This document presents research on developing a Turkey Financial Risk Index (TFRI) using daily data from the interbank, credit, equity, and foreign exchange markets between 2004-2014. Researchers constructed the index using principal components analysis and compared equal-weighting. GARCH and Markov switching models were used to model the index. The results showed the CDS market was the most significant factor influencing the index. The researchers conclude the TFRI can help monitor financial stress and be used as an early warning signal or exogenous variable in other models.

1. TURKEY FINANCIAL STRESS RISK INDEX AND
ECONOMETRIC MODELING USING GARCH AND MARKOV
REGIME SWITCH
Prof. Veysel Ulusoy, Özgür Ünal Onbirler and Yunus Emre
Özcan
Department of Financial Economics, Yeditepe University
Istanbul,Turkey

2. Turkey Financial Risk Index (TFRI)
• The Turkey Financial Risk Index (TFRI), which delivers a signal of financial
stress by means of the daily public data of major financial market areas the
credit, foreign exchange, equity, and interbank markets.
• Different types of weighting methods are applied and the methods are
compared in order to capture the relative significance of these four areas. The
results are compared to alternative indexes in order to demonstrate how this
index can be used for systemic stress monitoring or as an early warning
system exogenous variable.

3. Data & Methodology
• Four financial markets: interbank, credit, equity, and foreign exchange are
utilized to structure the index
• In order to provide continuous data market factors are selected according to
their availability. Continuous and reliable constructive data considerations
compensate index depth restrictions due to unavailable and missing data.
• The data set consists of daily values starting from 1 January 2004 until 24
January 2014

4. I—Interbank and swap markets
• The difference between the three-month LIBOR rate and three-month FX
implied TL interest serves as a common indicator of risk appetite. Liquidity
Spread =3 mo FX Swap – 3 mo Libor (1)
• Where 3moLiborrepresentsthree-month LIBOR rates and 3mo FS swap
represents 90-day FX implied interest rate.

5. II—Foreign exchange markets
• Weighted Lira crash –This indicator measures the rate of increase in
the USD/TRY rate with respect to the highest rate achieved in the last
one year period.
The formula for this factor is:
• Where x stands for the USD/TRY Exchange rate.

6. FX Volatility
• This indicator measures the rate of increase in the FX volatility rate
with respect to the highest rate in the last one year.
• The formula for this factor is:
• Where x stands for the USD/TRY 3 month implied USD/TRY
volatility rate

7. III—Credit markets
• CDS crash –This indicator measures the rate of increase in the CDS
rate with respect to the highest rate in the last one year.
• The formula for this factor is:
• Where x stands for the 5Y CDS of Turkey.

8. IV—Equity markets
• Stock market crash –This indicator measures the rate of decrease in the stock
index value with respect to the highest rate in the last one year.
• Where x stands for the stock index of Turkey.

9. Variable Transformation
• The individual time series must be transformed to prepare for
aggregation into the index. A cumulative density function (CDF) is
created for each factor.
• The process of creating a CDF involves an intermediary step of
computing a rank ordering of the data. The cumulative density
functions are computed according to the formula below subsequent to
construction of the rank series:
•

10. Variable Weighting
• Once the CDF’s are calculated the contribution of each factor to the overall index has to
be determined according a weighting scheme. There are different ways of weighting in
the literature; this study has compared two alternative weighting schemes:
• (i) Equal weights – In this methodology equal importance is given to all factors
according to the common weighting scheme. The apparent problem is this methodology
is arbitrary and has no economic explanation to give all factors same weight.
• (ii) Principal component – Orthogonal eigenvectors of the variance–covariance matrix
of the data is a common approach for detection of the interaction among factors. Every
eigenvector reveals a certain proportion of the variability in the data. Mainly a single
factor is responsible for the greater part of the overall variability. An examination of the
variance–covariance matrix of the 5 series in this study reveals that there is more than a
single eigenvector specifically four eigenvectors, which together add up for about 95
percent of variability. Ultimately the weighting vector is shaped by taking the weighted
sum of the stated four eigenvectors. This methodology is not justified by any a priori
analysis which is one of the main drawbacks; consequently, the quality of results is
related to the features of the data.

11. Descriptive statistics
• As it can be seen in Table 1 and Figure 1, Jarque-Bera test, skewness
and kurtosis of Turkey Risk Index data indicate that the data is not
normally distributed. It has to be taken into consideration in modeling
steps that the data is not normally distributed.
Table 1: This table presents results of Turkey Composite Risk Index distribution analysis
Mean Median Skewness Kurtosis Jarque-Bera Probability
Index 0,4997 0,5084 -0,4840 2,6247 113,7381 0,0000

12. Turkey Risk Index Histogram

13. An Application of Markov Switching Models
to TFRI

14. Results
Table 2: Parameter estimates of the MS(2) AR(1) model for the TRFI
Variable Coefficient Std. Error z-Statistic Prob.
mu(0) 0,3588 0,0293 12,226 0,0000
mu(1) 0,5020 0,0231 21,693 0,0000
AR(1) 0,9186 0,0188 48,949 0,0000
LOG(SIGMA) -3,1749 0,0408 -77,776 0,0000
P11-C -0,1070 0,5867 -0,182 0,8552
P21-C -3,6910 0,4390 -8,408 0,0000

15. Analysis of Results
• The mean level of regime 0 is 0,3588, which is stated in the table 2 as
mu(0) indicates financial high stress level of the Turkey as clearly differs
from the normal stress regime mean 0,5020 (mu(1) ) which is 39 %
higher than mu(0).On the other hand we can clearly see in the table 3
where the probability of moving regime 1 to regime 0 is %52,67, which is
very high probability as we consider the high stress regimes are rare
events. Moreover expected duration of high level of stress regime moving
to normal stress level regime is 41 weeks.

16. TFRI And Fitted Model

17. Transition Probabilities
• The probability regime graphs shows that the transition probabilities from
one regime to the other regime are considerably high violating the
assumption in former studies that the stress level periods are rare events.

18. Garch Model
• The five factors are modeled separately by GARCH and the residuals
are calculated accordingly. The outlier residuals above two standard
deviations are flagged as one and the remainders are set to zero which
provides 5 new dummy variable endogenous time series as factors for
modeling the risk index.

19. Results
Parameter Coefficent
Standard
Error T statistics
CDS
c 0.0014 0.0005 27.0020
k 0.0000 0.0001 8.4109
GARCH(1) 0.7911 0.0171 46.2441
ARCH(1) 0.1507 0.0135 11.1357
Stock Index
c -0.0013 0.0003 -4.4563
k 0.0001 0.0000 4.8623
GARCH(1) 0.8607 0.0140 61.4036
ARCH(1) 0.1118 0.0118 9.4993
USDTRY
c 0.0001 0.0001 0.4422
k 0.0000 0.0000 4.7979
GARCH(1) 0.8459 0.0127 66.8331
ARCH(1) 0.1435 0.0127 11.2699
Spread
c -0.0256 0.0725 -0.3536
k 0.1909 0.0106 17.9281
GARCH(1) 0.9462 0.0031 307.8695
ARCH(1) 0.0538 0.0049 10.9608
Implied Vol
c -0.0046 0.0008 -5.9752
k 0.0001 0.0127 11.8364
GARCH(1) 0.7540 0.0119 63.2126
ARCH(1) 0.2460 0.0129 19.0631

20. • The acquired GARCH values are used as stated for creating the dummy
variable time series. The stock exchange dummy set is given as example in the
figure. The exceedances beyond two 2 sigma standard deviations are the lags
with value 1.

21. Analysis of Results

22. Results
• The results revealed that, for the taken data period the only significant dummy
variable is CDS related one with a coefficient of 0.3572 and t-statistic 3.4225.
Variable Coefficient Std. Error t-Statistic Prob.
C 0.1605 0.0317 5.0631 0.0000
SQUARE_INDEX(-1) 0.9050 0.0087 103.6594 0.0000
DUMMYCDS 0.3572 0.1044 3.4225 0.0006
DUMMYEXCHANGE -0.1028 0.0917 -1.1206 0.2625
DUMMYIMPLIEDVOL -0.0178 0.1002 -0.1776 0.8590
DUMMYSPREAD 0.0247 0.0375 0.6596 0.5096
DUMMYXU100 -0.0064 0.1306 -0.0491 0.9608
R-squared 0.8508 Mean dependent var 1.9700
S.E. of regression 0.8966 Akaike info criterion 2.6224
Log likelihood -3311.65 Schwarz criterion 2.6386
F-statistic 2398.80 Hannan-Quinn criter. 2.6283
Prob(F-statistic) 0.0000 Durbin-Watson stat 2.2970

23. The regression model is constructed by excluding the insignificant
factors
• The regression results presented that the main affluent factor for the index
has been the CDS exceedances for the taken data set.
• The regression result is :
• SQUARE_INDEX = 0.1674 + 0.9063*SQUARE_INDEX(-1) + 0.3573*DUMMYCDS
Variable Coefficient Std. Error t-Statistic Prob.
C 0.1674 0.0236 7.1015 0.0000
SQUARE_INDEX(-1) 0.9063 0.0087 104.7353 0.0000
DUMMYCDS 0.3573 0.0896 3.9903 0.0001
R-squared 0.8507 Mean dependent var 1.9700
S.E. of regression 0.8962 Akaike info criterion 2.6199
Log likelihood -3312.51 Schwarz criterion 2.6268
F-statistic 7202.05 Hannan-Quinn criter. 2.6224
Prob(F-statistic) 0.0000 Durbin-Watson stat 2.2981

24. Conclusion
• A new composite index is proposed by combining different parameters like
FX Implied Volatilities, CDS and Interest Rates levels. This new risk index
that is modeled by GARCH and Markov autoregressive based models for
forecasting and identifying thresholds to be better and efficient in
comparison to single indicators
• As it can be seen many indicators can be used for estimating market tension
levels and a common composite index could be used as a general indicator
for market players. Eventually this index can be modeled by using
appropriate econometric forecasting procedures. The established index can
also be used as an exogenous input for modeling other variables in the
market.