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Country Risk Classification and Country Risk Classification and Multiriteria Decision AidMultiriteria Decision Aid

Xijun WangXijun Wang

January 26, 2004January 26, 2004

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OutlineOutline

Country Risk ClassificationCountry Risk Classification Country Risk Classification MethodsCountry Risk Classification Methods Utilities Additive DiscriminationUtilities Additive Discrimination Multigroup Hierarchical DiscriminationMultigroup Hierarchical Discrimination Dealing with Complex Factors Dealing with Complex Factors Future WorksFuture Works

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Country RiskCountry Risk

The overall risk of loaning money to foreign The overall risk of loaning money to foreign companies.companies.– How much is debt delayed and how much is the return? How much is debt delayed and how much is the return?

– Help financial institutions in decision-makingHelp financial institutions in decision-making

MeasurementsMeasurements– Risk levels CRisk levels C11, C, C22 ,…, C ,…, Cq, q,

Evaluation factorsEvaluation factors– Population structure, education, Population structure, education, political and social status, political and social status,

economics, financial statuseconomics, financial status

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risklevel

country farm

popul at i on(%)

R&D ratio(% ofGNP)

publiceducation

expenditure(% of GDP)

unemployment rate

(%)

real GDPgrowth(%

)

netexport s(% ofGDP)

govermentrevenue(% ofGDP)

val ue addedi n

agr i cul ture(% of GDP)

Totalexternaldebt toexportrat i o(%)

fi nanci alreserve(b

$)

1 Canada 2. 6 1. 7 5. 6 6. 8 1. 5 2. 9 22 2. 3 0. 73 33. 961 Uni ted Ki ngdom 1. 8 1. 8 4. 4 5. 5 2. 2 - 1. 9 36. 4 1. 5 0 37. 281 Uni ted States 2. 2 2. 5 5 4 1. 2 - 2. 8 21. 4 1. 7 119 57. 632 Aust ral i a 4. 6 1. 7 4. 8 6. 6 2. 4 - 2. 4 23. 8 3 208 17. 962 Si ngapore 0. 1 1. 1 3. 1 4. 4 - 2. 1 18. 5 26. 2 0. 1 0 75. 382 Spai n 7. 3 0. 8 4. 5 15. 9 2. 8 - 5. 6 40. 4 4. 3 73. 6 55. 33 Chi na 66. 6 0. 8 2. 3 3. 1 7. 3 2. 7 7. 8 15. 9 52. 1 266. 633 Czech Republ i c 8. 2 1. 3 4. 2 8. 8 3. 6 - 3. 7 33. 1 5 57 14. 343 Thai l and 49 0. 1 4. 7 2. 4 1. 8 8 16 11. 2 89 32. 354 Argent i na 10. 1 0. 5 3. 7 15 - 3. 7 - 0. 6 19. 9 5. 3 404. 2 14. 554 I ndonesi a 44. 1 0. 7 1. 4 5. 5 3. 3 7. 8 17. 9 16. 7 181. 8 27. 254 South Af r i ca 14. 2 1 6. 1 5. 4 2. 2 3 27. 3 3. 9 61. 4 6. 055 Egypt 36. 6 1. 9 4. 7 8. 1 3. 3 - 6. 6 23 13. 9 106. 5 12. 935 Ni ger i a 33. 3 0. 1 0. 6 50 4 11. 3 18 37. 2 117 3. 865 Paki stan 50. 9 0. 9 2. 7 5. 9 3. 4 - 3. 6 16. 7 24. 1 249. 3 3. 645 Turkey 30. 7 0. 5 2. 3 7. 3 - 6. 2 - 6 28 12. 5 195. 8 18. 88

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Country Risk ClassificationCountry Risk Classification

Determine the risk level of a country based on various factorsDetermine the risk level of a country based on various factors

risklevel

country farm

popul at i on(%)

R&D ratio(% ofGNP)

publiceducation

expenditure(% of GDP)

unemployment rate

(%)

real GDPgrowth(%

)

netexport s(% ofGDP)

govermentrevenue(% ofGDP)

val ue addedi n

agr i cul ture(% of GDP)

Totalexternaldebt toexportrat i o(%)

fi nanci alreserve(b

$)

? I srael 2. 7 3. 7 7. 7 8. 8 - 0. 6 - 6. 9 43. 3 3 153 23. 38? J apan 3. 9 2. 8 3. 5 4. 7 - 0. 4 1. 6 14 1 0 395. 15? Nether l ands 3. 4 2 4. 9 3. 3 1. 1 4. 8 45. 1 3 0 9. 03? I tal y 5. 3 1. 1 4. 7 10. 5 1. 8 1. 2 41. 3 3 0 25. 57? Mal aysi a 17. 7 0. 4 4. 6 3. 1 0. 4 21. 1 26. 4 8. 8 37. 9 30. 47? Mexi co 23. 6 0. 4 3. 6 1. 6 - 0. 3 - 1. 8 13. 8 5. 1 81. 4 44. 74? Pol and 20. 4 0. 7 5. 4 16. 1 1. 1 - 7 31 4 118. 2 25. 65? Brazi l 16. 5 0. 8 4. 6 9. 6 1. 5 - 1. 2 22. 8 8 323. 5 35. 74

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Country Risk Classification MethodsCountry Risk Classification Methods

Early used statistical methods: Bayesian discrimination, Early used statistical methods: Bayesian discrimination, – Simple to implementSimple to implement

– Not widely used due to unrealistic statistics assumptionsNot widely used due to unrealistic statistics assumptions

Recent approaches based on optimization: Multicriteria Recent approaches based on optimization: Multicriteria decision-aid methodsdecision-aid methods– No statistics assumptionNo statistics assumption

– Background knowledge incorporatedBackground knowledge incorporated

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Utility FunctionUtility Function

Utility function U(c) is an indicator of the risk level of a Utility function U(c) is an indicator of the risk level of a countrycountry

– Risk level of country a is higher than of b, then U(a)<U(b)Risk level of country a is higher than of b, then U(a)<U(b) Borderlines to separate different risk levelsBorderlines to separate different risk levels

μq-1 μk μk-1 μ1

Cq Ck C1

U(c)

n

iiin gUggU

11 )(),...,(

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Utilities Additive Discrimination (1)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 But, in practice, we might not find threshholds and utility functions that can

predict all the country risk levels correctly predict all the country risk levels correctly

μq-1 μk μk-1 μ1

Cq Ck C1

σ+(c)

U(c)

μq-1 μk μk-1 μ1

Cq Ck C1

σ-(c)

U(c)

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Utilities Additive Discrimination (2)Utilities Additive Discrimination (2)

Piecewise linear marginal utility functionPiecewise linear marginal utility function

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Utilities Additive Discrimination (3)Utilities Additive Discrimination (3)

Learning model: minimizing total training classification errorLearning model: minimizing total training classification error

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A Computation ExampleA Computation Example

Estimated Marginal Utility functionsEstimated Marginal Utility functions

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Weights of Factor GroupsWeights of Factor Groups

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Examples and their UtilitiesExamples and their Utilities

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Multigroup Hierarchical Discrimination (1)Multigroup Hierarchical Discrimination (1)

Hierarchical classification processHierarchical classification process– Is it in level CIs it in level C11??

– If not, is it in level CIf not, is it in level C22??

– ……

Suppose we haveSuppose we have– UUkk(c): similarity measure of c to countries in C(c): similarity measure of c to countries in Ckk

– UU¬¬kk(c): similarity measure of c to countries in C(c): similarity measure of c to countries in C¬¬kk=C=Ck+1k+1…… CCqq

Is Is cc in C in Ckk or C or C¬¬kk? ? Is Is UUkk(c)> U(c)> U¬¬kk(c) or not?(c) or not?

UUkk(c) UU¬¬kk(c)

CCkk CC¬¬kk

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Multigroup Hierarchical Discrimination (2)Multigroup Hierarchical Discrimination (2)

Learning ULearning Ukk(c) and U(c) and U¬¬k k (c)(c)– Minimizing the number of misclassifications?Minimizing the number of misclassifications?

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Multigroup Hierarchical Discrimination (3)Multigroup Hierarchical Discrimination (3)

First, minimize total classification error, like in UTADISFirst, minimize total classification error, like in UTADIS

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Multigroup Hierarchical Discrimination (4)Multigroup Hierarchical Discrimination (4)

Second, further minimize number of misclassificationsSecond, further minimize number of misclassifications

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Multigroup Hierarchical Discrimination (5)Multigroup Hierarchical Discrimination (5)

Finally, make UFinally, make Ukk and U and U¬¬kk most distinguished on training most distinguished on training examples, without changing the correctness of any training examples, without changing the correctness of any training exampleexample

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Dealing with Complex FactorsDealing with Complex Factors

Non-monotone factors exists, such as birthrate, military Non-monotone factors exists, such as birthrate, military expenditureexpenditure

Allow unimodal utility functionAllow unimodal utility function

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Effect of Unimodal FactorsEffect of Unimodal Factors

Leave one out testLeave one out test

Factors usedFactors used Correctness (%)Correctness (%)

26 monotone factors26 monotone factors 72.772.7

+birthrate+birthrate 78.878.8

+birthrate, military +birthrate, military expenditureexpenditure

81.881.8

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Estimated Marginal Utility functions of birthrate and military Estimated Marginal Utility functions of birthrate and military expenditureexpenditure

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Weights of Factor GroupsWeights of Factor Groups

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Examples and their risk levelExamples and their risk level

risklevel

country

2 I srael1 J apan1 Nether l ands2 I tal y3 Mal aysi a3 Mexi co3 Pol and4 Brazi l

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Conclusion and Future WorksConclusion and Future Works

Discussed two MCDA methods for country risk classificationDiscussed two MCDA methods for country risk classification– UTADISUTADIS

– MHDISMHDIS

Discussed an extension of MCDA modelsDiscussed an extension of MCDA models– Unimodal factorsUnimodal factors

Future workFuture work– Trade-off between correctness and computation effort for models with Trade-off between correctness and computation effort for models with

unimodal factorsunimodal factors

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Thank You for Your AttentionThank You for Your Attention

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BirthrateBirthrate