1. 1 Country Risk Classification and Multiriteria Decision Aid Xijun Wang January 26, 2004

2. 2 Outline Country Risk Classification Country Risk Classification Country Risk Classification Methods Country Risk Classification Methods Utilities Additive Discrimination Utilities Additive Discrimination Multigroup Hierarchical Discrimination Multigroup Hierarchical Discrimination Dealing with Complex Factors Dealing with Complex Factors Future Works Future Works

3. 3 Country Risk The overall risk of loaning money to foreign companies. The overall risk of loaning money to foreign companies. –How much is debt delayed and how much is the return? –Help financial institutions in decision-making Measurements Measurements –Risk levels C1, C2,…, Cq, Evaluation factors Evaluation factors –Population structure, education, political and social status, economics, financial status

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5. 5 Country Risk Classification Determine the risk level of a country based on various factors Determine the risk level of a country based on various factors

6. 6 Country Risk Classification Methods Early used statistical methods: Bayesian discrimination, Early used statistical methods: Bayesian discrimination, –Simple to implement –Not widely used due to unrealistic statistics assumptions Recent approaches based on optimization: Multicriteria decision-aid methods Recent approaches based on optimization: Multicriteria decision-aid methods –No statistics assumption –Background knowledge incorporated

7. 7 Utility Function Utility function U(c) is an indicator of the risk level of a country Utility function U(c) is an indicator of the risk level of a country –Risk level of country a is higher than of b, then U(a)<U(b) Borderlines to separate different risk levels Borderlines to separate different risk levels μ q-1 μkμk μ k-1 μ1μ1 CqCq CkCk C1C1 U(c)

8. 8 Utilities Additive Discrimination (1) Learning the utility function and the thresholds in the function space. Learning the utility function and the thresholds in the function space. But, in practice, we might not find threshholds and utility functions that can predict all the country risk levels correctly But, in practice, we might not find threshholds and utility functions that can predict all the country risk levels correctly μ q-1 μkμk μ k-1 μ1μ1 CqCq CkCk C1C1 σ + (c) U(c) μ q-1 μkμk μ k-1 μ1μ1 CqCq CkCk C1C1 σ - (c) U(c)

9. 9 Utilities Additive Discrimination (2) Piecewise linear marginal utility function

10. 10 Utilities Additive Discrimination (3) Learning model: minimizing total training classification error Learning model: minimizing total training classification error

11. 11 A Computation Example Estimated Marginal Utility functions Estimated Marginal Utility functions

12. 12 Weights of Factor Groups

13. 13 Examples and their Utilities

14. 14 Multigroup Hierarchical Discrimination (1) Hierarchical classification process Hierarchical classification process –Is it in level C 1 ? –If not, is it in level C 2 ? –… Suppose we have Suppose we have –U k (c): similarity measure of c to countries in C k –U ¬ k (c): similarity measure of c to countries in C ¬ k =C k+1  …  C q Is c in C k or C ¬ k ?  Is U k (c)> U ¬ k (c) or not? Is c in C k or C ¬ k ?  Is U k (c)> U ¬ k (c) or not? U k U k (c) U ¬ k U ¬ k (c) CkCkCkCk C¬kC¬kC¬kC¬k

15. 15 Multigroup Hierarchical Discrimination (2) Learning U k (c) and U ¬ k (c) Learning U k (c) and U ¬ k (c) –Minimizing the number of misclassifications?

16. 16 Multigroup Hierarchical Discrimination (3) First, minimize total classification error, like in UTADIS First, minimize total classification error, like in UTADIS

17. 17 Multigroup Hierarchical Discrimination (4) Second, further minimize number of misclassifications Second, further minimize number of misclassifications

18. 18 Multigroup Hierarchical Discrimination (5) Finally, make U k and U ¬ k most distinguished on training examples, without changing the correctness of any training example Finally, make U k and U ¬ k most distinguished on training examples, without changing the correctness of any training example

19. 19 Dealing with Complex Factors Non-monotone factors exists, such as birthrate, military expenditure Non-monotone factors exists, such as birthrate, military expenditure Allow unimodal utility function Allow unimodal utility function

20. 20 Effect of Unimodal Factors Leave one out test Leave one out test Factors used Correctness (%) 26 monotone factors 72.7 +birthrate +birthrate78.8 +birthrate, military expenditure +birthrate, military expenditure81.8

21. 21 Estimated Marginal Utility functions of birthrate and military expenditure Estimated Marginal Utility functions of birthrate and military expenditure

22. 22 Weights of Factor Groups Weights of Factor Groups

23. 23 Examples and their risk level Examples and their risk level

24. 24 Conclusion and Future Works Discussed two MCDA methods for country risk classification Discussed two MCDA methods for country risk classification –UTADIS –MHDIS Discussed an extension of MCDA models Discussed an extension of MCDA models –Unimodal factors Future work Future work –Trade-off between correctness and computation effort for models with unimodal factors

25. 25 Thank You for Your Attention

26. 26 Birthrate