\chapter{Comparison and Predications}
\label{ch:compare}


\section{Comparison of Results}

In this paper, there are three other default models that are used to compare the results of the logistics regression outputs to currently accepted models that are structural and statistically based.  The models and a brief description is provided below.

\begin{itemize}
\item CreditSights: BondScore CRE Default Model: Statistical logistic Model that incorporate economic factors (GDP)
\item Barclay's (formerly Lehman): BASE CDP Default Model: Structural based that incorporates on and \textbf{off} financial balance sheets items
\item Altman Z-Score Model: Structural model that uses financial balance sheet items.  
\end{itemize}


Of the three models, only CRE and CDP provide actual probabilities of default.  The Altman Z-score provides a score that can be interpretation as a certian standard deviation away from an issuer's likelihood of default.  The layout is provided below.  Also, not all models incorporate the same issuers that was used in this paper's model building process.  Because of proprietary usage, only the results of each of the three models can be provided.  If the model does not have a score or probability, a $\#N/A$ is labeled.  The results in the figure below are sorted by the yellow column.  The rankings are also provided based on this paper's reduced logistic model 3. It can be compared that many of the issuers that a likely to default are pairing up with the current models.  There was a relatively high positively correlation CRE Model and model 1 (0.861727971), CRE Model and model 2 (0.905134001),CRE Model and model 3 (0.585281804).  This may be because of the fact that all models are statistically based.   There was a relatively high positively correlation CDP Model and model 1 (0.69824494), CDP Model and model 2 (0.813915174), CDP Model and model 3 (0.43992355).  Each current model were more correlated with logistic model 2.  Because of lack of data, the Altman Z-score was unable to be calculated.  This Z-score is still able derived, however, more modern techniques since its original release in 1968 have replaced this calculation.

\newpage

\begin{figure}
\includegraphics[scale=0.35]{sortmodelmod.png} 
\caption{Sorted Comparison of Prediction Results: By Reduced Logistic Model 3}
\end{figure}

%[scale=0.4]

\newpage

\begin{figure}
\includegraphics[scale=0.35]{sortmodelcre.png} 
\caption{Sorted Comparison of Prediction Results: By Reduced CRE Model}
\end{figure}

%[scale=0.4]

\newpage

\begin{figure}
\includegraphics[scale=0.35]{sortmodelbase.png} 
\caption{Sorted Comparison of Prediction Results: By Reduced CDP Model}
\end{figure}

%[scale=0.4]

\newpage

\begin{figure}
\includegraphics[scale=0.35]{sortmodelalt.png} 
\caption{Sorted Comparison of Prediction Results: By Reduced Altman's Z-Score}
\end{figure}

%