183Interest Rate Risk In Turkish Financial Markets Across Different Time Periods
INTEREST RATE RISK IN TURKISH FINANCIAL
MARKETS ACROSS DIFFERENT TIME PERIODS
A measuring the risk associated with interest rates is important since it is beneficial in taking measures
before negative effects can take place in an economy. We obtain a risk measure for interest rates by
fitting the generalized Pareto distribution (GPD) to positive extreme day-to-day changes of the interest
rate, using data from the Istanbul Stock Exchange (ISE) Second Hand Bond Market, namely Government
Bond interest rate closing quotations, for the time period 2001 through 2009. Although the use of the
GPD in the context of absolute interest rates is well documented in literature, our approach is different
insofar and contributes to the literature as changes in interest rates constitute the target of our analysis,
reflecting the idea that risk arises from abrupt changes in interest rate rather than in interest rate levels
themselves. Our study clearly shows that the GPD, when applied to interest rate changes, provides a good
tool for interest rate risk assessment, and permit a period-specific risk evaluation.
Keyword: Interest rate risk; covered interest parity; Turkey; generalized Pareto distribution
JEL Classification: G1; C1
1 Corresponding author: Istanbul Bilgi University, Department of Economics, Dolapdere Campus, Kurtulus Deresi Cad., Yahya Köprüsü
Sok.No: 1, 34440 Beyoglu, Istanbul, Turkey, Tel.+902123115326, Fax+902122970134, E-mail: email@example.com.
No: 2/13, 34060 Eyup, Istanbul, Turkey, Tel.+902123117789, E-mail: firstname.lastname@example.org.
184 Bulletin of Monetary, Economics and Banking, January 2014
The risk expresses the chance of occurrence of an undesired event or events and non-
accrual of an intended and/or planned expectation. In an economic sense risk is the probability
of a monetary loss regarded with a transaction or loss resulting due to decreasing financial
returns. Cyclical fluctuations and price changes can increase the risk of occurrence of the
Risk is divided into two as systemic and systematic risks. All securities in financial markets
are subject to systematic risks, and systematic risks arise for example when fluctuations within
political and economic conditions affect the behavior of assets in financial markets. As a result
systematic risks are unavoidable in the sense that keeping them under control in a way is
impossible. Systemic risks on the other hand are risks related with controllable processes such
as intra-firm investment risks or a risk that may be likely to occur due to a decision on a financial
Interest rate risk should therefore be considered within the context of systematic risks.
The fluctuations in interest rates could not totally be controlled but some measures may be
taken or certain tools may be applied to cope with interest rate risk.
Measuring the interest rate risk is important since it may be beneficial in taking measures
before negative effects can take place in an economy (see Woodford (1999)). From the
perspective of finance interest rate should be considered not only with economy but with
but also have the power to alter the structure of the markets.
There are many other perspectives as well. For example financial income perspective says
that the income going to be generated in the future is effected by interest rates because today’s
value calculation is made by an assumed interest rate level. If there is an unexpected change in
the interest rates there is a risk that the value of income may be lower than expected. From an
institutional perspective, changes in interest rates affect a financial institution’s market value
on the one hand and off-balance-sheet contracts written on interest rates on the other are
affected by a change in rates, the present value of future cash flows and in some cases even
the cash flows themselves can change.
The focal point of the present study is to measure the interest rate risk in the Turkish spot
market for government bonds. We will first look at what has happened in the Turkish economy
withinthe period under investigation (2001–2009).Afterthiswewilllookatthestatistical
properties of changes in the daily series of interest rates.
Interest Rate Risk In Turkish Financial Markets Across Different Time Periods
Our analysis is based on the tail index of the generalized Pareto distribution (GPD),
applied to threshold excesses of changes in interest rate series. The tail index characterizes
whether the underlying distribution has heavy tails. A similar approach (however, applied to
the estimation of risk measures associated with fat tails for stock market returns in several
countries. The behaviour of joint threshold exceedances of returns on international stock
contribute to financial risk assessment among markets in bull and bear periods.
Gencay, Selçuk and Ulugulyağcı(2002)appliedthissettingtodatafromIstanbulStock
Exchange and derive a VaR measure meant to be an alert system for the market. Gencay and
money markets in order to derive a measure querying whether the ex-ante interest overnight
levels are indicators of the 2001 crisis or not.
Next section outline the literatures study and the underlying theory on interest rate. Section
3 discuss the data and methodology, while section 4 provide result and analysis. Conclusion
will be provided on last section and concludes the study.
Many factors may determine the shape of interest rate distribution. From micro level
behaviour, macro aggregated, and external factors including negative shock may change the
dynamics of interest rate; gradually or drastically. On international perspective, the rule of covered
interest provides basic relationship among interest rate, exchange rate, and inflation.
Common dynamic of interest rate is well recognized, one of them is that the interest
rate volatilities is stochastic. It is also recognized that interest rate tends to cluster, particularly
whenshifting formlow tohigh volatility; seeAndersenand Lund (1997)inAllan SallTang
international trade within the BRIC countries, and found that countries with lower interest rates
experience growth of the share of machinery industry exports rather than agriculture and food
products, and, on the contrary. On the other hand, in countries with higher interest rates, the
share of agriculture and food exports increases and the share of machinery industry products
declines. The investigation has shown that a relative shift in the interest rate can affect the
specialization of countries.
home and foreign potentially contribute to trade imbalances and push down the interest rate,
which is claimed to be inline with Bernanke’s global saving glut hypothesis.
186 Bulletin of Monetary, Economics and Banking, January 2014
the Bank of England purchase government bonds on a massive scale to lower the long-term
interest rate, and to stimulate aggregate demand. It shows low long-term rate has recently
become an important intermediate target of central banks in the advanced economies, which
affect the short term rate as well. The relationship between the exchange rate, short term rate,
and long term interest rate may be illustrated as follows:
is exploited by global investors. This model indentify three categories of the determinants of
interest rate dynamics; economic fundamentals, short run deviations of bond yields from their
long run levels, and global financial integration.
Desroches and Francis (2007) identify the behaviour of the world real interest rate
which is determined by a number of key variables that change relatively slowly over time. They
include the growth of labour force, which affects investment demand, and the age structure
of the world economy, which influences savings, and also the level of financial development.
term structure. Using panel of international yield curves, they show that global factors account
for more than 80 percent of term premia in advanced economies, while domestic factors are
more relevant to explain the short-run dynamics of the rate.
Those factors explained above will determine the shape of interest rate, which is appearing
Interest Rate Risk In Turkish Financial Markets Across Different Time Periods
method for modeling extreme-value data is based on the extreme-value limiting distributions.
of distributions or exceedances over a threshold. Later on there other studies extended the theory
model-free estimates of the volatility and skewness priced in interest-rate options, it can be
shown that interest rate distributions also show time-varying skewness (see Trolle and Schwartz
stochastic volatility and skewness. Finally, calibrating the model to time-series of the market
data is interesting, as it shows the applicability of the model.
3.1. The Generalized Pareto Distribution (GPD)
Let (it)designateadailyseriesofinterestrates(t indicatestheday),anddefinetheseries
of daily changes as
The focal point of this paper is to study the upper threshold exceedance behaviour of
the series (rt)onthebasisofthegeneralizedParetodistribution(GPD),whichisamodelfor
excesses of a random variable. The rationale behind using the GPD is a limit theorem which
states3: Let r1,..., rn be iid random variables, and let R be distributed like ri. Then, for large n
and u, there are ξ and σ such that the distribution function of the excess (r – u)conditionalon
R > u, is approximately given by:
188 Bulletin of Monetary, Economics and Banking, January 2014
Here, σ > 0 is a scale parameter; it depends on the threshold and on the probability
density function of ri. The shape parameter ξ is called the tail index, since it characterizes the
tail of the density function:
• Thecaseξ > 0 corresponds to fat-tailed distributions; in this case, the GPD reduces to the
• The case ξ = 0 corresponds to thin-tailed distributions; the GPD then reduces to the
exponential distribution with mean σ.
• Whenξ = 1, the GPD becomes a uniform distribution on the interval [0, σ ].
Figure 1. Fitting the GPD to data
consideration is shown in Figure 1. The histogram represents the upper tail of the empirical
distribution of daily changes in the series interest rate (456 daily closing quotations of interest
rates to maturity government bonds trading at the ISE Bounded Bond Purchasing Market;
used as cut off point through out our study. The red line is the density of the normal distribution
with the same mean and variance as faiz456 in period 2, and the green line is the density of the
GPD fitted to the data. It is obvious that the normal distribution overestimates the probability
of moderate changes and underestimates the probability of large changes. This makes it
inappropriate for risk analysis in our case.
software environment R (The R CoreTeam,2013)tofittheGPDtodata.Theestimationmethod
implemented in “evd” is maximum likelihood. Standard errors were cross-checked using
bootstrap to ensure the reliability of results.
189Interest Rate Risk In Turkish Financial Markets Across Different Time Periods
We use daily closing quotations of interest rates of 90, 182, 273, 365 and 456 days to
maturity government bonds trading at the ISE Bounded Bond Purchasing Market. The periode of
Prior the application of GPD method, we identify the presence of structural break over the
observation horizon. The investigation provides us four periods. A plot of the series is shown in
Figure 2 for the four periods under investigation. There are no corporate bonds in this market.
The Turkish Bond Market is dominated by Treasury Bonds.
IV. RESULT AND ANALYSIS
4.1. Structural Breaks in the Interest Rate Series
We shall now approach the question of how to divide the period under consideration
into sub-periods by applying a statistical test for structural changes to the time series of daily
interest rates. This will provide further arguments for a separate risk analysis in the three sub-
periods.4 In addition, we will clearly see the limitations of regression models when applied to
the interest rate series.
The method we use will find breakpoints in a regression relationship, with interest rates
Breakpoints are computed with the objective of minimizing the residual sum of squares under
4, was adjoined for economic reasons.
5 Faiz091 is a daily closing quotations of interest rates of 90 days to maturity government bonds trading at the ISE Bounded Bond
Figure 2. Breakpoint analysis of faiz0915
190 Bulletin of Monetary, Economics and Banking, January 2014
The number of breakpoints is not predetermined, but results from the procedure.
The test for structural changes finds four breakpoints in the series faiz091, which we chose
for this purpose to represent interest rate evolution. The results of the breakpoint analysis are
displayed in Figure 3. In our subsequent analysis, we shall ignore the first breakpoint and form
period 1 with 2003-10-06 as last day. This is justified because of the relative homogeneity of
circumstances and events in this period. We are there fore led to a definition of sub-periods
and their characterization as shown in Table 1.
4.2. Characteristics of the Sub-Periods
First of all, it is justifiable to separate this whole period into only two periods: the period
until 2002, and the period from 2003 through 2009. Starting from the beginning of 2001
and ending with the end of 2002 there were three events that mainly shaped this period: the
economic crises experienced on 28 February 2001, the September 11, 2001; and the Turkish
General Elections in November 2002. The period was comprised of many instabilities in terms
Number 1-2. Available online at http://www.bddk.org.tr/english/Reports/Financial Markets Report/1971fprMart Hazi ran2006ingilizce.
pdf. Accessed October 2008.
191Interest Rate Risk In Turkish Financial Markets Across Different Time Periods
The period between January 2001 and September 2003
As mentioned above this period was stricken with economic and political insta bilities. The
resolution which authorized the Turkish National Assembly to send troops to Iraq was approved
perceived as a manifestation of “political integrity” by the markets7.
It should also be mentioned that the inflation was reported to be the lowest in 30 years
in October 20038. Shortly afterwards the Treasury explained a debt structuring in the sense of
swapping the short term government bonds with longer maturities. Interest rates had dropped
200 basis points, and the Turkish Govern ment was subsequently able to borrow for longer
7 Hurriyet Online: “TezkereGeçti Asker IrakaGidiyor, Kabul 358 Red 183”, date: 2003-10-07. Available online at http://webarsiv.
hurriyet.com.tr/2003/10/07/hurriyetim.asp. Accessed October 2008.
8 Hurriyet Online: “Enflasyona Eylül Çelmesi”, date: 2003-10-04. Available online at http://webarsiv.hurriyet.com.tr/2003/10/03/
hurriyetim.asp. Accessed October 2008.
asp. Accessed October 2008.
Figure 3. The faiz series, Perıod 1
The Period between October and May 2006
There were four main events 2003 shaping this period: WTO abolished trade barriers,
capital flows rendered more liberalised, growth of developed economies had increased, and
inflation in developed countries.
It can be said that this period was a period of capital flows between diverse mar kets.
Total volume of capital circulation throughout the world had reached ap proximately $15 trillion
192 Bulletin of Monetary, Economics and Banking, January 2014
10 InternationalMonetary Fund (IMF) World Economic Outlook,October 2006, pp. 1–6. Available online at http://www.imf.org/
external/pubind.htm.Accessed October 2008.
11 Turkish Central Bank, Inflation Report 2006-IV, pp. 41–46. Available online at http://www.tcmb.gov.tr/.Accessed October 2008.
Available online at http://www.imf.org/external/pubs/ft/weo/2008/02/pdf/text.pdf. Accessed October 2008.
Figure 4. The faiz series, Period 2
Figure 5. The faiz series, Period 3 and 4
according to the IMF Economic Outlook10. Developing countries in this sense were also among
the beneficiaries. An amount of $2 trillion out of $15 trillion had flown to them, Turkey’s share
be ing $90 by foreign investment, according to the Turkish Central Bank Inflation Report11.
The Period between 2006-06-02 and 2008-08-29
There were four main events that shaped the period12: inflation fear of developed countries,
the increase in interest rates, the sub-prime crises through the end of the year 2007, and the
banking crises throughout the world.
193Interest Rate Risk In Turkish Financial Markets Across Different Time Periods
4.3. Statistical Properties of Daily Interest Rate Changes
Tables 4 and 5 in the Appendix give an analysis of the distributional properties of the
percent point changes in the five series for the four periods in terms of mean, variance and
standard deviation, skewness, kurtosis, minimum, median, and maximum. Our goal in the
present paper is an evaluation of the interest rate risk. Therefore, the two most important items
in the list are the variance and the kurtosis.
There are obvious differences between the periods: The range of daily changes is widest
for period 1; the variance and the kurtosis are largest for period 1. The behaviour of the five
series within the periods gives insight into the characteristics of the different maturities, but
also reveals further differences between the periods. In particular, some of the characteristics
resulting from Tables 4 and 5 are:
faiz456 most pronouncedly in period 1. An explanation may be that period 1 was regarded
as risky by many investors in the sense that the Turkish financial market’s risk premium is still
high. As a conse quence, investors demanded high long-maturity interest rates as a compen-
sation for risks in future periods.
The interest rate risk increases with maturity.
kurtosis becomes larger as maturity increases only in pe riod 1. This points again to an
elevated risk for higher maturities in period 1. The results of Tables 4 and 5 point to a high
reduced “surprise potential”, indicated by the lower kurtosis) in period 4. The kurtosis
generally points to heavy tails in all periods across all series, with a few exceptions. The more
complex kurtosis structure justifies using the GPD as a means to study the tail behaviour of
the interest rate change distributions.
• Theratio betweenminimum andmaximum percentage pointchange isincreasing with
maturity during periods 1, 2, 3, with a reduced rate during period 4. This is also clearly visible
in the boxplots in Figure 4.
4.4. GPD-Based Interest Rate Risk Measurement
The estimation results are reported in Table 2. In our context of risk measurement, the
estimated tail index ξˆ is more important than σˆ. As stated above, a positive tail index indicates
194 Bulletin of Monetary, Economics and Banking, January 2014
• EstimatesoftheGPDparametersξ and σ, together with their standard errors, based on
daily interest rate changes (computed as rt = ln (it - it-1))) areabovetheirempirical 80%
• 95%and99%quantilesoftheinterestratechanges(thecolumnsdesignatedasq95 and
The relatively close agreement between the latter pairs throughout the periods we
considered and across the interest rate maturities can be seen as a confirmation of the model
A comparison of the four periods with respect to the tail properties of the interest rate
change distribution leads to the following remarks:
• Period1hasexceptionallyhighvaluesofξ for each interest rate series con sidered: All five
tail indices are significantly positive (which indicates heavy tails, here: an elevated risk that
of the interest rate change distributions is heavy-tailed, with the exception of faiz456. This
points to an elevated overnight increase in interest rate only for long-term bonds.
in Turkey. The GPD, derived as an explicit model for distribution tails, fits very well and
provides a close fit between the theoretical VaRs and empirical quantiles.
In this section we will try to discuss the economic implications of our study to explain
how our study fits into economic arguments. We have examined the interest rate risk in the
Turkish economy. Statistical modelling is the key to the development of such risk scores.
There are many economic reasons to have dif ferent levels of risks in interest rates. Statistical
risk scores can make a useful contribution to economic decision making under uncertainty. A
general assump tion of a decision or action depends on the occurrence of some adverse event,
and that we have data which indicate how the likelihood of this event depends on values of
observable risk factors.
195Interest Rate Risk In Turkish Financial Markets Across Different Time Periods
A risk indicator can be provided by the ex amination of extreme values of interest rates
in the framework of extreme value theory. Extreme value theory is a powerful framework to
study the tail behaviour of a distribution; hence it can be a good indicator for risk.
Figure 6. Boxplots of Interest Rate Changes, Four Periods
Period 1 Period 2
Period 3 Period 4
196 Bulletin of Monetary, Economics and Banking, January 2014
risk for the pe riod starting in 2001 till the end of 2009. Estimating GPDs to the data resulted
in a good fit between the model and our data for all periods and maturities. It turned out
197Interest Rate Risk In Turkish Financial Markets Across Different Time Periods
that the tail indices, indicating the weight of the upper tail of distribu tions of daily interest
rate changes, became smaller and smaller, indicating that tails became thinner from period to
reducing interest rate risk.
As summarized in Figure 3, the interest rates have three significant structural brakes in
this period. Due to justifiable economic reasons, the entire period is divided into four sub-cycles.
These cycles are important because, for example, during re cession consumers are likely to cut
back on luxury items, and thus firms in the consumer durable goods sector should see their
credit risk increased. Moreover, there is considerable evidence that macroeconomic conditions
growth will slow down the adjustment speed of capital. Economic agents borrow less. Thus
GDP growth is positively associated with the likelihood of debt issue (see Hackbarth, Miao and
Keeping this argument in mind, in our sample periods, the highest risk is in the first period
with a highest value of ξ. As far as high risk is concerned, the first period is followed by the
third period, but the only risky periods of borrowings are the longer maturity borrow ings, i.e.
a year or more maturity borrowings. The second period, starting with 2003-07-10 and ending
in 2006-06-01, has zero ξvaluesexceptforthelongestmaturity(faiz456).Ageneraleconomic
rule applying here is that the longer is the maturity, the more risk will emerge. Period 4 shows
zero ξ values for all ma turity levels, which indicates that this period is associated with a lowest
interest rate risk period. This result appeared to be contradictory at the beginning because this
period is the first period of the impact of the global financial crisis on the Turkish economy.
An obvious question is, why does an economic crisis affect the risk associated with
interest rates in Turkey? An interpretation of this result can be found in the macroeconomic
implications of an economic crisis. During global crises, price levels and the level of interest
rates will generally decrease. Prices decrease because of lowering demand for goods, and the
rates of interest will also decrease for a similar reason. Compared to the earlier periods, in the
fourth period, the sensitivity of interest rates with respect to investment decreases, implying a
reduced demand for loans.
Figure 5 depicts the weekly observations of the total consumer loans and the claims under
legal proceedings between 2004 -06-25 and 2010-01-01. It is very clear that the consumer
borrowing demand is slowing down for the latest period, and there is a dramatic increase in
the claims under legal proceedings. Hence the decrease in the risk of the rates of interest for
this period is smaller than expected.
These interpretations are statistically confirmed by the results of Table 3: Statistical
properties of interest rate changes for the four periods indicate that the results are significant.
Higher kurtosis means that a larger share of the variance is due to infrequent extreme deviation,
as opposed to frequent modestly sized deviations.
198 Bulletin of Monetary, Economics and Banking, January 2014
199Interest Rate Risk In Turkish Financial Markets Across Different Time Periods
Moreover, our results are also in line with the covered interest parity link. Table 3 depicts
the joint threshold exceedances for our four sub-periods in the Turkish economy. We have
used the dollar TL exchange rate as a proxy measure of the Turkish exchange rate. The joint
behaviour of changes in Turkish interest rates and the USD/TL is in line with our approach to
interest rate risk assessment to investigate the occurrence of joint daily threshold exceedances.
For each period, we define indicator variables as follows:
Figure 7. Total Consumer Borrowing And Claims
Under Legal Proceedings
1 If a USD-return exceedance happened on day t,
1 If an interest rate change exceedance happened on day t,
Here, we speak of a USD-return exceedance if the change in price of a USD in TL was
largerthanits 90% quantileor lowerthan its 10%quantile, wherethe quantile isperiod-
specific. Likewise, an interest rate change exceedance is said to happen if the change in interest
period-specific. Contingency tables for X and Y, together with their odds ratios, are shown in
Table 3. An odds ratio larger than 1 indicates a positive association of X and Y, that is, the main
diagonal of the contingency table has higher frequencies than expected under the hypothesis
that X and Y are independent.
Table 3 reveals that, as expected, a positive association was found for all periods, the odds
ratio indicating the strongest link for Period 1. Furthermore, a significantly positive association
200 Bulletin of Monetary, Economics and Banking, January 2014
will also entail a change in interest rates. This link is similar for all four periods. Thus we observe
a covered interest parity condition in Turkish financial markets.
Measuring the interest rate risk is important for the emerging markets as well as the
globalised financial system. A risk hidden in the behavior of interest rates has not only directly
effect the functioning of markets but also have the power to alter the structure of the markets.
It is obvious that the normal distribution overestimates the probability of moderate changes and
underestimates the probability of large changes. This makes it inappropriate for risk analysis
in our case.
The use of the GPD in the context of absolute interest rates is well documented in
literature, our approach is different insofar as changes in interest rates constitute the target
of our analysis, reflecting the idea that risk arises from abrupt changes in interest rate rather
than in interest rate levels themselves. Our study clearly shows that the GPD, when applied
to interest rate changes, provides a good tool for interest rate risk assessment, and permit a
period-specific risk evaluation.
201Interest Rate Risk In Turkish Financial Markets Across Different Time Periods
APPENDIx: STATISTICAL PROPERTIES OF INTEREST
202 Bulletin of Monetary, Economics and Banking, January 2014
203Interest Rate Risk In Turkish Financial Markets Across Different Time Periods
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