1. Prediction of Insolvency in Property-Casualty Insurance Using Weight of Evidence Approach
Chenghsien Tsai
Department of Risk Management and Insurance
National Chengchi University, Taipei, Taiwan, R.O.C.
Hsiao-Tzu Huang
Department of Banking and Finance
Kainan University, Taoyuan, Taiwan, R.O.C

2. Outline Introduction Method Modeling, Variables and Data
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Outline
Introduction
Method
Modeling, Variables and Data
Model Evaluation
Results
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

3. Introduction
Insolvency of insurers has been a major concern for the regulators and the public
Most previous studies have implemented various methodologies and selected variables
used the observations for explanatory variables based on the amount of finance or financial ratios with the original forms (continuous data)

4. The problem of the original data (continuous data)
Extreme data (outliers)
Outliers might exist in the wide range data
Skewed distribution
if assumptions of the adopted methodology have the restriction of the symmetric distribution.
Unstable variance
Unexpected noise might arise in the process of prediction

5. The method to solve the problem
Data transformation is a method to deal with some problems that emerge from the original data (Chao and Hwang, 1997).
Some literatures have shown that the accuracy of the prediction of transformed data outperform the results of the original data

6. Advantages of using data transformation
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Advantages of using data transformation
Modifying the asymmetry
Facilitating variable operations
Reducing the effect of outliers
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

7. Method
Why use WOE ?
use the weight of evidence (WOE) method to convert continuous data into some specific values for different groups.
expect the transformation of variables to reduce the influence of outliers and noise.
WOE is commonly used in financial institutions and applied in scoring models
Banasik et al., 2003; Siddiqi, 2006; Abdou, 2009; Abdou, 2011; Matuszyk et al., 2010

8. 8/7/2018 5:02 PM
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

9. Group
Solvent
Number
Insolvent Number
%Solvent
%Insolvent
WOE IV
<0.34
528 11
0.2848
0.5789
0.2087
0.34~0.957
589 1
0.3177
0.0526
1.7978
0.4766
0.957~4.102
711 5
0.3835
0.2632
0.3766
0.0453
>4.102 26 2
0.0140
0.1053
0.1840
Total
1854 19
0.9146

10. The number of groups and Segmenting Principle
Objective
Maximum : IV value of the variable
Subjective to: variables exceeding the threshold remain for modeling would be in the model
optimization algorithm

11. Modeling, Variables and Data
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Modeling, Variables and Data
Modeling
Logistic Regression
= the status for the insurer i to fail in year t’
= the factor effecting the status for the insurer to fail
=the intercept term
=the coefficient in the linear combination of independent variables
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

12. Variables
employ ten variables in FAST which have significant impacts on predictive accuracy in Pottier and Sommer (2011)
two RBC-related variables

13. X1: Natural log of total assets
X2: Affiliated investments/surplus
X3: Investment yield=Net Investment Income/Average Cash and Invested Assets
X4: Change in combined ratio=
X5: Gross premiums written/surplus
X6: Change in net premiums written =
X7: Change in gross premiums written=
X8: Reinsurance recoverable unpaid losses/surplus
X9: Reserves/surplus
X10: Change in surplus=
X11: RBC ratio=
X12: Change in RBC ratio=

14. Data
The dependent variable for insurers is whether an insurer is likely to become insolvent in the following three years t+1, t+2 or t+3.
The insolvent status are from Best's Insurance Reports: Property-Casualty from 1997 to 2003
Data of the independent variables:
based on year t and will be drawn from NAIC annual statement databases. The available data for prediction are for the period from 1996 to 2000

15. Model Evaluation Receiver Operating Characteristic (ROC) Curve
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Model Evaluation
Receiver Operating Characteristic (ROC) Curve
Pseudo R-square: McFadden's R-square
Type I/Type II error trade off
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

16. Results Fitting Results ROC curve 1996 1997 8/7/2018 5:02 PM
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

17. 1998
1999
2000

18. Fitting Results ROC Area One-sided p-value Year Ori Rank WOE Ori-Rank
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Fitting Results
ROC Area
One-sided p-value
Year
Ori
Rank
WOE
Ori-Rank
Ori-WOE
Rank-WOE
1996
0.8354
0.8143
0.9128
0.3426
0.0240
0.0136
1997
0.7675
0.7931
0.8749
0.2963
0.0024
0.0128
1998
0.6295
0.6523
0.8207
0.3572
1999
0.6609
0.7770
0.8727
0.0144
0.0009
2000
0.75
0.8297
0.9035
0.0031
0.0003
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

19. Fitting Results Logistic regression analysis (2000) Variable/Method
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Fitting Results
Logistic regression analysis (2000)
Variable/Method
Ori
Rank
WOE X1
***
***
*** X2 - X3 ** X4 **
*** X5 ** X6 X7 X8
*** X9
X10
-3.196***
***
X11
***
***
***
X12
0.3891***
***
Psuedo R2
13%
22.1%
30%
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

20. Fitting Results Type I/II error tradeoffs Type I Error Rate (%)
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Fitting Results
Type I/II error tradeoffs
Type I Error Rate (%)
Type II Error Rate (%)
Ori
Rank
WOE 5 68 61 45 10 57 47 30 15 49 38 21 20 43 31 25 26 11 33 22 8
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

21. Results Prediction Results ROC curve 1997: 1998-2000 1998: 1999-2001
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Results
Prediction Results
ROC curve
1997:
1998:
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

22. 8/7/2018 5:02 PM
1999:
2000:
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

23. Prediction Results ROC Area One-sided p-value Year Ori Rank WOE
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Prediction Results
ROC Area
One-sided p-value
Year
Ori
Rank
WOE
Ori-Rank
Ori-WOE
Rank-WOE
1997:
0.7545
0.7528
0.8587
0.4888
0.0134
0.0152
1998:
0.6705
0.6243
0.7867
0.0718
0.0002
0.0000
1999:
0.6825
0.7158
0.8466
0.1036
2000:
0.7326
0.7880
0.8598
0.073
0.0004
0.0104
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

24. Thank you for listening !