\documentclass{beamer}
\usetheme[secheader]{Boadilla}

\title{Estimating Value at Risk with the Kalman Filter}
\author{Jaime Frade}
\institute[Florida State University]{
\inst{}Department of Statistics\\
Florida State University
\and
\inst{}Anuj Srivastava\\
STA5107
}
\date{\today}

\begin{document}

\frame{\titlepage}

\section[Outline]{}
\frame{\tableofcontents}


\section{Objective}
\frame
{
\begin{center}
\underline{Goal}
\end{center}
In this project, the goal is to apply one technique of risk management which measures as a percent the maximum loss which is likely to be exceeded on the portfolio, given a certain probability and time horizon within a given confidence level under assumed market conditions.  Using Value-at-Risk,  VaR, will estimate the $\beta$'s of the assets of the portfolio with a Kalman Filter.  Overall, the results showed more market sensitivity compared to historical simulation, depending on the assets of the portfolio or on the type of fund itself, for instance a hedge fund.  
\vspace{.25cm}
}



\section{Data of Model}
\frame
{
Time horizon: (01/02/2004- 3/12/2009).  Daily Stock last trade price for two individual companies, GE and IBM.  S$\&$P as my market variable.  $n=1306$ observations.
}




\section{Kalman Filter Process}
\frame
{
\begin{figure}
\includegraphics[scale=0.25]{table1.png} 
\caption{Kalman Filter Process}
\end{figure}
}


\section{Results: VaR: Calculations}
\frame
{
\begin{tabular}{l|c}
Procedure & VaR
\\
Historical Simulation & loss of $2.32\%$
\\
Kalman Filter & loss of $2.74\%$
\end{tabular}
\vspace{.25in}
\\
\underline{Intrepretation:}  With $95\%$ confidence, we expect that the worst daily loss will not exceed given percentage
}

\section{Plot VaR:}
\frame
{
\begin{equation}
VaR = z\sqrt{w'\beta \beta' w \sigma^2_m} \sqrt{\Delta t}
\end{equation}
Plot of daily VaR calculations based on porfolios of equal weights. 
\begin{figure}
\includegraphics[scale=0.15]{SequenceofVaR.png} 
\caption{Sequence of VaR Calculations}
\end{figure}
}


\section{Plots of Error:}
\frame
{
Plots of a comparsion of between using the predicted $X_{(t+1)P}$ and $X_{(t+1)P-ADJ}$ to predict the $R_{(t+1)P} (=Y_{(t+1)P})$
\begin{figure}
\includegraphics[scale=0.15]{GEerrorplots.png} 
\includegraphics[scale=0.15]{IBMerrorplots.png} 
\caption{Relizations of Error Plots}
\end{figure}
}

\end{document}

%http://www.hennesseegroup.com/releases/pitfalls.html