Transcript xwang

Country Risk Classification and
Multiriteria Decision Aid
Xijun Wang
January 26, 2004
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Outline






Country Risk Classification
Country Risk Classification Methods
Utilities Additive Discrimination
Multigroup Hierarchical Discrimination
Dealing with Complex Factors
Future Works
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Country Risk

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
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Measurements
– Risk levels C1, C2 ,…, Cq,
Evaluation factors
– Population structure, education, political and social status,
economics, financial status
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farm
R&D ratio
public
unemploy real GDP
net goverment value added Total financial
in
external reserve(b
population (% of
education ment rate growth(% exports revenue
)
(% of
(% of agriculture debt to
$)
(%)
GNP) expenditure
(%)
GDP)
GDP)
(% of GDP) export
(% of GDP)
ratio
(%)
Canada
2.6
1.7
5.6
6.8
1.5
2.9
22
2.3
0.73
33.96
United Kingdom
1.8
1.8
4.4
5.5
2.2
-1.9
36.4
1.5
0
37.28
United States
2.2
2.5
5
4
1.2
-2.8
21.4
1.7
119
57.63
Australia
4.6
1.7
4.8
6.6
2.4
-2.4
23.8
3
208
17.96
Singapore
0.1
1.1
3.1
4.4
-2.1
18.5
26.2
0.1
0
75.38
Spain
7.3
0.8
4.5
15.9
2.8
-5.6
40.4
4.3
73.6
55.3
China
66.6
0.8
2.3
3.1
7.3
2.7
7.8
15.9
52.1
266.63
Czech Republic
8.2
1.3
4.2
8.8
3.6
-3.7
33.1
5
57
14.34
Thailand
49
0.1
4.7
2.4
1.8
8
16
11.2
89
32.35
Argentina
10.1
0.5
3.7
15
-3.7
-0.6
19.9
5.3
404.2
14.55
Indonesia
44.1
0.7
1.4
5.5
3.3
7.8
17.9
16.7
181.8
27.25
South Africa
14.2
1
6.1
5.4
2.2
3
27.3
3.9
61.4
6.05
Egypt
36.6
1.9
4.7
8.1
3.3
-6.6
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13.9
106.5
12.93
Nigeria
33.3
0.1
0.6
50
4
11.3
18
37.2
117
3.86
Pakistan
50.9
0.9
2.7
5.9
3.4
-3.6
16.7
24.1
249.3
3.64
Turkey
30.7
0.5
2.3
7.3
-6.2
-6
28
12.5
195.8
18.88
risk country
level
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2
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Country Risk Classification
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Determine the risk level of a country based on various factors
farm
R&D ratio public unemploy real GDP net goverment value added Total financial
in
external reserve(b
population (% of education ment rate growth(% exports revenue
)
(% of
(% of agriculture debt to
$)
(%)
GNP) expenditure
(%)
GDP)
GDP) (% of GDP) export
(% of GDP)
ratio
(%)
Israel
2.7
3.7
7.7
8.8
-0.6
-6.9
43.3
3
153
23.38
Japan
3.9
2.8
3.5
4.7
-0.4
1.6
14
1
0
395.15
Netherlands
3.4
2
4.9
3.3
1.1
4.8
45.1
3
0
9.03
Italy
5.3
1.1
4.7
10.5
1.8
1.2
41.3
3
0
25.57
Malaysia
17.7
0.4
4.6
3.1
0.4
21.1
26.4
8.8
37.9
30.47
Mexico
23.6
0.4
3.6
1.6
-0.3
-1.8
13.8
5.1
81.4
44.74
Poland
20.4
0.7
5.4
16.1
1.1
-7
31
4
118.2
25.65
Brazil
16.5
0.8
4.6
9.6
1.5
-1.2
22.8
8
323.5
35.74
risk country
level
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Country Risk Classification Methods
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Early used statistical methods: Bayesian discrimination,
– Simple to implement
– Not widely used due to unrealistic statistics assumptions
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Recent approaches based on optimization: Multicriteria
decision-aid methods
– No statistics assumption
– Background knowledge incorporated
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Utility Function
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Utility function U(c) is an indicator of the risk level of a country
n
U ( g1 ,..., g n )   U i ( g i )
i 1
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– Risk level of country a is higher than of b, then U(a)<U(b)
Borderlines to separate different risk levels
Cq
Ck
C1
U(c)
μq-1
μk
μk-1
μ1
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Utilities Additive Discrimination (1)
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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
Cq
Ck
C1
σ+(c)
U(c)
μq-1
μk
Cq
μk-1
μ1
Ck
C1
σ-(c)
μq-1
μk
μk-1
U(c)
μ1
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Utilities Additive Discrimination (2)
Piecewise linear marginal utility function
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Utilities Additive Discrimination (3)
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Learning model: minimizing total training classification error
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A Computation Example
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Estimated Marginal Utility functions
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Weights of Factor Groups
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Examples and their Utilities
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Multigroup Hierarchical Discrimination (1)
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Hierarchical classification process
– Is it in level C1?
– If not, is it in level C2?
– …
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Suppose we have
– Uk(c): similarity measure of c to countries in Ck
– U¬k(c): similarity measure of c to countries in C¬k=Ck+1… Cq
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Is c in Ck or C¬k?  Is Uk(c)> U¬k(c) or not?
C¬k
Ck
Uk(c)
U¬k(c)
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Multigroup Hierarchical Discrimination (2)
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Learning Uk(c) and U¬k (c)
– Minimizing the number of misclassifications?
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Multigroup Hierarchical Discrimination (3)
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First, minimize total classification error, like in UTADIS
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Multigroup Hierarchical Discrimination (4)
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Second, further minimize number of misclassifications
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Multigroup Hierarchical Discrimination (5)
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Finally, make Uk and U¬k most distinguished on training
examples, without changing the correctness of any training
example
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Dealing with Complex Factors
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Non-monotone factors exists, such as birthrate, military
expenditure
Allow unimodal utility function
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Effect of Unimodal Factors
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Leave one out test
Factors used
Correctness (%)
26 monotone factors
72.7
+birthrate
+birthrate, military
expenditure
78.8
81.8
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Estimated Marginal Utility functions of birthrate and military
expenditure
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Weights of Factor Groups
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Examples and their risk level
ris k country
level
2
1
1
2
3
3
3
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Israel
Japan
Netherlands
Italy
Malaysia
Mexico
Poland
Brazil
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Conclusion and Future Works
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Discussed two MCDA methods for country risk classification
– UTADIS
– MHDIS
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Discussed an extension of MCDA models
– Unimodal factors
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Future work
– Trade-off between correctness and computation effort for models with
unimodal factors
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Thank You for Your Attention
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Birthrate
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