Download On the Construction of an Early-Warning System for Systematic Risk

On the Construction of an Early-Warning System for Systematic Risk
in China’s Banking
TANG Lingxiao, FAN Xiaofeng
School of Economics Changsha University of Science & Technology, P.R. China, 410076
：
Abstract An early warning system for systematic risk in China’s banking industry helps us to eliminate
systematic risk at its embryonic stage. The early warning system is composed of four subsystems: the
macro economy risk subsystem, the external impact risk subsystem, the internal banking risk subsystem
and the bubble risk in stock market subsystem. The systematic risk in China’s banking industry can be
measured by employing entropy method and fuzzy comprehensive evaluation.
Key Words: Systematic risk, Entropy method, Fuzzy comprehensive evaluation, Early warning
Introduction
An early warning system for systematic risk helps us to eliminate systematic risk at its embryonic
stage. Many scholars such as Kaminsky (1998) and Andrew Berg& Catherine Pattillo 1999 have built
successful models to measure risks in developing countries. However, early warning system for
systematic risk in China’s banking industry is still at its early stage, and the design of such a system
should take into account the unique conditions in China.
（
）
1 Indicators and Their Implications
⑴
There are mainly four types of systematic risks in China’s banking industry:
the macro economy
risk caused by the instability of macro economy;
the external impact risk brought forth by the
impact of external debts and foreign exchange;
the internal banking risk given rise to by banks’
inherent fragility;
the bubble risk in stock market generated by the stock bubble risk. Accordingly,
we build the four subsystems and choose the following indicators, as shown in table 1.
⑷
Type
of
indicators
The macro
economy
risk
subsystem
A1
（ ）
Table 1 the Early-warning Indicator System
Name of indicators
Possible effect on banking
The growth rate of GDP(X11)
The rate of inflation(X12)
The growth rate of investment in
fixed assets(X13)
The deficit budget/GDP(X14)
The dependency ratio of central
fiscal debt(X15)
The external
impact risk
subsystem
⑶
⑵
Short-term external debts/ external
debts(X21)
Foreign exchange reserve/ Balance
The moderate growth of GDP can ensure the stable
development of banking industry.
The fluctuation of price may affect the enterprises’
operation cost, the debt paying ability and the profitability.
Certain growth of investment in fixed assets can ensure the
stable development of economy. And the growth rate
should be in accord with the speed of economic
development.
When the deficit budget is too large, it may affect the
healthy development of economy.
When the dependency ratio of central fiscal debt is too
high, it means that the fiscal expenditure relies too heavily
on liability income, and the finance is fragile.
Moderate short-term external debts/ external debts can
avoid the mass debts to repay.
It reflects the capacity of using foreign exchange reserve to
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（A ）
2
of Foreign Debts(X22)
Terms of trade(X23)
Foreign exchange reserve/M2(X24)
The rate of payment of debts (X25)
the internal
banking risk
subsystem
A3
（ ）
Bank deposit/ loan(X31)
The growth rate of credit(X32)
The rate of non-performing loan in
four
state-owned
commercial
banks(X33)
The growth rate of M2 (X34)
the bubble
risk in stock
market
subsystem
A4
The stock Price/Earnings ratio (X41)
stock market value/GDP (X42)
repay external debts, when the country has no other means
to repay.
When the terms of trade increase, the condition of foreign
trade will be improved, and hence it will contribute more
to the stability of economy.
The indicator reflects the country’s external liquidity and
international prestige.
The indicator measures the scale of the foreign debts and
the country’s capacity to repay debts.
If the rate is too high, it would weaken the bank’s capacity
to avert risk.
If the credit grows too fast, it would increase the fragility
of the banking.
It reflects the quality of the banks’ operation.
If M2 grows too quickly, it may cause inflation and bubble
in economy.
It measures the stock risk and the degree of bubble in the
stock market.
It reflects the overrating degree of the stock.
（ ）
2 Threshold Values
According to the financial risk grades that are often employed in China, this paper divides the
systematic risk in banking into no warning, slight warning, mid-warning and serious warning grades,
which are denoted by R1 R2 R3 R4 respectively. The setting of the threshold value is on the basis of
international standard such as the Basel Agreement, some scholars’ research and historical data.
， ， ，
Table 2 the Threshold Value of Risk Grade for Specific Indicator
Name of indicators
No Warning
Slight Warning
Mid-warning
Serious Warning
The growth rate of GDP
7% 8%
＜3%
～
～
1%～2%
3%～5%
6%～10%
15%～25%
3%～4%
～
～
0.5%～1%
5%～6%
3%～6%
25%～30%
4%～5%
＜3%
＞11%
＜0.5%
＞6%
＜3%
＞30%
＞5%
The rate of inflation
2% 3%
The growth rate of
investment in fixed assets
10% 15%
The deficit budget/GDP
The dependency ratio of
central fiscal debt
＜30%
30% 50%
～
50% 80%
～
＞80%
～
～
～
5% 7%
8% 10%
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3% 5%
10% 11%
Short-term external debts/
external debts
＜25%
25% 35%
～
35% 40%
～
＞40%
Foreign exchange reserve/
Balance of Foreign Debts
＞30%
15% 30%
～
10% 15%
～
＜10%
Terms of trade
＞0.9
0.7 0.9
～
0.6 0.7
～
＜0.6
Foreign exchange
reserve/M2
＞10%
8% 10%
～
7% 8%
～
＜7%
The rate of payment of
debts
＜20%
20% 40%
～
40% 60%
～
＞60%
Bank deposit/ loan
＜75%
75% 80%
80% 90%
The growth rate of credit
14% 16%
～
8%～10%
20%～22%
＞90%
＜8%
＞22%
The rate of non-performing
loan in four state-owned
commercial banks
＜6%
6% 12%
～
12% 15%
～
＞15%
The growth rate of M2
14% 16%
～
10% 14%
16% 20%
～
～
8% 10%
20% 22%
～
～
＜8%
＞22%
The stock Price/Earnings
ratio
＜40
40 60
～80
＞80
stock market value/GDP
＜30%
30% 60%
～
＞90%
～
～
10%～14%
16%～20%
～
～
60
60% 90%
3 Index Weight Calculation
This paper employs the entropy method to calculate the index weight. As some indicators are
positive, some are negative, and others are moderate indicators, before calculating the index weight, we
should do the non-dimensional processing to ensure the indicators’ comparability. Suppose there are n
indicators and m projects for assessment, n indicators xij ( i = 1 2 … n j = 1 2 … m), t subsystems,
and X = x


ij 

 n ×m
，， ，； ，， ，
is the original index data matrix.
，
3.1 Non-dimensional processing
For positive indicators let
yij =
xij − min( x1 j ,L, xnj )
max( x1 j, L, xnj ) − min( x1 j ,L, xnj )
，
For negative indicators let
max( x1 j ,L, xnj ) − xij
yij =
max( x1 j, L, xnj ) − min( x1 j ,L, xnj )
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，
For moderate indicators let
L1 j − xij

1 − max[L1 j − min( x1 j , L, xnj ), max( x1 j , L , xnj ) − L 2 j

yij = 1

xij − L 2 j
1 −
 max[L1 j − min( x1 j , L, xnj ), max( x1 j , L , xnj ) − L 2 j
，


xij p L1 j
L1 j p xij p L 2 j


xij f L 2 j
[L1j L2j] is the best index value interval.
After the non-dimensional processing, yij is in the interval of [0 1],and it becomes a positive index.
，
3.2 Data processing
As some indicators still have negative value even if they have undergone non-dimensional processing,
it may be unable to get the logarithm when we use entropy method to calculate the index weight. And
data processing can solve that problem. We employ the standardization method, that is, to translate the
index value.
Make yij ' = yij + 1 (i = 1, 2, L, m; j = 1, 2, L, n)
3.3 Proportion calculation for the index value of the item i for the index j in the index system
pij =
xij
(i = 1, 2, L, m; j = 1, 2, L, n)
m
∑x
ij
i =1
3.4 Entropy value calculation for the j index
m
ej = -(1/lnm)∑ pijlnpij (i = 1, 2, L , m; j = 1, 2, L , n)
i =1
3.5 Diversity factor gj of the j index
gj = 1 − ej
The larger gj is, the smaller the diversity factor is, and the slighter the effect that the indicator places
on the comprehensive assessment is.
3.6 Calculation for the weight of the j index
n
aj = gj/ ∑ gj ( j = 1, 2, L , n)
j =1
3.7 Comprehensive assessment vj of the j index
m
vj = ∑ ajpij ( i = 1, 2, L, m; j = 1, 2, L, n)
i =1
3.8 Weight Aj of subsystem
Firstly, sum up comprehensive assessment of all the indexes in the subsystem, and we can get the
comprehensive assessment Vj of the subsystem. Then do the normalization processing on the weights
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as follows:
t
Aj = Vj/ ∑ Vj ( j = 1, 2, L, t )
j=1
Following the above steps, we can calculate the weight for indicators and subsystems:
A= c1 c2 c3 c4 ; A1= a11 a12 a13 a14 a15 ; A2=
a21 a22 a23 a24 a25 ;
A3=
a31 a32 a33 a34 ; A4= a41 a42
（，，，） （ ， ， ， ， ）
（ ， ， ， ） （ ， ）
（ ， ， ， ， ）
4 Construction of Indicator Assessment Model
4.1 Indicator assessment
We use membership grade to judge the indicator’s risk grade. This paper uses trapezoidal method to
build membership function, and calculates the indicators’ membership function value. For positive
indicators such as terms of trade and foreign exchange reserve/ balance of foreign debts, their
membership grade should be calculated as follows:
0
 x − r2

bij ( R1) = 
r3 − r2
1
0
 r3 − x

bij ( R 2) = 
r3 − r2
0
0
 x − r1

bij ( R 3) = 
 r 2 − r1
0
1
 r2 − x

bij ( R 4) = 
 r 2 − r1
0
r0 ≤ x ≤ r2
r 2 p x p r3
(1)
r3 ≤ x ≤ r4
r0 ≤ x ≤ r2
r 2 p x p r3
(2)
r3 ≤ x ≤ r4
r 0 ≤ x ≤ r1
r1 p x p r 2
(3)
r2 ≤ x ≤ r4
r 0 ≤ x ≤ r1
r1 p x p r 2
(4)
r2 ≤ x ≤ r4
As for negative indicators such as short-term external debts/ external debts and the growth rate of
credit, their membership grade should be calculated as follows:
1
 r2 − x

bij ( R1) = 
 r 2 − r1
0
r 0 ≤ x ≤ r1
r1 p x p r 2
r2 ≤ x ≤ r4
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(5)
0
 x − r1

bij ( R 2) = 
 r 2 − r1
0
0
 r3 − x

bij ( R 3) = 
 r3 − r2
0
0
 x − r2

bij ( R 4) = 
r3 − r2
1
r 0 ≤ x ≤ r1
r1 p x p r 2
(6)
r2 ≤ x ≤ r4
r0 ≤ x ≤ r2
r 2 p x p r3
(7)
r3 ≤ x ≤ r4
r0 ≤ x ≤ r2
r 2 p x p r3
(8)
r3 ≤ x ≤ r4
（ ， ， ， ），
bij ( Bm ) means Xij belongs to the risk grade of Bm m=1 2 3 4 and bn is the critical value of various
， ≦ ≦ ≦ ≦
（ ， ， ， ） （ ， ， ， ， ） ; B = （b ，b ，b ，b ，b ）
（ ， ， ， ） （ ， ）
risk grades b0 b1 b2 b3 b4.
The membership grade matrix is composed by following:
B= B1 B2 B3 B4 T; B1=
b11 b12 b13 b14 b15
B3=
b31 b32 b33 b34 T; B4=
b41 b42 T.
bij ={ bij ( B1), bij ( B 2), bij ( B 3), bij ( B 4 ) }
T
2
21
22
23
24
T
25
4.2 Overall system assessment
In order to avoid loss of information, this paper employs the weighted mean fuzzy synthetic
discrimination model.
Suppose M is the membership grade of the overall system, Mi (i=1,2,3,4)is the membership grade of
the risk subsystem.
M 1 = A1B1 = (a11, a12, a13, a14, a15)(b11, b12, b13, b14, b15)T = (m11, m12, m13, m14, m15)
M 2 = A2 B 2 = (a 21, a 22, a 23, a 24, a 25)(b 21, b 22, b 23, b 24, b 25)T = (m 21, m 22, m 23, m 24, m 25)
M 3 = A3 B3 = (a 31, a 32, a33, a34)(b31, b32, b33, b34)T = (m31, m32, m33, m34)
M 4 = A4 B 4 = (a 41, a 42)(b 41, b 42)T = (m31, m32)
M = AB = (c1, c 2, c 3, c 4)( B1B 2 B3 B 4)T = (m1, m2, m3, m 4)
4.3 Risk grade judgment
This paper uses the rank eigenvalue method to judge the systematic risk state in China’s banking
industry. The rank eigenvalue method means giving various risk ranks various eigenvalues, and then
calculating the comprehensive risk index. We give the no warning risk grade eigenvalue of 1, give the
slight warning risk grade eigenvalue of 2, give the mid-warning risk grade eigenvalue of 3, and give the
serious warning risk grade eigenvalue of 4. The computational formula is y= 1×b1′+ 2×b2′+ 3×b3′+ 4×b4′.
bi ′ is the membership grade of risk grade of Vi. And in the model, it means the possibility of various risk
grades.
When y belongs to [0 1] it means the risk is at the grade of no warning; if y belongs to 1 2], it
means the risk is at the grade of slight warning; if y belongs to 2 3], it means the risk is at the grade of
mid-warning; and if y belongs to 3 4], it means the risk is at the grade of serious warning.
， ，
（，
（，
38
（，
Conclusion
The above model can reflect the main types of systematic risk in China’s banking, and measure the
risk comprehensively through four subsystems. Of course, along with the deepening of China’s reform,
the early-warning indicator system should be an open system; that is to say, it may admit new indicators
and eliminate some old indicators to keep pace with the development of China’s banking.
References
[1] Graciela Kaminsky, Saul Lizondo, Carmen M. Reinhart. Leading Indicators of Currency Crises. Staff
Papers, International Monetary Fund, 1998,45( 1 ) : 1 4 8
[2] Frankel, J., A. Rose. Currency Crises in Emerging Markets: An Empirical Treatment. Journal of
International Economics, 1996(41): 351 366
[3] Demirguc-Kunt, Detragiache. The Determinants of Banking Crises in Developing and Developed
Countries. IMF Staff Papers, 1998, 45(1): 81 109
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