Modern Economy, 2012, 3, 759-765
http://dx.doi.org/10.4236/me.2012.36097 Published Online October 2012 (http://www.SciRP.org/journal/me)
A Research on Interbank Loan Interest Rate
Fluctuation Characteristics and the VaR Risk
of China’s Commercial Banks
Baoqian Wang, Cheng Wang, Xikun Zhang
Business School, Hohai University, Nanjing, China
Email: Bq64@163.com, hhucwangcheng@126.com, zxk19870910@163.com
Received June 20, 2012; revised July 22, 2012; accepted August 1, 2012
ABSTRACT
According to the historical time series data of commercial interbank, this paper examines the interest rate fluctuation
distribution characteristics, indicating that EGARCH Model can b etter fit the rate volatility of th e interbank market in-
terest. This paper calculates the value at risk (VaR) of five major commercial banks using EGARCH Model with such a
conclusion that the difference that major commercial banks face is various. The interest risk of state-owned commercial
banks and other financial institutions is more serious than the city commercial banks and foreign banks. The interest
risk of rural credit cooperatives is the least serious.
Keywords: GARCH Model; Interest Rate; VaR
1. Introduction
Since 1996, the speed of China’s market interest rate
process put fast gradually, letting go the interest rate of
the inter-bank market interest treasury bonds and policy
financial bonds. Domestic and foreign currency loans
and large foreign currency deposit rates are also involved.
Long-term RMB large deposit agreement is available and
at the same time china gradually expands the floating
range of RMB deposit and lending rates. With the market
operation of china’s interest rate, the issue of interest rate
risk measurement and management has become unavoi-
dable. By using statistical knowledge and VaR model,
this paper analyzes China’s interest rate market risk dis-
tribution patterns and quantifies the interest rate risk of
commercial banks in China.
2. Literature Review
Since 1978, china’s commercial banks have experienced
a series of management system reforms. But before 1993,
commercial bank interest rate has always been under
control, never out of the planned economic system. In
this period, domestic focus is on the research of the
regulation of commercial bank interest rate. Huang Jian-
feng (2001) systematically expounds on the normative
operations of the commercial bank deposit and loan in-
terest rate [1]. Ge Qi (2003) systematically introduces
foreign measurements and management methods on in-
terest rates. In practice, he actively explores the advanced
technologies and methods to be used in commercial
banks’ interest rate risk management approach [2]. Dai
Guoqiang (2005) uses the VaR method, the stochastic
analysis method and the option pricing method to put
forward the choice of benchmark interest rate of china’s
commercial banks, together with the interest rate trend
forecast in order to effectively control the interest rate
risk, and enhance their own competitiveness [3].
China’s interbank market interest rate research begins
relatively late. In the early days; it is primarily based on
qualitative analysis, but in recent years it terms into
quantitative analysis. Tang Qiming and Gao Xiang
(2002): interbank market interest rate of different terms
is in line with the expectations of interest rate term
structure theory [4]. Xu Hanfei (2004): by using ECM
model, Xu studies the transmission mechanism of central
bank loan interest rate to interbank loan interest rate
transmission, and finds that the transmission mechanism
is asymmetric and dynamic, and the adjustment that cen-
tral bank transmits to refinancing interest rate is only
about 60% direct conducted to the inter-bank market
interest rates [5]. Lin Hai, Zheng Zhenlong (2003): by
integrating Vasicek model and CIR model into GARCH
model, Lin and Zhang discusses china’s interest rates,
but they don’t give a further research on rate volatility
[6]. Dong Le (2006): Dong validates the dual asymmetry
of china’s short-term interest rate in terms of mean ve-
locity and the conditio nal variance. He gives the features
that the correlation coefficient of the inter-bank market
C
opyright © 2012 SciRes. ME
B. Q. WANG ET AL.
760
interest buyback rates is close to 1a suppose, namely,
foreign classic model doesn’t create very effective results
about the prediction of the term structure of interest rate,
which will even worse than the random walk. But he has
no further validation [7]. Zhang Na, Huang Xinfei, Liu
Deng (2006): in the process of constructing GARCH
model to analysis China’s various term interbank market
interest rate volatility, they discover GARCH model can
better explain the interbank market interest rate fluctua-
tion. Such fluctuation and the lag period fluctuation are
smooth and show a smoothly decreasing trend, but the
volatility is not serious [8]. Zheng Yaotian, Du Ziping
(2007): Zheng and Du fit the inter-bank overnight rates
by using EGARCH model, finding out the EGARCH (1,
3) model the best fitting one, which fully embodies the
overnight lending market information asymmetry. They
also do the short term prediction by EGARCH (1, 3) and
obtain ideal forecasting effect, thereby determine a suit-
able model for China’s interbank market interest rate
forecasting [9]. Li Jie, Gao Ning, Chai Jun (2007): Li and
Gao establish AR (P)-EGARCH model in China’s in-
terbank market. From liquidity, transaction volume and
structural changes terms, they explore the various influ-
ence factors for daily overnight interest rates of varieties,
proving that the positive leverage effect exists for the
sequence fluctuation in overnight lending market [10].
Liu Xiangyun (2007): doing a theoretical and practical
analysis for china’s commercial bank interest rate risk in
terms of interest rate term structure on the basis of
drift—jumping methods. A mean reversion phenomenon
is discovered in the short term market interest rate, such
as 7-day period Chinese bond repurchase rate and 7 days
interbank rates [11 ].
The VaR method was first adopted in J. P. Morgan
risk management practice of the last 90th century. Phil-
ippe Jore (1995) publishes the master piece systemati-
cally introducing VaR and its application. Philippe Jore
dose the all round discussion about VaR’s mathematical
statistics basis, calculation process and ways of applica-
tion [12].
Chew & Lilian (1996): summing up the calculation
parameter method for VaR, historical simulation method
and the Moncaro simulation method [13]. Futher more,
Duffle & Pan (1 997) and Jorion (200 0) respectively does
profound summary in Risk Value and Value at Risk:
Risk Control Reference. Among them, the application of
various methods to compare the effects of the research is
particularly enlightening [14,15].
To sum up, foreign researches mainly focus on the
model application, while the domestic researches mainly
concentrate on the model selection , rarely on risk quanti-
tative analysis and forecast. China’s interbank offered
rate (CHIBOR) is China’s first market-oriented interest
rates, so it could sensitively react to the supply and de-
mand situation in monetary market. As a result, the in-
terbank interest rate can be regarded as the benchmark
interest rate for China’s monetary market. With this hy-
pothesis, the paper tests the applicability of GARCH
model and makes a short-term prediction for the 7 days’
interest rate. Given a certain degree of confidence of
china’s commercial banks, based on the fitted model an d
various periods of different variance, by using bank in-
terbank borrowing trading positions, the commercial
bank risk values can be measured and compared analysis
will be available.
3. The Selection and Construction of Interest
Rates Model
3.1.The Normality Test for the Sample of
Inter-Bank Interest Rate
This paper uses the interbank market interest rate as the
market interest rate (Shanghai Interbank Offered Rate,
referred to as Shibor )to inspect china’s commercial bank
lending position risk. The purpose is to reflect the inter-
est risk of China’s commercial banks under the back-
ground of market orientated interest. At present, been
announced Shibor varieties includes overnight, 1-week,
2-week, 1-month, 3-month, 6-month, 9-month and 1-year.
This paper analyzes the data from 2007 to 2011, accord-
ing to the 1-week Sh ibor.
Sample of this paper is from 01/01/2007 to 31/12/2011.
There is totally 1249 statistics of 1 -week Shib or. And the
fitting prediction sample is from the first quarter of 2012.
Data processed by Eviews software.
From 1-week Shibor wave pattern (Figure 1), it could
be seen that the market interest rate violates strongly, so
the sequence is not stable. In order to get a stable return
time series data, some techniques need to be done. Using
the equation 1t
log log
tt
yrr
for the logarithm of a
first-order differential treatment, and make its become
more stable income sequence (Figure 2).
0.0
0.5
1.0
1.5
2.0
2.5
3.
0
200 400 600 8001000 1200
R7
Figure 1. 1-week shibor rate fluctuation.
Copyright © 2012 SciRes. ME
B. Q. WANG ET AL. 761
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
200 400 600 800 1000 1200
Y7
Figure 2. The rate difference fluct uation f i gure. Data sources
: Time series of daily interbank interest rate market.
st
3.2. Inspection of ARCH Effects
of information in
ina’s commercial
ba
3.2.1. Autocorrel at i on Test Y7 on a delay of 18 orders,
of Figures 1 and 2: http//:www.bba.org.uk/;
http//:www.chinamoney.com.cn/.
t
r
Do the normality test using the differential logarithmic
atistics and the results (Table 1) show that, in the 1-week
inter-bank lending market, the average rate of return is
0.001097; the skewness (S) is 0.419 660; t he k urt osi s (K) i s
42.33005; the statistic value of J-B test of normality is
81398.90 with a probability of 0. Information got from the
above statistical value is that the volatility of the return
rate is strong and the time series is not in line with the
normal distribution for the presentation of “fat-tail phe-
nomenon”. The intermediate portion contains a large
amount of statistical information. Therefore, we need to
use the GARCH model distribution instead of normal dis-
tribution so as to im prove the model fitting effect s.
Because of the different availability
different moments, financial time series usually has a
peak, thick tail and cluster characteristic. In order to deal
with these characteristic, Engle proposed “Conditional
Heteroscedasticity Regression Model” (Auto Regressive
Conditional Heteroscedasticity, ARCH Model) to deal
with such problems. The model uses a regression form
and all the available in formation to describe the variance
of the variance. In 1986, Bollerslev proposed “GARCH
Model” (Generalized Auto Regressive Conditional Het-
eroscedasticity Model), which was also called the gener-
alized autoregressive conditional heteroscedasticity mo-
del. It is the expansion from of the most basic conditional
variance function ARCH model, and it has a strong ad-
vantage in the explanation and establishment of variance
of time series. In 1990, Zakoian proposed “TARCH
Model” (Threshold ARCH), namely the asymmetric con-
ditional heteroscedasticity regression model. It explains
the phenomenon in the stock market that while the
crash and the roar margin are the same, the crash process
is always accompanied by the serious fluctuation. In
1991, Nelson propo sed “EGARCH Model”, it ef fectively
depict the conditional variance of positive, negative in-
terference of the asymmetric response.
The above analysis shows that ch
nk lending rate distribution does not conform to the
normal distribution hypothesis, therefore, through a vari-
ety of conditions heteroscedastic model comparison, we
need select the optimal GARCH model to fit china’s
commercial bank interb ank market interest rates.
Do the autoco rr elatio n test on
and the test results are shown in Table 2. On the 0.05
significance level, th e probability P valu e was 0, which is
less than 0.05. Inspection instructions show that until
higher-order sequence, the yields still remain a strong
correlation relationship. So now the return series auto-
regressive model is being fitted. Given the yield of the
sequence
t
y
after autocorrelation and partial auto-
correlation the following model is selected to fit the
sequence test,
t
y
. Use maximum likelihood estimation me-
thod to est the parameters.
112 2
yc yy
imate
33tttt
y
t
 
 
(1)
3.2.2. The Stationary Test 3) to check the smooth of se-Use the unit root test (Table
quence. As the stationary of the sequence directly affect the
model fitting result, and the non-stationary data sequence
will produce a false return we have to test the stationary of
the sequence. Here we use the method of Augmented
Dickey-Fuller (ADF) to make unit root test for yield se-
quence
t
y
. The ADF value is –17.20466, which is less
than 1% 5% significance level. So the unit root
and
Table 1. Normal inspection result.
Mean Kurtosis st P value
Standard Partial J-B
deviation degree atistics
Y7 0 0.0020.050760.41955042.32008 81398.900.000000
D sof
Table 2. The autocorrelation test of yields.
ata ources: The result f the empirical study by using the software o
Eviews. Statictics database: Figures 1 and 2 http//:www.bba.org.uk/; http//:
www.chinamoney.com.cn/.
7 days lending of inter-bank
Delay in order e Q-statistic P valu
6 56.492 0.000
12 71.981 0.000
18 77.592 0.000
Data sour result of the estudy by using are of ces: Thempirical the softw
Eviews. Statictics database: Figures 1 and 2 http//:www.bba.org.uk/; http//:
www.chinamoney.com.cn/.
Copyright © 2012 SciRes. ME
B. Q. WANG ET AL.
762
hypothesis are rejected by the test values, indicating that
the sequence of yield

t
y
is a stationary sequence.
3.2.3. ARC H T e st
In order to see whether the Conditional Heteroscedastic
exists in the return series
t
y
, the paper uses Lagrange
multiplier method to do thst. Make a 3 lag ARCH
effect test for the residuals of the regression equation,
and from the test results (Table 4), we could see that the
F-statistic and the LM-statistic probability value is rela-
tively 0.000227 and 0.000241, less than 0.05. The origi-
nal assumptions rejected hence ARCH effect exists in the
model.
3.3. Int
e te
erest Rate Model Selection
nd TARCH mo-
t
Compare ARCH, GARCH, EGARCH a
del in terms of the residuals, depending on the Akaike
Information Criterion (AIC), Schwarz (SC) guidelines
and the LL principle of maximum likelihood function
value, and hence select the most suitable model.
The modeling process: select the inter-bank lending of
1249 continuous-time series data and compare the re-
siduals of ARCH (1), GARCH (1, 1), TGARCH (1, 1)
and EGERCH (1, 1) (Appendix 1). The appendix shows
the AIC and SC of EGARCH (2, 1) is the smallest; the
LL value of TGARCH (1, 1) is smaller than EGARCH (2,
2); the fitting coefficients of EGARCH (2, 1) are higher
than TGARCH (1, 1). Consider the overall results;
EGARCH (2, 1) model is selected to fit the inter-bank
interbank of fer ed rat e seque n ce
According to the results of fitting model, the 7-day in-
ter-bank lending yield model is:
0.11742
t
y2
9t
y
 (2)
Table 3. The unit root test results.
alue ADF statistics Critical v
1% –3.4384
5% –2.8643
Inter-bank 7
day lending –17.20466
10%–2.5682
Data sources: The result of the empirical studyng e of
Eviews. Statictics database: Figures 1 and 2 http//:www.bba.org.uk/; http//:
4. ARCH effect test.
by usithe softwar
www.chinamoney.com.cn/.
Table
ARCH Test
F-stat 20709 P 0.000227
istics 4.8
Inter-bank 7
day lending L M-statistics23.76079 P 0.000241
Da reicasthf
Eviews. Statictics database: Figures 1 and 2 http//: www.bba.org.uk/; http//:
ta sources: The sult of the empirl study by uing e software o
www.chinamoney.com.cn/.
1
log0.642986 0.947445log
tt
hh
12
12
2
2
0.647886 0.125999
0.110117
tt
tt
t
t
hh
h





(3)
Do the ARCH effect test for the above model, and the
accom
lly
panied probability of the F-statistics and LM are
bigger than 0.05. Test results indicate that the model can
be accepted for there is not any Conditional Heterosce-
dastic.
In order to further empirically test the validity of
EGARCH (2, 1) model, we selected 72 data of inter-bank
lending ra te from January to March of 2012 to make p re-
diction. Compare the pred ictive value with the true value
(Figure 3). From the prediction results, we could see that
the predicted rates fluctuate around the real rates, and the
margin between them is very small. The trend of the fit-
ted curve is in line with the real rates curve, and the pre-
diction error is very small which also shows the applica-
bility of the model. Consequently, EGARCH (2, 1) pre-
diction is applicable in the lending and borrowing inter-
est rate risk management of china’s commercial banks.
4. VaR Estimation of China’s Commercial
Banks
The size of commercial bank interest rate risk is usua
measured by the value at risk VaR. The so-called value at
risk is the maximum possible loss given a certain confi-
dence interval and time interval. The equation is (given
confidence level
):

VaR WEr r
0
 (4)
In the equation, means the init
cial asset or 0
W
ial value of a finan-
portfolio;
Er means the expected rate of
Figure 3. Predictive value compared with the actual val-
ues.
Copyright © 2012 SciRes. ME
B. Q. WANG ET AL. 763
return. Use Equation (1) to calculate the relative losses of
VaR equivalent to the expected rate of return.
If the yield submits to normal distribution

2
~0,rN t
”, we could calculate sub-sites
Z
, and
then we could calculate “rZ


”. He the
following equation:


VaR WE
nce
00
r rWZ

 (5)
However, because of the peak, thick tail
tion c
onditions of Different Vari-
nce.
and aggrega-
haracteristics of financial time series, normal dis-
tribution will underestimate the interest rate risk.
Thus according to the previous analysis, the EGARCH
(2, 1) conditional variance model is used to measure the
VaR of interest rate market in order to solve the underes-
timated interest rate risk.
According to EGARCH (2, 1), this paper calculates
the different variance in lending and borrowing market
conditions (Table 5). Take conditional standard devia-
tion into Equation (2), and dynamic VaR estimation will
be got according to the net position of the main five
commercial banks given the condition of 99% confidence
level. And according to the daily VaR of the first quarter
of five commercial banks, the dynamic VaR map (Figure
4) can be got. From the figure, the interest risk of China’s
commercial banks is intense.
Table 5. 2012 First 1uarter C
a
r1 0.019198 r21 0.000714 r41 0.001287
r2 0.012258 r22 0.000530 r42 0.001630
r3 0.008530 r23 0.000906 r43 0.001971
r4 0.006222 r24 0.000542 r44 0.002027
r5 0.005144 r25 0.000478 r45 0.002202
r6 0.003876 r26 0.000516 r46 0.002645
r7 0.002743 r27 0.000403 r47 0.003544
r8 0.001922 r28 0.000446 r48 0.002305
r9 0.001886 r29 0.000560 r49 0.001849
r10 0.002054 r30 0.000621 r50 0.001699
r11 0.001352 r31 0.000515 r51 0.001951
r12 0.001609 r32 0.000411 r52 0.001609
r13 0.001127 r33 0.000330 r53 0.001699
r14 0.001250 r34 0.000353 r54 0.001644
r15 0.000828 r35 0.000384 r55 0.029758
r16 0.000821 r36 0.000424 r56 0.018808
r17 0.000628 r37 0.000574 r57 0.013634
r18 0.000506 r38 0.000524 r58 0.009183
r19 0.000396 r39 0.001812 r59 0.006265
r20 0.000900 r40 0.001438 r60 0.004414
So Ch(w hin)rdom-
mbaositi lcuuday
urce:
ercial ina currency
nk lending pww.c
on caamoney.com.cn
lation of first q, a cco
arter ing to the c
s.
0
4
8
12
16
510 15 20 25 30 35 40 45 50 55 60
VAR1 VAR4
VAR2
VAR3 VAR5
Figure 4. Dynamic VaR value of the interbank mark
he above VaR of the first quarter of dif-
onclusions
(2, 1) model can
et
lending position.
According to t
ferent commercial banks, by using Eviews software this
paper could draw the VaR statistical analysis of China’s
interbank borrowing position on the 7-day dynamic for
china’s commercial banks (Appendix 2).
According to the statistical results of Appendix1, the
standard deviation of the national commercial banks and
other financial institutions is 2.168015 and 2.098728,
indicating the dramatic violations in its VaR, and the
correspondingly larger risks. The VaR of city comercial
banks and foreign banks is relatively small, with the
standard deviation of 0.380789 and 0.353807 respec-
tively and the performance is relatively stable. The VaR
of the rural credit cooperatives are the most minimum
with a standard deviation of 0.023426, which is the most
stable one in terms of the performance.
Through the analyses, it could be seen that the scale of
assets and liabilities of China’s rural credit cooperatives
and foreign banks is relatively small, with a small
amount of money lending and more borrowing money
from the capital side, which means a small corresponding
dynamic VaR. For national commercial banks, city com-
mercial banks and other financial institutions, their scale
of assets and liabilities is larger and more dynamic, so it
has the higher risk in VaR (Appendix 3).
The results of the analysis in Appendix 1 are consis-
tent with Appe ndix 2.
5. Summary and C
This article has proved that EGARCH
better describe the characteristics of interest rates distri-
bution in china’s commercial interbank loan market
through theoretical and empirical research. Therefore, it
Copyright © 2012 SciRes. ME
B. Q. WANG ET AL.
Copyright © 2012 SciRes. ME
764
success
si
rket conditions heteroscedastic. Take the condi-
tio
e of statistical description, it can be
th
could be a useful tool for commercial banks to undergo
the risk management by using VaR estimation.
Establish the model of ARCH (1), GARCH (1, 1),
TGARCH (1, 1) and EGARCH (2, 1) and make- [2
ve comparison. The AIC and SC of EGARCH (2, 1) is
the smallest, the LL value of TGARCH (1, 1) is smaller
than EGARCH (2, 1) but the fitting coefficient of
EGARCH (2, 1) is larger than TGARCH (1, 1). In com-
prehension, EGARCH (2, 1) can better describe the dis-
tribution of the series of the interest rate of inter lending
and borrowing market in china’s commercial banks, and
as a result, EGARCH (2, 1) could be used as the fitting
model.
Use EGARCH (2, 1) model to calculate the interest
rate ma
ns heteroscedastic into VaR model so that the dynamic
VaR estimation of night and 7-day lending position could
be figured out according to the daily net trading positions,
on the confidence level of 99%. From the final results, it
could be seen that the fluctuation of china’s interest rate
in the interbank lending and borrowing market is serious
and violate, indicating china’s interest rate in the inter-
bank lending and borrowing market has been fully mar
ket-oriented.
From the Bank lending and borrowing yields dynamic
the VaR valuseen [9] Y.-T. Cheng and Z. P. Du, “EGARCH Model in the In-
terbank Offered Rate Forecast,” Hubei Institute for Na-
tionalities, Vol. 1, No. 6, 2007, pp. 234-237.
at the risk value and the standard deviation of national
commercial Banks and other financial institutions is big-
ger, and dramatically changed. City commercial Banks
and foreign banks’ interest rate risk value is smaller, the
performance was stable. The risk of rural credit coopera-
tives is the smallest and the most stable. According to the
value, the risk of china’s state-owned commercial Banks
and other financial institutions is the largest, followed by
city commercial banks and foreign banks and finally are
the rural credit cooperatives the scale of assets and li-
abilities of China’s rural credit cooperatives and foreign
banks is relatively small, with a small amount of money
lending and more borrowing money from the capital side,
which means a small corresponding dynamic VaR. For
national commercial banks, city commercial banks and
other financial institutions, their scale of assets and li-
abilities is larger and more dynamic, so it has the higher
risk in VaR.
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B. Q. WANG ET AL. 765
Appendix
Appendix1. The inter-bank lending mode l c ompar ison.
Project CH (1, 1) EGARCH (2, 1) Coefficient ARCH (2) GARCH (1, 1) TGAR
AR (2) 2
–0.288315 –0.095982 –0.117429
AR (3) 3
–0.143736 –0.088460 –0.154973
C 0
0.000612 6.24E-05 2.36E-05 –0.643986
ARC) H (11
0.000612 0.415604 0.171395
ARCH (2) 2
0.596140
GARCH (1) 1
0.723542 0.771214
(RESID<0)
)*ARCH (1
0.514711
|RES|/SQR[GARCH] (1) 1
0.647886
RES/SQR[GARCH] (1) 1
–0.
|RES|/S
065162
QR[GARCH] (2) 2
–0.125999
RES/SQR[GARCH] (2) 2
–0.110117
EGARCH (1)
0.947445
AIC –3.634324 –3.861316 –3.914027 –3.
R-squared
940930
SC –3.613932 –3.845002 –3.889557 –3.912399
LL 2294.624 2436.629 2471.837 2491.757
0.018445 0.006557 0.024882 0.027082
ppendix 2. Commrcial intertions dyR value (Uillion).
dard Deviation
Aebank posinamic Vanit: 100 M
Mean Minimum Maximum Stan
National commercial banks 0.804891 0.005253 13.65921 2.168015
City commercial banks 0.255048 0.000601 1.917143 0.380789
Foreign banks 0.198768 0.002183 1.910912 0.353807
Rural credit cooperatives
VAR value
0.019253 0.000434 0.166527 0.023426
Other financial institutions 0.524792 0.001202 15.86409 2.098728
sitions of theer-bag (Unllion).
in Max
Appendix 3. Net po 7-day intnk lendinit: 100 Mi
Net Position Mean M
National commercial banks –243.197.–4691.1640 –78.18607 2900 0000
City commercial banks 2943.8800 49.06467 –9.800000 105.9300
Foreign banks 1529.3140 25.48857 –42.72000 132.7900
Rural credit cooperatives
Lending position
–266. –228.
215.7400 3.595667 –8.10000 25.64000
Other financial institutions 7100 –4.445167 8000 201.4400
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