Novel Approaches on Sovereign Credit Ratings


EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS
Vol. 11, No. 4, 2018, 1014-1026
ISSN 1307-5543 – www.ejpam.com
Published by New York Business Global

Novel Approaches on Sovereign Credit Ratings

Nisa Ozge Onal1,∗, Ertugrul Karacuha1

1 Department of Applied Informatics, Istanbul Technical University, Istanbul, Turkey

Abstract. In this study, sovereign credit rating methodologies of CRAs and studies in the relevant
literature are examined in detail, and two dynamic methods are proposed. These models classify
countries as investable or speculative in the short term. In the first model, we used stock market
values and macroeconomic variables with the Normalized Least Mean Square (NLMS) algorithm.
Ratings for 15 countries are determined according to the short-term domestic currency. The results
that we obtained from this model are fully consistent with those of Fitch. When we compared the
results with Standard and Poor’s, we obtained different results for Turkey and Portugal. In the
second model, we used only stock market closing data from 40 composite indexes with the Artificial
Neural Networks (ANNs). Ratings are determined according to short-term foreign currency. The
results that we acquired from this model are fully compliant with Standard and Poor’s. However,
when compared to the ratings of Fitch, the results differed in the case of Russia. It has been
shown that contrary to standard approaches, high predictability is achievable for countries using
short-term data. The suggested models are more objective and dynamic due to only short-term
data being required.

2010 Mathematics Subject Classifications: 92B20, 62-07, 62F10

Key Words and Phrases: Artificial neural networks, Adaptive filters, Normalized least mean
square algorithm, Sovereign credit ratings, Stock market prediction

1. Introduction

Sovereign credit rating is determined using quantitative and qualitative features devel-
oped by the CRAs, taking into account the economic and political risks of the countries.
With the complexity of financial markets and the increase in asymmetric information, the
importance of credit ratings has increased over time. The impact of internationalization
and the widespread free market economy have removed obstacles for investors. With the
increase of international financial and economic integration, country credit ratings have
become one of the most important elements that direct the global capital flow. The impact
of CRAs on global and national economies has increased. Over time, increased financial
market complexity and borrowing diversity have gained confidence investors and regula-
tors in the views of CRAs [12]. Credit ratings affect investor decisions, thus influencing

∗Corresponding author.
DOI: https://doi.org/10.29020/nybg.ejpam.v11i4.3333

Email addresses: onal16@itu.edu.tr (N. O . Onal), karacuhae@itu.edu.tr (E. Karacuha)

http://www.ejpam.com 1014 c© 2018 EJPAM All rights reserved.



N. O . Onal, E.Karacuha / Eur. J. Pure Appl. Math, 11 (4) (2018), 1014-1026 1015

fund inflow and borrowing costs. Due to these factors, credit ratings play a major role in
the economic development and progress of countries. Factors of the CRAs affecting the
economies of the countries and the methodologies of CRAs have begun to be examined
from the 20th century [1, 7, 8, 11, 27, 34]. The implications of credit ratings and their
role in financial markets have been examined [3, 4, 9, 12, 22, 28, 36]. However, CRAs
had negative impacts on the 1997 Asia financial crises. Also, in 2008, CRAs were not
able to predict the crisis which befell many countries and companies. Furthermore, the
2008 financial crisis occurred in many countries that had been highly rated by CRAs, and
many of the high rated companies went bankrupt at that time. The realization that the
illusion of high credit ratings led to crises made people lose trust in CRAs. Studies on
the effects that CRAs have on crises, the duration of crisis and the later period have been
carried out [2, 5, 10, 16, 32, 35]. The impact of sovereign credit ratings on developing
countries, in particular, has been examined and discussed by analyzing the credit ratings
of developed and developing countries after the crisis period [14, 23, 25, 26]. These studies
were criticized for the fact that CRAs used non-public data and rated subjective evalua-
tions in their methodologies. The statistical models used by the CRAs for credit rating
have been examined and alternative models have been proposed [6, 15, 17, 29–31, 33]. In
this study, we propose alternative models to sovereign credit rating methods that classify
countries as investable or speculative. The first model assesses countries using macroe-
conomic variables and the stock market index monthly values with the NLMS algorithm.
The stock market composite index values are estimated with six macroeconomic variables
and historical stock market composite index values. Then, according to the estimation
results, a model was developed that classifies countries according to their predictability.
The results are compared with the short-term domestic currency credit ratings for the
period. In the other model, we classified the countries using the values of daily closing
stock market indices with ANNs. In the training process based on the sovereign credit
ratings of the CRAs in terms of short-term foreign currency.

2. NLMS Algorithm

Normalized Least Mean Square (NLMS) algorithm is a type of the LMS algorithm.
The difference between the LMS and NLMS algorithms is the speed of convergence. The
convergence rate of the NLMS algorithm is faster than the LMS algorithm. In the NLMS
algorithm, weight updating in time n+1 compute differently according to the LMS algo-
rithm [19, 20]. The NLMS formulation is illustrated in the following: [19]

• The output value yn is obtained by multiplying the input data by weights, as can
be seen in (1).

yn =

k∑
K=1

inkw
n
k (1)

• The error signal is calculated in (2) by the difference between the desired value and
the output value.



N. O . Onal, E.Karacuha / Eur. J. Pure Appl. Math, 11 (4) (2018), 1014-1026 1016

en = dn − yn (2)

• Minimization of error signal is made according to the Mean Square Error, as can be
seen in (3).

J =
1

2
E[e2] =

1

2
E[(dn − inkwn

k )2] (3)

• Initial weights are zero. Weight updating is calculated in (4) by minimizing the error
signal for each variable according to the following formula [13].

wk
(n+ 1) = wn +

µen

‖ink ink‖2
ink (4)

The norm process is calculated according to the following equation (5).

‖ink‖ =

√√√√ n∑
n=1

(ink)2 (5)

where k is the number of variables, n is the time series vector dimension of variables, ink
is the input variable of k in time n, weight coefficient is wn

k , the output of the system yn

is the estimation value for time n, the desired value is dn, error value is en, and µ is the
learning rate. Figure 1 shows the NLMS adaptive system.

Figure 1: NLMS Adaptive System.



N. O . Onal, E.Karacuha / Eur. J. Pure Appl. Math, 11 (4) (2018), 1014-1026 1017

2.1. Proposed Model for NLMS

The proposed model consists of two phases. In the first step, stock market value is
estimated by macroeconomic variables and stock market historical values using the NLMS
algorithm. Macroeconomic variables were determined by considering the parameters used
by the CRAs and the studies about CRAs. In the second stage, classification of countries is
carried out according to the estimation results. In the NLMS model, the µ value is used as
0.12. Although convergence is faster when the selected µ value is big, convergence is slower
but better if the µ value is smaller. For this reason, the µ value is determined by trial. The
initial weights were determined as 0.1, which is the end result of the experiments. After
the estimation, Mean Absolute Percentage Error (MAPE) values for the last 12 months
of each country are calculated. The average of differentiation of the MAPE function is
1.18. Therefore, the threshold value was set at 11.8%. Countries with a value below the
threshold value of MAPE can be invested, while those above are classified as speculative.
MAPE is calculated by the equation (6) below.

MAPE = 1/n
n∑

i=1

∣∣∣∣(v(n)− ṽ(n))

v(n)

∣∣∣∣× 100 (6)

2.2. Dataset for NLMS

In this study stock composite indices, GDP per capita, U.S. foreign exchange rate,
foreign trade, overnight interest rate, and consumer price index values are used. The
dataset includes 15 countries monthly values between January, 2007-August, 2017. The
countries in the dataset are Germany, USA, Brazil, France, Netherlands, UK, Spain, Italy,
Canada, Mexico, Norway, Portugal, Russia, Turkey, and Greece. The value of the stock
composite index for the end of the next month is estimated with this dataset. Therefore,
the results are compared with stock composite index values between 02.2007-09.2017.
Initially, the data are adjusted with the normalization equation (7). In normalization
techniques, Min-Max Normalization is used for normalization of the data. Thus, the data
are limited between 0.1 and 0.9. All data normalize in itself for it can be comparable.

x̃ = 0.8× xi − xmin

xmax − xmin
+ 0.1 (7)

where xi are the actual values of the series, the maximum value of the series is xmax, the
minimum value of the series is xmin, and normalized values are x̃ in the series.

2.3. Results for NLMS

This study proposes a new model for sovereign credit ratings with the NLMS algorithm.
Stock composite indices are estimated in the first stage. After the forecasting, MAPE
values for the last 12 months are calculated for all countries. Figure 2 shows the calculated
MAPE values of the countries. In Figure 2, MAPE values of countries are sorted from
small to large. As seen in Figure 2, there is a first biggest break in values after Spain’s



N. O . Onal, E.Karacuha / Eur. J. Pure Appl. Math, 11 (4) (2018), 1014-1026 1018

Figure 2: MAPE Values of Countries.

MAPE value. On the other hand, when we look at the derivation of MAPE function
in Figure 3, in the first increase of the series, we see that there is a deviation after the
eleventh point. Because the average of differentiation of MAPE function (T) is 1.18 to the
equation (8), the threshold value is set at 11.8%.

Figure 3: Derivation of MAPE Function.

T =
1

14

14∑
n=1

∂MAPE(n)

∂n
(8)

Therefore, if the MAPE value of a country is less than 11.8%, it can be an investable
country. If the MAPE value is greater than 11.8%, the country is classified as speculative.

Table 1 lists the stock code, MAPE values and investable and speculative classes of the
countries as of October 2017. The classification for the NLMS method completely corre-
sponds to the classification of Fitch. Additionally, compared with the Standard and Poor’s



N. O . Onal, E.Karacuha / Eur. J. Pure Appl. Math, 11 (4) (2018), 1014-1026 1019

Table 1: Stock Codes, MAPE Values and Investable Classes of Countries for NLMS.

Country Stock Code MAPE

USA DJI 2.261589
Norway OBX 2.873660
UK FTSE 3.972231
Germany GDAXI 4.149399
Mexico MXX 4.853806
Canada GTPSE 4.997015

Investable Countries Holland AEX 5.684330
Turkey XU030 6.308618
Italy FTMIB 6.901017
France FCHI 7.892553
Russia MCX 8.280763
Spain IBEX 8.875445

Greece ATG 12.24368
Speculative Countries Brazil BVSP 13.91732

Portugal PSI20 18.8586

classification, it was identical except for Turkey and Portugal. The application was made
with the Matlab 2016 (b) program. Macroeconomic data in the dataset was obtained from
the OECD database, stock index values and sovereign credit ratings from the Thomson
Reuters Eikon program in Istanbul Technical University Finance Laboratory.

3. Artificial Neural Networks

ANNs are a system that has layers in parallel with each other and has enough neurons
in each layer.

3.1. A Neuron Model

A neuron is called by Haykin (1994), an information processing unit that is fundamental
to the operation of a neural network. The basic structure of a neuron as shown in Figure
4 is mathematically as follows;

• A signal ij at the input of synapse j connected to neuron k is multiplied by synaptic
weight wkj in (9). The associated synapse is excitatory if the weight wkj is positive,
the synapse is inhibitory if it is negative.

uk =

n∑
j=1

wkjij (9)

• Bias bk is the positive or negative external parameter of a neuron k. It is added to
the output of linear combiner uk in (10).



N. O . Onal, E.Karacuha / Eur. J. Pure Appl. Math, 11 (4) (2018), 1014-1026 1020

vk = uk + bk (10)

• An activation function is called as a squashing function in the literature. The acti-
vation function determines limiting amplitude of the output of the neuron. Output
shown by in equation (11);

yk = ϕ(uk + bk) = ϕ(vk) (11)

where j=1,2, n, uk is the output of linear combiner, vk is the summing output, ϕ(.) is the
activation function, and yk the output signal of the neuron [18, 21].

3.2. Multilayer Perceptron

Multilayer neural network is a feed forward network having at least one hidden layer
between the input and output layers. The hidden layer is composed of hidden neurons
directly related to the neurons of the input and output layers and it includes a non-linear
activation function [21].

3.3. Application Model for ANN

In this study, multilayer feed-forward networks consisting of one hidden layer were
used. In the hidden layer, the hyperbolic tangent function was used as a transfer function.
A linear function was used in the output layer. The hidden layer contains three cells,
and the output layer contains one cell.In Figure 4 represents that the application neural
network architecture.

Figure 4: The Application Neural Network Architecture.

In the network training process, Mean Square Error was used as a cost function. Gradient
descent with momentum and adaptive learning rate were used to update the weight values
to equation (12).

∆wkj(n) = −µ∂E(n)

∂wkj
+ α∆wkj(n− 1) (12)

where α is a momentum constant, wkj is weight, and E is the mean square sum of differ-
ences between the values of target and output of the network [18]
. In the model, credit ratings are set as 1 for the investable grade and 0 for the speculative



N. O . Onal, E.Karacuha / Eur. J. Pure Appl. Math, 11 (4) (2018), 1014-1026 1021

grade. The stock price of the countries included in the training set have been trained ac-
cording to the determined credit ratings (1 or 0). After the training, the rating classes of
the countries in the test set were estimated. In the training and test results, ’1’ is assigned
to the values that are greater than 0.6 for investable class. Values smaller than 0.4 are
assigned to the speculative class by assigning a value of ’0’. For the remaining values, it is
planned to assign a value of ’0.5’. However, when we look at training and test results as
shown in Table 2, there is no class of ’0.5’ because none of the countries are between 0.4
and 0.6. If we had value in this range, we would use fuzzy logic methods to decide which
one is investable or not [24].

3.4. Dataset for ANN

The model aims to classify the countries as investable or speculative with the Artificial
Neural Networks method based on the sovereign credit ratings of the CRAs in terms of
short term foreign currency. Changes in macroeconomic variables also affect and reflect the
stock exchange market. Therefore, in this study, we only used stock exchange variables. A
feed-forward network consisting of a single layer of three hidden neurons was used. For this
model, 239 trading days daily closing data until 29.08.2017 from 40 stock exchange indices
of 38 countries were used. Countries from various regions of the world were included.
The dataset is divided into 70% training data and 30% test data because the best results
obtained in that rates. Various rates of train, validation, and test have tried and see
the results in the Table 2 below. Test data consist of the stock composite index of 12
countries in the America-Dow Jones Index, Argentina, Indonesia, Ghana, India, Hong
Kong, Sweden, Malaysia, Mexico, Russia, Turkey, and Greece.

Table 2: The Rate of Train, Validation, and Test Data and Its Error.

Train Rate Validation Rate Test Rate Number of Error

1/3 1/3 1/3 3

4/10 - 6/10 2

5/10 - 5/10 2

6/10 - 4/10 2

7/10 - 3/10 0(S&P) and 1(Fitch)

3.5. Results for ANN

The results were compared with the sovereign credit ratings of the CRAs in terms of
short-term foreign currency. Table 3 indicates ANN results and class of the countries in the
train and test set. The results that we acquired from this model are fully compliant with
Standard and Poor’s. However, when compared to the ratings of Fitch, the results differed
in the case of Russia. In the Table 4 represent the accuracy rate of test result. Thus, this
method can be used for determining the changes in the credit ratings of countries and
predicting the credit ratings of countries. The application was made with the Matlab
2016 (b) program.



N. O . Onal, E.Karacuha / Eur. J. Pure Appl. Math, 11 (4) (2018), 1014-1026 1022

Table 3: Stock Codes, MAPE Values and Investable Classes of Countries for ANN.

Country Stock Index Spot Code Results Class

America NASDAQ NDX 1.002 1
America SP 500 SPX 0.98 1
Australia AXS 200 AXJO 0.99 1
Belgium BEL 20 BDX 1.00 1
Britain FTSE 100 FTSE 0.98 1
Brazil BOVESPA BVSP 0.006 0
Canada SP/TSX GSPTSE 1.006 1
Chile IPSA IPSA 0.99 1
China CSI 300 CSI300 1.009 1
Egypt EGX 30 EGX 30 -0.0002 0
France CAC 40 FCHI 0.97 1
Germany XETRA DAX GDAXI 1.01 1
Israel TEL AVIV TA125 0.99 1
Italy FTMIB FTMIB 1.002 1
Netherlands AEX AEX 1.01 1
New Zealand NZX 50 NZ50 1.00 1
Nigeria NSE 30 NGSE30 -0.002 0

Training Set Norway OBX OBX 0.99 1
Pakistan KSE 30 KSE 0.001 0
Philippines PSEI PSI 0.99 1
Portugal PSI 20 PSI20 0.003 0
Qatar DOHA QEAS 0.99 1
South Korea KOSPI 200 KS200 1.00 1
Spain IBEX35 IBEX 1.00 1
Switzerland OMXS30 OMXS030 0.99 1
Taiwan TSEC TSE50 1.00 1
Ukraine UX UAX -0.005 0
Vietnamese HNX HNXI 0.0002 0

America DJI DOW-JONES 30 DJI 1.05 1
Argentina MERVAL MERV -0.15 0
Ghana GSE GSECI 0.04 0
Greece ATG ATG 0.34 0
Hong Kong HANG SENG HSI 0.61 1
India CNX NIFTY NSEI 1.02 1

Test Set Indonesia JAKARTA JKSE 0.85 1
Malaysia KLCI KLSE 1.00 1
Mexican IPC MXX 0.94 1
Russia MICEXFNL MICEX -0.02 0
Sweden SMI SSMI 1.06 1
Turkey XU30 XU030 -0.05 0



REFERENCES 1023

Table 4: Accuracy Rate of Test Result in ANN model.

STANDARD and POOR’S FITCH
Results Investable Speculative Investable Speculative

Investable 7 0 7 1
ANN Speculative 0 5 0 4

Accuracy Rate 100% 91.67%

4. Conclusion

In this study, proposed two novel approaches about sovereign credit rating. The appli-
cation results have been shown that contrary to standard approaches, high predictability
can be made for countries using short-term data. In NLMS method, we have differentiated
the data set of 15 countries using macroeconomic data. However, it is not possible to reach
the data of every country, especially underdeveloped and developing countries. Due to this
problem, we wanted to develop a more general model using ANNs that predicts sovereign
credit ratings. It is important that the data set is sufficient for learning in ANNs. For this
reason, we have included 40 countries from various regions of the world in our ANN data
set. Because of the changes in macroeconomic variables also affect and reflect the stock
exchange market, we only used stock exchange variables in the ANN data set.
Therefore, two novel approaches were obtained with two different data sets. The suggested
models are more objective than CRAs ratings and offer more dynamic results because only
short-term and public-data are required. Consequently, investors will be able to produce
their own estimates with current values using the models recommended at intervals when
the CRAs do not update.

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