rf.col = 10
trailing12.rows = ((managers.length - 11):managers.length)
trailing36.rows = ((managers.length - 35):managers.length)
trailing60.rows = ((managers.length - 59):managers.length)
#assume contiguous NAs - this may not be the way to do it na.contiguous()?
frInception.rows = (length(managers[,1]) -
length(managers[,1][!is.na(managers[,1])]) + 1):length(managers[,1])
@

\begin{frame}
  \frametitle{Outline}
  \tableofcontents
  % You might wish to add the option [pausesections]
\end{frame}

\section{Visualization}

%\subsection{Objectives}

\begin{frame}
  \frametitle{Overview}

  \begin{itemize}
    \item
    Exploratory data analysis with finance data often starts with visual examination to:
      \begin{itemize}
        \item
          examine properties of asset returns
        \item
          compare an asset to other similar assets
        \item
          compare an asset to one or more benchmarks
      \end{itemize}
    \item
    Application of performance and risk measures can build a set of statistics for comparing possible investments
    \item
    Examples are developed using data for six (hypothetical) managers, a peer index, and an asset class index
    \item
    Hypothetical manager data was developed from real manager timeseries using \emph{accuracy} and \emph{perturb} packages to disguise the data while maintaining some of the statistical properties of the original data.
  \end{itemize}
\end{frame}

\begin{frame}[fragile]
  \frametitle{Draw a Performance Summary Chart.}
  \begin{figure}

\centering
\begin{tiny}
<<Graph1,echo=T,fig=T>>=
charts.PerformanceSummary(managers[,c(manager.col,indexes.cols)],
colorset=rich6equal, lwd=2, ylog=TRUE)
@
\end{tiny}

\end{figure}

\end{frame}

\begin{frame}[fragile]
  \frametitle{Show Calendar Performance.}
  \begin{figure}
    \begin{tiny}

<<CalendarReturns,echo=T>>=
t(table.CalendarReturns( managers[,c(manager.col,indexes.cols)]) )
@

    \end{tiny}
  \end{figure}
\end{frame}


\begin{frame}[fragile]
  \frametitle{Calculate Statistics.}
  \begin{tiny}
<<MonthlyReturnStats,echo=T>>=
table.Stats(managers[,c(manager.col,peers.cols)])
@
  \end{tiny}
\end{frame}


\begin{frame}[fragile]
  \frametitle{Compare Distributions.}
  \begin{tiny}
  \begin{figure}
  \centering
<<Graph10,echo=T,fig=T>>=
chart.Boxplot(managers[ trailing36.rows, c(manager.col, peers.cols,
indexes.cols)], main = "Trailing 36-Month Returns")
@
  \end{figure}
  \end{tiny}
\end{frame}


\begin{frame}[fragile]
  \frametitle{Compare Distributions.}
  \begin{figure}
  \begin{tiny}
<<Graph13,echo=T,fig=T>>=
layout(rbind(c(1,2),c(3,4)))
chart.Histogram(managers[,1,drop=F], main = "Plain", methods = NULL)
chart.Histogram(managers[,1,drop=F], main = "Density", breaks=40,
methods = c("add.density", "add.normal"))
chart.Histogram(managers[,1,drop=F], main = "Skew and Kurt", methods = c
("add.centered", "add.rug"))
chart.Histogram(managers[,1,drop=F], main = "Risk Measures", methods = c
("add.risk"))
@
  \end{tiny}
  \end{figure}
\end{frame}


\begin{frame}[fragile]
  \frametitle{Show Relative Return and Risk.}
  \begin{figure}
  \centering
  \begin{tiny}
<<Graph3,echo=T,fig=T>>=
chart.RiskReturnScatter(managers[trailing36.rows,1:8], Rf=.03/12, main =
"Trailing 36-Month Performance", colorset=c("red", rep("black",5), "orange",
"green"))
@
  \end{tiny}

  \end{figure}

\end{frame}

\begin{frame}[fragile]
  \frametitle{Examine Performance Consistency.}
  \begin{figure}
\centering
\begin{tiny}

<<Graph5,echo=T,fig=T>>=
charts.RollingPerformance(managers[, c(manager.col, peers.cols,
indexes.cols)], Rf=.03/12, colorset = c("red", rep("darkgray",5), "orange",
"green"), lwd = 2)
@

\end{tiny}
\end{figure}
\end{frame}


\begin{frame}[fragile]
  \frametitle{Display Relative Performance.}
  \begin{figure}
\centering
\begin{tiny}

<<Graph6,echo=T,fig=T>>=
chart.RelativePerformance(managers[ , manager.col, drop = FALSE],
managers[ , c(peers.cols, 7)], colorset = tim8equal[-1], lwd = 2, legend.loc
= "topleft")
@

\end{tiny}
\end{figure}
\end{frame}



\begin{frame}[fragile]
  \frametitle{Compare to a Benchmark.}
  \begin{figure}
\centering
\begin{tiny}

<<Graph6a,echo=T,fig=T>>=
chart.RelativePerformance(managers[ , c(manager.col, peers.cols) ],
managers[, 8, drop=F], colorset = rainbow8equal, lwd = 2, legend.loc =
"topleft")
@

\end{tiny}
\end{figure}
\end{frame}


\begin{frame}[fragile]
\frametitle{Compare to a Benchmark.}
\begin{figure}
\centering
\begin{tiny}
<<tableCAPM,echo=T>>=
# CRAN (questionably(ahem) requires these methods to not run if you don't have Suggests loaded)
if(requireNamespace("RobStatTM", quietly = TRUE)){
  table.CAPM(managers[trailing36.rows, c(manager.col, peers.cols)],
  managers[ trailing36.rows, 8, drop=FALSE], 
  Rf = managers[ trailing36.rows,Rf.col, drop=FALSE ])
} 
@
\end{tiny}
\end{figure}
\end{frame}

\section{Methods}

\begin{frame}[shrink=10]
 \frametitle{Calculate Returns.}

\begin{itemize}
\item
The single-period arithmetic return, or simple return, can be calculated as \\
\begin{equation}
    R_{t} = \frac{P_{t}}{P_{t-1}} - 1 = \frac{P_{t} - P_{t-1}}{P_{t-1}}
\end{equation}

\item
Simple returns, cannot be added together. A multiple-period simple return is calculated as: \\
\begin{equation}
    R_{t} = \frac{P_{t}}{P_{t-k}} - 1 = \frac{P_{t} - P_{t-k}}{P_{t-k}}
\end{equation}

\item
The natural logarithm of the simple return of an asset is referred to as the continuously compounded return, or \emph{log return}:\\
\begin{equation}
    r_{t} = ln(1+R_{t}) = ln \frac{P_{t}}{P_{t-1}} = p_{t} - p_{t-1}
\end{equation}

\item
Calculating log returns from simple gross return, or vice versa: \\
\begin{equation}
    r_{t} = ln(1 + R_{t}), R_{t} = exp(r_{t}) - 1.
\end{equation}
\item
\emph{Return.calculate} or \emph{CalculateReturns} (now deprecated) may be used to compute discrete and continuously compounded returns for data containing asset prices.
\end{itemize}
\end{frame}

\begin{frame}
  \frametitle{table.CAPM underlying techniques}
  \begin{itemize}
    \item
    Return.annualized --- Annualized return using \\
     \begin{equation}
        prod(1+R_{a})^{\frac{scale}{n}}-1=\sqrt[n]{prod(1+R_{a})^{scale}}-1
     \end{equation}
    \item
    TreynorRatio --- ratio of asset's Excess Return to Beta $\beta$ of the benchmark
    \begin{equation}
        \frac{(\overline{R_{a}-R_{f}})}{\beta_{a,b}}
    \end{equation}
    \item
    ActivePremium --- investment's annualized return minus the benchmark's annualized return
    \item
    Tracking Error --- A measure of the unexplained portion of performance relative to a benchmark, given by \\
    \begin{equation}
        TrackingError = \sqrt{\sum\frac{(R_{a}-R_{b})^{2}}{len(R_{a})\sqrt{scale}}}
    \end{equation}
    \item
    InformationRatio --- ActivePremium/TrackingError
  \end{itemize}
\end{frame}

\begin{frame}[fragile]
\frametitle{Compare to a Benchmark.}
\begin{figure}
\centering
\begin{tiny}

<<Graph8,echo=T,fig=T>>=
charts.RollingRegression(managers[, c(manager.col, peers.cols), drop =
FALSE], managers[, 8, drop = FALSE], Rf = .03/12, colorset = redfocus, lwd =
2)
@

\end{tiny}
\end{figure}
\end{frame}



\begin{frame}[fragile]
  \frametitle{Calculate Downside Risk.}
  \begin{figure}
\centering
\begin{tiny}

<<tableDownside,echo=T>>=
table.DownsideRisk(managers[,1:6],Rf=.03/12)
@

\end{tiny}
\end{figure}
\end{frame}

\begin{frame}
    \frametitle{Semivariance and Downside Deviation}
    \begin{itemize}
        \item
        Downside Deviation as proposed by Sharpe is a generalization of semivariance which calculates bases on the deviation below a Minimumn Acceptable Return(MAR)
        \begin{equation}
            \delta_{MAR} = \sqrt{ \frac{\sum^{n}_{t=1}(R_{t} - MAR)^{2}}{n} }
        \end{equation}
        \item
        Downside Deviation may be used to calculate semideviation by setting MAR=mean(R) or may also be used with MAR=0
        \item
        Downside Deviation (and its special cases semideviation and semivariance) is useful in several performance to risk ratios, and in several portfolio optimization problems.
    \end{itemize}
\end{frame}

\begin{frame}[shrink=10]
    \frametitle{Value at Risk}
    \begin{itemize}
        \item
        Value at Risk (VaR) has become a required standard risk measure recognized by Basel II and MiFID
        \item
        Traditional mean-VaR may be derived historically, or estimated parametrically using \\
           \begin{equation}
                z_{c} = q_{p}=qnorm(p)
            \end{equation}
            \begin{equation}
                VaR=\bar{R} -  z_{c} \cdot \sqrt{\sigma}
            \end{equation}
        \item
        Even with robust covariance matrix or Monte Carlo simulation, mean-VaR is not reliable for non-normal asset distributions
        \item
        For non-normal assets, VaR estimates calculated using GPD (as in VaR.GPD) or Cornish Fisher perform best
        \item
        Modified Cornish Fisher VaR takes higher moments of the distribution into account: \\
           \begin{equation}
                z_{cf}=z_{c}+\frac{(z_{c}^{2}-1)S}{6}+\frac{(z_{c}^{3}-3z_{c})K}{24}+\frac{(2z_{c}^{3}-5z_{c})S^{2}}{36}
            \end{equation}
            \begin{equation}
                modVaR =\bar{R} - z_{cf}\sqrt{\sigma}
            \end{equation}
        \item
        Modified VaR also meets the definition of a coherent risk measure per Artzner,et.al.(1997)
    \end{itemize}
\end{frame}

\begin{frame}[shrink=10]
  \frametitle{Risk/Reward Ratios in \emph{PerformanceAnalytics}}

  \begin{itemize}
    \item
    SharpeRatio --- return per unit of risk represented by variance, may also be annualized by \\
    \begin{equation}
        \frac{\sqrt[n]{prod(1+R_{a})^{scale}}-1}{\sqrt{scale}\cdot\sqrt{\sigma}}
    \end{equation}

    \item
    Sortino Ratio --- improvement on Sharpe Ratio utilizing downside deviation as the measure of risk \\

    \begin{equation}
        \frac{(\overline{R_{a} - MAR})}{\delta_{MAR}}
    \end{equation}

    \item
    Calmar and Sterling Ratios --- ratio of annualized return (Eq. 1) over the absolute value of the maximum drawdown
    \item
    Sortino's Upside Potential Ratio --- upside semdiviation from MAR over downside deviation from MAR

    \begin{equation}
        \frac{ \sum^{n}_{t=1} (R_{t} - MAR) }{ \delta_{MAR} }
    \end{equation}

    \item
    Favre's modified Sharpe Ratio --- ratio of excess return over Cornish-Fisher VaR

    \begin{equation}
        \frac{(\overline{R_{a}-R_{f}})}{modVaR_{R_{a},p}}
    \end{equation}

  \end{itemize}
\end{frame}

\section{Summary}

\begin{frame}[fragile]
  \frametitle<presentation>{Summary}

  \begin{itemize}
    \item
        Performance and risk analysis are greatly facilitated by the use of charts and tables.
    \item
        The display of your infomation is in many cases as important as the analysis.
    \item
        \emph{PerformanceAnalytics} contains several tool for measuring and visualizing data that may be used to aid investment decision making.
  \end{itemize}

  % The following outlook is optional.
  \vskip0pt plus.5fill
  \begin{itemize}
  \item
    Further Work
    \begin{itemize}
    \item
      Additional parameterization to make charts and tables more useful.
    \item
      Pertrac or Morningstar-style sample reports.
    \item
      Functions and graphics for more complicated topics such as factor analysis and optimization.
    \end{itemize}
  \end{itemize}
  \begin{figure}
    \centering
      \subfigure
          {
%             \includegraphics[totalheight=0.1\textheight,width=.36\textwidth]{Diamond_Logo_Tag.jpg}
          }
      \hfill
      \subfigure
          {
%             \includegraphics[totalheight=0.15\textheight,width=.15\textwidth]{Rlogo.jpg}
          }
  \end{figure}
\end{frame}

\section{Appendix: Set Up PerformanceAnalytics}

\begin{frame}[fragile]
  \frametitle{Install PerformanceAnalytics.}
  \begin{itemize}
      \item
        As of version 0.9.4, PerformanceAnalytics is available in CRAN
      \item
        Version 0.9.5 was released at the beginning of July
      \item
        Install with: \linebreak \texttt{>
        install.packages("PerformanceAnalytics")}
      \item
        Required packages include \texttt{Hmisc}, \texttt{zoo}, and Rmetrics packages such as \texttt{fExtremes}.
      \item
        Load the library into your active R session
  using: \linebreak \texttt{> library("PerformanceAnalytics")}.
  \end{itemize}
\end{frame}

\begin{frame}[fragile]
  \frametitle{Load and Review Data.}
        % The noweb code must be flush left
        \begin{figure}
        \begin{tiny}
<<LoadData,echo=T>>=
data(managers)
head(managers)
@
        \end{tiny}
        \end{figure}

\end{frame}

\begin{frame}[fragile]
  \frametitle{Set Up Data for Analysis.}
  \begin{figure}

  \begin{center}
     \begin{tiny}
<<CalcDataDimensions,echo=T>>=
dim(managers)
managers.length = dim(managers)[1]
colnames(managers)
manager.col = 1
peers.cols = c(2,3,4,5,6)
indexes.cols = c(7,8)
Rf.col = 10
#factors.cols = NA
trailing12.rows = ((managers.length - 11):managers.length)
trailing12.rows
trailing36.rows = ((managers.length - 35):managers.length)
trailing60.rows = ((managers.length - 59):managers.length)
#assume contiguous NAs - this may not be the way to do it na.contiguous()?
frInception.rows = (length(managers[,1]) -
length(managers[,1][!is.na(managers[,1])]) + 1):length(managers[,1])
@
     \end{tiny}
  \end{center}
  \end{figure}
\end{frame}

\begin{frame}[fragile]
  \frametitle{Draw a Performance Summary Chart.}
  \begin{figure}

\centering
\begin{tiny}
<<Graph1,echo=T,fig=T>>=
charts.PerformanceSummary(managers[,c(manager.col,indexes.cols)],
colorset=rich6equal, lwd=2, ylog=TRUE)
@
\end{tiny}
\end{figure}
\end{frame}

\end{document}
