ï»¿ WPS6091
Policy Research Working Paper 6091
Turkish Treasury Simulation Model
for Debt Strategy Analysis
Emre Balibek
Hamdi Alper Memis
The World Bank
Financial Advisory and Banking
June 2012
Policy Research Working Paper 6091
Abstract
Governments raise funds to meet their financing Treasury to assist the decision-making process in debt
needs using a range of fixed income securities and strategy formulation. The model is used to analyze the
loans with different maturities, interest rates, and medium and long-term consequences of alternative
exchange rate structures. Public debt managers need debt management strategies in terms of cost and risk
to consider various policy objectives when deciding on characteristics, and provides key inputs to decision
the structure of the public liability portfolio. This paper making.
describes a simulation model developed at the Turkish
This paper is a product of the Turkish Treasury, supported by the Financial Advisory and Banking Department, World
Bank. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to
development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://
econ.worldbank.org. The authors may be contacted at emre.balibek@treasury.gov.tr and alper.memis@treasury.gov.tr.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
Turkish Treasury Simulation Model for Debt Strategy Analysis1
Emre BALIBEK, PhD2 and Hamdi Alper MEMIS3
JEL Classification: H63, G32, G17
Key words: Public debt management, risk management, simulation models, financial markets
1
This work was extensively supported by the World Bank through technical assistance during 2006-2007. The
ideas expressed in this paper are only those of the authors and do not necessarily reflect the views and policies of
the Turkish Treasury. No responsibility for them should be attributed to Turkish Treasury. In this paper, aspects
of the model are described to the extent that confidentiality policies of the Turkish Treasury allow.
2
Deputy General Director, Risk Management Unit, Turkish Treasury (emre.balibek@treasury.gov.tr)
3
Senior Associate, Market Risk Management Department, Turkish Treasury (alper.memis@treasury.gov.tr)
Acknowledgements
We would like to express our gratitude to the World Bank Treasury, particularly Lars Jessen,
for continuous support, guidance, useful comments and helpful discussions during the
development stage of the model introduced in this paper. We would also like to acknowledge
Prof. Dr. Burak SaltoÄŸlu of Bogazici University and David Jamieson Bolder of Bank for
International Settlements (who worked with us during his tenure at the Bank of Canada) for
their assistance in building the model. We are very grateful to our colleagues FatoÅŸ KoÃ§ and
H.Hakan Yavuz for their invaluable contributions and support during all stages of our work
and to our general director, Dr. M.CoÅŸkun CangÃ¶z, not only for being the motivating force
behind the project, but also for sharing his comments on this paper. Last but not the least, we
would like to thank Prof. Dr. Murat KÃ¶ksalan of Middle East Technical University, Cigdem
Aslan, Antonio Velandia, Rodrigo Cabral, Eriko Togo, Alex Sienaert and Farah Hussain of
the World Bank and Myrvin Anthony of the International Monetary Fund for their feedback
on the final draft of this paper. All thanks are without implication and we retain full
responsibility for any omissions or errors.
2
Acronyms and Abbreviations
ATR Average Time to Re-fixing
CIR Cox, Ingersoll and Ross Model
CKLS Chan, Karolyi, Longstaff and Sanders Model
CPI Consumer Price Index
DM Decision Maker
GDP Gross Domestic Product
GUI Graphical User Interface
IMF International Monetary Fund
OECD Organization for Economic Cooperation and Development
PDM Public Debt Management
TDSM Turkish Debt Simulation Model
TRY Turkish Lira
USD US Dollar
VaR Value at Risk
3
1. Introduction
Public debt managers borrow funds to finance the cash needs of the government and to
refinance maturing debt; and they issue a range of borrowing instruments with different
maturities, interest rates, and exchange rate structures. The choice of instruments to be issued
depends on the objectives of public debt management (PDM), as well as other factors such as
the local and international market environment, the governmentsâ€™ credit rating, and
macroeconomic environment. Formulation of debt issuance strategies, i.e., determining the
portfolio composition of government debt, is a complicated process since the objectives of
PDM usually conflict with each other and there is uncertainty regarding the movements of
variables that affect the outcomes of the decisions made.
One of the basic objectives of PDM is to borrow at the lowest possible cost. The risks
associated with the debt portfolio should also be considered to avoid any adverse effect on
debt service. A countryâ€™s financial stability is affected by the health of public sector balances
and the sustainability of debt service; therefore distress in debt management, such as
difficulties in fulfilling liabilities on a timely basis or excessive costs on the debt, has
spill-over effects on the entire economy. Hence, debt managers should form sound debt
management policies that reflect the governmentâ€™s cost and risk preferences together with
other debt management goals (IMF and the World Bank, 2003).
One of the major risks that public debt managers are concerned with is â€•market riskâ€–, which is
defined as the risk of an increase in the cost of debt service due to fluctuations in market
conditions (IMF and the World Bank, 2001). In financial markets, there generally exists a
trade-off between return and risk. As a result, for a portfolio manager, achieving a higher
return requires investing in riskier assets. Since the government is the issuer of financial assets
(securities), from the governmentâ€™s perspective, the trade-off is between creating a low-cost
portfolio and containing the associated risks.
Frequently, in financial markets, due to the uncertainty perceived for future periods, the yield
curve is upward sloping, and thus short-term interest rates are usually lower than those for
longer term. In such a context, a trivial choice for minimizing costs is to issue short-term debt
to make use of lower interest rates. However, a portfolio consisting of short-term instruments
(or instruments indexed to short-term rates) will result in the need to renew (or re-fix the
interest on) debt more frequently, which in turn induces high sensitivity to developments in
financial markets since future interest rates are unknown and the shape of the yield curve
4
varies through time. In addition to increasing exposure to changes in interest rates,
dependence on short-term debt may increase the issuerâ€™s roll-over risk.
Similar to other financial decision-making problems, an important characteristic of the public
debt management strategy problem is that decisions are made under uncertainty. There is no
perfect information regarding the future states of relevant financial variables, such as interest
and exchange rates. For example, a debt management office may issue floating rate bonds
anticipating a decline in interest rates in order to reduce cost. However, the actual cost of this
strategy depends on the interest rate realizations until the redemptions of these bonds. On the
other hand, issuing fixed rate securities also carries a risk, that of locking in high rates in an
environment of declining rates. A similar argument also applies for decisions regarding
whether or not to issue in foreign currency, if the country is implementing a floating rate
currency regime. In summary, uncertainty about the future raises the need to consider risk
objectives.
Thus, formulation of borrowing strategies, taking into consideration the dilemma between
attaining a minimum cost portfolio and diminishing the associated risks, is an important
decision-making problem. In order to deal with this dilemma and to make better informed
decisions, debt managers use several analytical tools, ranging from deterministic models to
stochastic approaches. In deterministic scenario-based methods, cost and risk is analyzed
under a handful of future market scenarios defined by debt managers, or other policy makers.
Debt management offices have also adapted simulation modeling techniques that were
pioneered by private financial institutions. The stochastic simulation models of PDM offices
are generally derived from the â€•Value at Riskâ€– (VaR) concept used by banks and other
financial firms. VaR models provide an estimate of the maximum expected loss of market
value that the assets may suffer within a given period at a certain confidence interval. The
results from VaR models can easily be communicated to policy makers, and therefore they
became widely popular in the mid-1990s.
While the focus of VaR is on market value, the focus of a public debt manager is on the cost
of the debt. For sovereigns, therefore, the approach is modified as a â€•Cost-at-Riskâ€– or â€•Cash-
Flow-at-Riskâ€– model.4 These models provide an estimate of the variability of debt service
4
One major difference between VaR model and its adaptations to public debt management is the time horizon
used in decision making and modeling. Although, VaR is used for short-term decision making, Cost-at-Risk type
models are used to analyze medium-long term consequences of strategy alternatives. This difference in the time
horizon makes the task for debt managers much more complex, as they will have to make forecasts/simulations
for longer periods.
5
costs and/or cash-flows, and enable debt managers to test cost and risk performances of
alternative debt management strategies under various simulation scenarios for interest and
exchange rates, and to identify and understand the trade-offs.
This paper presents a description of the stochastic simulation model developed by the Turkish
Treasury. In the following sections, we provide a description of the model, elaborate on how
the model was developed, and discuss issues with regard to implementation. The main aim of
this paper is not only to contribute to literature in this field, but also to invite comments from
researchers and practitioners, which will be invaluable for further development of the model.
This paper is organized in six sections. Section two begins with a discussion on conceptual
aspects of model building and simulation modeling, and also provides the general structure of
sovereign debt strategy models. In Section three, we discuss the evolution of the conceptual
framework of the Turkish Treasury simulation model. We focus particularly on the cost and
risk concepts, horizon and granularity choices, as well as debt metrics used in strategy
formulation framework. In Section four, we describe the technical aspects of the model.
Section five discusses the analysis performed within the experimental framework and in
Section six we conclude and indicate prospects for future work.
2. Models for Debt Management Strategy Analysis: Why Do We Need a Model?
A â€•systemâ€– is defined as â€•a group of objects that are joined together in some regular
interaction or interdependence toward accomplishment of some purposeâ€– (Banks and Carson,
1984, p.6). The links and interactions between components of a system are generally complex
and in many real life cases can be beyond limits of direct comprehension. Therefore, a tool is
needed to understand and study the details of functioning of a system. A model is developed
as a simplified substitute for a complex reality, to represent a particular system where all
details of the system under focus are not required to reach the purpose of analysis.
Mitchell (1993) considers two main perspectives while analyzing models: models as device
for predicting the output from a real system and models as a statement of collection of beliefs
about the real world that are considered relevant. These two meanings correspond to two main
uses of building models: assisting decision making as a device for experimentation to make
predictions and securing comprehension of the relationships between system elements.
In mathematical models, the system is represented by symbolic notations and equations and it
can be solved and analyzed by mathematical methods. However, in real life, many problems
6
are too complex to be solved mathematically and in these instances, other tools such as
simulation are needed.
Simulation is â€•the imitation of the operation of a real-world process or system over timeâ€–
(Banks and Carson, 1984, p.2). It helps us compress the functioning of the system in time and
space and enables the researcher to analyze the interactions that would not otherwise be
observable. In the case of debt management, for example, one needs to wait until maturity to
be able to detect the final cost of a floating rate note. A computer-based simulation model
generates an artificial account of the life of a bond at a moment in time and enables analysts
to evaluate its possible costs under a set of scenarios.
Once built and validated, a simulation model can be used to answer â€•what-ifâ€– questions about
the real system. Simulation modeling can not only help the modeller predict current system
behavior considering a set of future scenarios, but can also be used as a design tool by
enabling the analysts to make modifications in the system. That is, potential changes in the
system components and/or their interactions can be simulated to analyze their possible
impacts on system performance. A simulation model, once set up properly, can be used
repeatedly to analyze suggested set-ups or strategies in a short period of time at a relatively
low cost. Therefore, simulation modeling is a powerful tool that enables the investigation and
experimentation of a complex system.
2.1 Overview of Debt Strategy Models
In the context of government debt management, scenario analysis based on a limited number
of deterministic scenarios and more advanced simulation models are used to support the
decision-making process in strategy formulation. Many countries use simple models based on
deterministic scenarios (IMF and the World Bank, 2003 and Jensen and Risbjerg, 2005). In
these models, there exists a base-line scenario of relevant variables, and risk is measured by
the variability of costs under a limited number of user-defined scenarios of shocks to the
baseline scenario (Velandia, 2002). The deterministic model outcomes are typically easier to
understand and interpret compared to stochastic simulation models. Therefore, developing
deterministic models can be seen as a simple and efficient method in cost-risk modeling of
public debt, since they are also easy to communicate to policy makers. Despite these
advantages, â€•as only a limited number of scenarios are generated in deterministic models, it is
not possible to achieve a direct quantification of the risk by relating potential outcomes to
their likelihoodâ€– (Risbjerg and Holmlund, 2005, p.46). Furthermore, determining the size and
7
directions of shocks to the financial or macroeconomic variables can be quite arbitrary and the
relationship of these variables may not be captured well under this approach.
Stochastic simulation models have also been implemented or are under development by a
number of debt management offices in recent years in order to analyze the complex systems
of debt strategy formulation and to evaluate alternative policy designs, i.e., different portfolio
compositions. These tools, generally referred to as â€•Cost-at-Riskâ€– or â€•Cash-Flow-at-Riskâ€–
models, allows comparison of alternative debt management strategies under various
simulation scenarios. The performance analysis of different settings with respect to various
policy objectives are then used to assist decision makers. In stochastic simulation models, cost
and risk depend on the evolution of stochastic variables that are typically generated by a
model, the parameters of which will be based on the historical paths of the variables. 5 In these
models, hundreds or thousands of alternative scenarios for future market rates are generated,
allowing the generation of statistical distributions. The relationships among financial variables
can be maintained in simulated paths through the use of several analytical techniques. The key
challenges in stochastic modeling include the complexity of the structure, the distributional
assumptions of financial variables, and the stability of estimated relationships
(Anderson, 2011).
Given their pros and cons, deterministic and stochastic techniques are not necessarily
substitutes for each other, nor should simulation be interpreted as a required further step in
debt strategy modeling. These approaches are similar in essence, with differences in structural
forms, and both can provide useful input for decision makers. The choice between methods
should be based on available resources, the degree of detail needed for analysis, and other
country-specific circumstances. It is also possible to employ deterministic and stochastic
models as complementary tools.
Other than these models, which are practically used in several debt offices, optimization
approaches have also been proposed for PDM strategy formulation in recent years. Bolder and
Rubin (2007) and Bolder and Deeley (2011) attempt to combine simulation and optimization
approaches with the aim of approximating the debt management objective function through
simulations by using function approximation algorithms and then to optimize this
approximation. Balibek and KÃ¶ksalan (2010) and Consiglio and Stanio (2010) suggest
employment of stochastic programming models to formulate an issuance strategy. However,
5
In some economies, the past may not always be a good predictor for the future, so that debt managers resort to
alternative methods in generating scenarios.
8
to the best of our knowledge, optimization models have not yet been put into practical use due
to challenges with regard to their complex structure, which impedes interpretation and
maintenance.
2.2 Simulation Models for Public Debt Management
A detailed description of government debt simulation models is provided by Risbjerg and
Holmlund (2005). The general structure contains inputs such as the initial debt portfolio,
assumptions about future borrowing requirements and the strategy; a scenario generator that
creates various paths for macroeconomic/financial variables; and a computation engine that
calculates the issuance amounts and cash flows of the instruments. Debt service costs,
associated risks and other key indicators are computed as outputs. The authors classify
simulation models into several categories: in terms of the scope of the modelled variables and
with regard to the modeling approach. Based on the variables included in the model,
simulation models can be categorized in two classes. In one class of models, the analysts only
represent the evolution of financial variables, mainly the interest rate, as endogenous, and
treat macroeconomic variables such as the growth rate and/or primary budget balance as
exogenous. In these applications, the model is run under various scenarios, generated for the
interest rate, based on growth and primary balance projections provided externally.
Another approach is to develop a model of the economy in general, and model the co-
movement of interest rates, the business cycle, the primary surplus, etc. This method enables
the analysts to consider the relationship between financial and macroeconomic variables. The
simulation model developed at the Swedish National Debt Office (BergstrÃ¶m et al. 2002),
where the evolutions of the economic growth rate, inflation, the real exchange rate, and short-
and long-term interest rates are represented, and the Canadian model (Bolder, 2002 and 2003
and Bolder and Deeley, 2011) in which the business cycle, the interest rate, and the
government financial position are modelled together, are two advanced examples in this
category. The United Kingdom Debt Management Office developed a simulation model (Pick
and Anthony, 2006) that consists of a macroeconomic model (in which output gap, primary
net financing requirement, inflation rates and short-term interest rate are modelled as inter-
related equations), yield curve models, and a debt strategy component. In practice, there are
relatively few examples of the use of macroeconomic models by debt management offices
(Risbjerg and Holmlund, 2005), since maintaining and improving these models is quite
challenging due to their highly complex nature.
9
On the other hand, the Danish model (Danmarks Nationalbank, 2005), which only considers
the movement of interest rates, can be classified in the first group. Austrian and Portuguese
models can be also classified in this category (Kocher and NebenfÃ¼hr, 2005 and Granger,
2005). The Austrian model uses monthly updated projections made by the Ministry of
Finance for the future path of primary budget balances and generates future financial market
rates and prices through Monte Carlo simulation procedures. The simulation engine of the
Portuguese Debt Management Agency computes the portfolio dynamics based on simulation
paths for interest rates and a set of reference for macroeconomic scenarios.
The Brazilian model offers a combination of the two groups discussed here. In this model, the
scenarios can be generated by two different methods: in the first, financial stochastic models
are used for domestic and external interest rates, inflation and real exchange rates, while the
second approach uses a macro-structural model to describe main macroeconomic variables
(Silva et al., 2010).
As suggested by Risbjerg and Holmlund (2005), another possible classification can be made
by examining the approach taken in modeling variables. In the first group of models, the
relationship between variables is based on a statistical analysis of their correlations. The other
approach is to represent the relationship by structural equations as in the case of the Swedish
Model (BergstrÃ¶m et al. 2002).
The Turkish Treasury has been using a debt management strategy simulation model since
2003 to assist decision makers in formulating issuance policies (Turkish Treasury, 2004). As a
result of approximately one year of research and development work by a dedicated Treasury
team with the help of external consultants, not only was the conceptual framework of the
model revised, but the model itself was also moved to a state-of-the art modeling platform
Matlab (Turkish Treasury, 2008). The model in its current form provides a powerful and
robust analytical framework for strategic analysis of alternative issuance decisions.
In the following sections, we elaborate on the conceptual framework and components of the
Turkish Debt Simulation Model (TDSM).
3. Conceptual Framework of TDSM
Problem formulation and conceptual design are essential steps in modeling. The main
rationales for developing the strategy model in the Turkish case are to assess the sensitivity of
public debt to market movements and to quantify the costs and risks associated with
alternative financing strategies, i.e., provide assistance in developing the strategic guidelines.
10
The definition of cost and risk measures is therefore of vital importance in addressing the
intended objectives.
3.1 Cost and Risk Metrics
A clear definition of â€•costâ€– and â€•riskâ€– measures is a precondition for developing a sound debt
management strategy (the World Bank and IMF, 2009). In the context of PDM, the cost of
debt measure can be defined in many different ways. In general, country-specific factors such
as the risk profile of public debt, market conditions, and methods used in measuring and
reporting debt are the main drivers determining the relevant cost metric.
Traditionally, interest cost has been the most common measure for cost of borrowing. In other
words, cost of borrowing is reflected in the governmentâ€™s budget in terms of interest
expenditures. Governments that employ cash accounting standards record interest
expenditures when payments are actually made, while countries that follow accrual
accounting standards depict interest expenses as they accrue. Normalized cost figures such as
share of nominal interest expenditures in budget items and/or GDP are also used as cost
indicators by some debt management offices.
On the other hand, unlike many developed countries, most of the emerging countries issue
debt in foreign currencies. Inflation-linked securities are also widely used by a significant
number of debt management offices. Therefore, it could be misleading to analyze the cost of
the total debt portfolio, including foreign currency bonds and/or inflation-linked bonds, by
just taking interest payments into account. The changes in the value of foreign currency debt
measured in local currency, due to fluctuations in the exchange rate also affect the cost of debt
and the size of the outstanding debt. For inflation-linked bonds the accrued inflation on the
nominal value of the bond is paid at maturity date, while interest payments prior to maturity
date reflects inflation differential only on real coupon rate. This may result in lower interest
payments for inflation-linked bonds compared to fixed coupon bonds for the period prior to
maturity. Hence, cost of debt measure(s) should also properly capture the payment structure
of inflation-linked debt.
The mark-to-market value of the debt portfolio is a cost indicator used by debt management
offices that engage in frequent secondary market activities such as debt buy-backs or bond
exchanges. However, for countries that usually redeem bonds at maturity, the marked-to-
market value of debt stock is of little relevance. Also, since the market value of the debt does
11
not provide information on cost and risk in relation to the budget, it is not often applied in
strategy analysis.
In the Turkish case, until 2007, the â€•cost of debtâ€– was measured by â€•interest costs in accrual
basis plus changes in debt amortization (principal payments) due to exchange rate movements
for foreign currency denominated (or linked) debtâ€–. This enabled to assess the impact of the
fluctuations in interest rates as well as exchange rates. However, this cost metric was
measured solely for modeling purposes and it was not computed or monitored regularly for
statistical or accounting reports. Hence, this created a problem for debt managers in
evaluating the cost of the implemented financing strategy.
In order to address this issue and enhance communication with senior management, two
different cost concepts were put into effect in 2007. Starting from 2010, a third cost metric
has also been included following the increasing share of inflation-linked bonds in the debt
stock. As of 2011, the following cost measures are computed:
1. Cash-Based Interest Expenditures: This cost indicator reflects the interest
expenditures in the government budget.
2. Level of Debt Stock: According to current national budgetary standards, the changes
in the value of foreign currency debt measured in Turkish Lira (TRY), the local
currency, are tracked under the principal payments item rather than interest payments.
If cash-based interest expenditures were chosen as the sole cost metric, this would lead
to an underestimation of the expected cost of a strategy that is based mostly on foreign
currency debt. In order to assess the exchange rate risk associated with alternative
strategies, a secondary cost indicator, â€•Level of Debt Stockâ€–, measured in local
currency, is also used as a cost measure.
3. Accrued Inflation-Adjusted Level of Debt Stock: In 2007, Turkish Treasury started
to issue CPI-Indexed bonds, for the first time since the end of the 1990s, with a new
design. These bonds became an integral part of Treasuryâ€™s financing strategy. CPI-
Indexed bonds differ significantly with other instruments in terms of the structure of
interest payments and interest rate volatility. While the real coupon payments of these
instruments are made in coupon periods, all of the accrued inflation on the nominal
value of the bonds is carried until the maturity date. Due to this structure, relying on
the traditional cost metrics to compare CPI-Indexed bonds with other financing
instruments is misleading. Therefore, in 2010 the Turkish Treasury introduced a new
12
cost indicator wherein accrued inflation compensation for inflation-indexed bonds is
added to level of debt stock.
Given the trade-off between cost and risk of alternative financing instruments, choosing the
appropriate risk metric is also very important. From the issuerâ€™s perspective, risk can be
defined as the likelihood of an increase in the expected cost of the debt portfolio (debt service,
interest expenditures, etc.) as a result of fluctuations in relevant variables.
In the Cost-at-Risk methodology of the Turkish Treasury, the upper 95th percentile of the cost
distribution was used as the risk indicator between 2003 and 2007. In spite of its extensive use
in portfolio management and risk measurement, this approach has some shortcomings. It does
not provide any additional information about the level of risk when the chosen confidence
level is exceeded. For this reason, the Turkish Treasury adopted in 2007 a more sophisticated
metric, namely the Conditional Cost-at-Risk or Tail Cost-at-Risk. The conditional Cost-at-
Risk metric focuses on the average of the expected cost values that occur in the tail of the
probability distribution rather than a single value in the confidence level determined
(Figure 1).
Figure 1: Conditional Cost-at-Risk Approach
Frequency
Conditional
Cost-at-Risk
Cost
Cost-at-Risk
3.2 Decision Horizon and Granularity
The length of the decision perspective and the degree of granularity are important
determinants of the level of complexity of any model. In Turkey, until 2007, a 3-year period
based on monthly figures was chosen as the decision horizon in order to provide parallelism
with the budget preparation process. Cost and risk indicators of alternative financing
strategies were evaluated in cumulative basis.
In recent years, the average maturity of domestic issuances extended considerably, reaching
almost four years as of end-2011 from a level of 9.4 months in 2002. Accordingly the reliance
on short-term zero-coupon bonds was reduced with a shift towards fixed-coupon bonds, CPI-
13
indexed bonds and floating rate notes in local currency issuance policies. Therefore, the
decision horizon was extended to five years in order to analyze the cost-risk characteristics of
these instruments more precisely.
In cost-risk modeling of public debt, many developed debt management offices use longer
decision horizons to get a better picture of the medium- and long-term policy responses.
Although, the flexible nature of the model enables us to easily extend the decision horizon,
volatile historical data regarding macroeconomic and financial variables, mostly attributable
to financial crises and regime changes before 2002, and the limited extent of future
projections for fiscal data make simulations for horizons greater than 5 years difficult.
The granularity of the model was modified from monthly to quarterly in order to simplify
cash-flow modeling. Although a monthly frequency to calculate cash flows is very useful for
a highly detailed understanding of governmentâ€™s financing strategy, i.e., annual financing
plan, from a longer-term strategic perspective, such a high degree of model granularity leads
to a higher degree of complexity and potentially unwieldy calculations.
Typically, debt managers focus on annual cost and risk figures and combine annual
observations with averages across years. With the adjusted cost and risk metrics, annual
figures are taken into account, instead of using cumulative (or average) figures for the
decision horizon. This prevents the possible information loss that may arise from the
aggregation approach. Although it may be reasonable for debt management offices that have a
long decision horizon to focus on averages, in the Turkish case the relatively short length of
the decision horizon creates an incentive to analyze each yearâ€™s expected debt dynamics
separately in a more detailed manner. This helps identify possible concentrations in cost and
repayment profiles in specific years.
3.3 Debt Structure Metrics
A main objective of cost-risk modeling is to provide guidance for the formulation of strategic
benchmarks. Strategic benchmarks describe the policies designed to reach the desired debt
structure and they are typically expressed as numerical targets for key portfolio indicators
(IMF and the World Bank, 2001). In other words, strategic benchmarks are generally
structured and communicated through the use of key portfolio indicators (debt structure
metrics). Although the most common debt structure metrics are the average term-to-maturity,
duration and share of maturing debt, countries use a variety of metrics based on their market
14
structures and debt profiles. In addition, countries have different frequencies and bases
(average value, end point or mixed) across metrics (OECD, 2010).
In Turkeyâ€™s case, the strategic benchmarks, and thus the debt metrics, aimed at the
composition of financing before 2007. Between 2003 and 2007, the one-to-one
correspondence between issuances and the debt portfolio, due to relatively shorter maturity of
borrowing, necessitated the management of cash flows rather than debt portfolio figures. In
parallel to the extension of maturities, Turkeyâ€™s strategic benchmarks now focus on the
composition of the debt portfolio. The current method allows for a holistic approach to cover
outright sales, buy-backs, debt exchanges and possible use of derivative instruments.6
Therefore, the front offices should also consider the effects of debt exchange and buyback
auctions on targets for key portfolio indicators when designing their auction schedules.
The evolution of debt structure metrics are summarized in the following section.
3.3.1 Debt Roll-over Metrics
The main metric used to track re-financing risk was the â€•average maturity of borrowingâ€– until
2007. Although the strategies implemented in line with this metric proved to be useful in
improving the re-financing risk profile of the Treasury, this metric does not take into account
the redemption profile in each period and may thus lead to high redemptions in specific
periods. The adjusted debt rollover metric, â€•portion of debt maturing within 12 months,â€– takes
into consideration the rollover risk in the short run. Furthermore, since this metric is
employed from a multi-year perspective (for each year in the decision horizon) it also helps
smooth the redemption profile. Several â€•maturityâ€– related indicators (i.e., issuance maturities,
remaining time to maturity of outstanding debt) are also monitored as complementary
measures. Second metric for re-financing risk management is the â€•level of liquidity buffer.â€– 7
Maintaining a certain level of liquidity buffer enables Treasury to reduce roll-over risk and
surpass adverse effects of short-term interest rate volatility. In addition, it provides flexibility
during auctions and improves market confidence.8
6
Turkish Treasury resorts to debt exchange and buy-back operations, occasionally.
7
TDSM is not used to determine the desired level of liquidity buffer. Instead, a comprehensive analysis of debt
redemption profile, demand for Treasury auctions and availability of non-financing sources is used to set
strategic benchmarks regarding the level of liquidity buffer. Then, these targets are used as inputs for the
implementation of TDSM.
8
It should be also noted that excessive or idle cash balances may be costly due to the cost of carry. Given the
benefits associated with maintaining a certain level of liquidity buffer, this cost of carry can be considered as an
equivalent of the insurance premium.
15
Table 1: Debt Roll-over Metrics for Liquidity Risk Management
Before 2007 After 2007
Average maturity of borrowing Portion of debt maturing within 12 months
Level of liquidity buffer Level of liquidity buffer
3.3.2 Interest Rate Risk Metrics
â€•Fixed-float share of borrowingâ€– was the primary interest rate risk metric before 2007.
However, managing public debt portfolio with respect to a specific fixed-floating rate target is
quite challenging. This metric lacks information on interest rate sensitivity and maturity
profile of financing instruments. For example, a 6-month Treasury bill and a floating rate note
with 6-month coupon payment period are classified differently under this metric whereas both
instruments have the same interest rate sensitivity, namely duration of six months at the time
of issuance.
In 2007, the interest rate risk metric was modified to â€•average time to re-fixingâ€– (ATR) in
order to identify the exposure of different financing instruments to the changes in interest
rates more precisely. Duration and ATR are highly popular among public debt managers due
to their ease of use and interpretation (OECD, 2010). These metrics are useful to track the
evolution of interest rate exposure over time and for cross country comparisons. However,
duration and ATR of a debt portfolio provide information only about the average time at
which changes in market interest rates will affect the debt service. Thus they present limited
information about the dispersion of the debt stockâ€™s interest rate exposure over time and
associated re-financing risk. Therefore, these metrics are typically used together with other
supplemental risk indicators (Jensen and Risbjerg, 2005). For countries, including Turkey,
that issue a varying range of instruments from floating rate notes to long-term fixed coupon
bonds, using interest rate metrics that focus more on interest-rate risk dispersion and related
re-financing risk is very important.
Therefore, â€•portion of debt with interest rate re-fixing period of less than 12 monthsâ€– was
chosen as the interest rate risk metric in 2008. In 2011, due to increasing share of CPI-indexed
bonds in Treasuryâ€™s debt portfolio and unconventional payment pattern of these instruments,
this metric was re-organized into two sub metrics for a more comprehensive analysis of the
interest rate risk exposure of the public debt portfolio: â€•share of CPI-indexed bonds in the
TRY denominated debt stockâ€– and â€•share of TRY debt stock with interest re-fixing period of
less than 12 months, excluding CPI-indexed bonds.â€– The re-classification of interest rate risk
16
metrics provides for examining interest rate sensitivity of debt stock within three sub groups:
fixed-rate instruments, floating-rate securities and CPI-indexed bonds, where fixed rate
instruments are the ones with average time to re-fixing periods over 12 months. Since the
multi-year perspective also applies to this measure, the concentration is not only on the
immediate 12 months, but the projections for the following periods are also considered. The
aim is to distribute the re-fixing periods evenly over the decision horizon.
Table 2: Interest Rate Risk Metrics
Before 2007 2008-2010 2011 Onwards
- Portion of debt with interest - Share of CPI-indexed
- Fixed-float ratio of borrowing,
rate re-fixing period of less than bonds in TRY- denominated
- Average time to interest re-
12 months debt stock
fixing
- Share of TRY debt stock
with interest re-fixing period
of less than 12 months-
excluding CPI-indexed
bonds
3.3.3 Exchange Rate Risk Metrics
Issuance strategies that rely on foreign currency-denominated debt introduce another facet of
market risk for countries. Although foreign currency debt may appear, ex ante, to be cheaper
when compared to local currency debt of the same maturity, it could lead to additional costs if
the exchange rate depreciates (IMF and the World Bank, 2001). Foreign currency-
denominated or indexed debt may deteriorate public debt dynamics by increasing both debt
repayments and debt stock levels in a floating exchange rate regime. This type of debt could
also be very costly in a fixed exchange rate regime if the regime becomes untenable.
Therefore countries that issue debt in foreign currency-denominated or indexed debt should
give special attention to exchange rate risk. In addition, countries like Turkey that issue
foreign currency debt in multiple currencies should also address risks arising from cross
currency movements.
Prior to 2007, the Turkish Treasury used â€•roll-over ratio of foreign currency borrowingâ€– and
â€•currency composition of foreign currency borrowingâ€– metrics to manage exchange rate risk.
Since strategic benchmarks were re-designed for the composition of the debt portfolio after
2007, the exchange rate risk metrics for exchange rate and cross currency risks were modified
accordingly for a more holistic approach (Table 3).
17
Table 3: Exchange Rate Risk Metrics
Before 2007 After 2007
Roll-over ratio of foreign currency Currency composition of debt stock (local
borrowing vs. foreign)
Currency composition of foreign Currency composition of FX-debt stock
currency borrowing
4. Technical Framework of TDSM
Based on the conceptual framework described above, the TDSM was built on the Matlab
platform interacting with MS Access, Excel, and Word for data input and output. The TDSM
operates within three main modules. The first of these modules, â€•Debt Stock Database,â€–
operates in MS Access, and consists of detailed records of outstanding bond issues. The
â€•Scenario Generatorâ€– module produces scenarios for relevant financial variables in the Matlab
environment. The â€•Cash-Flow Engineâ€– module in Matlab subsequently calculates the
borrowing requirement based on the payment profile of debt stock, the financial scenarios,
and the assumptions about the primary surplus and other cash-flows. The calculated financing
need is met using user supplied issuance strategies. The â€•Cash-Flow Engineâ€– also calculates
the overall cost and risk metrics for all strategies iteratively. The following sections elaborate
on the technical aspects of TDSM.
4.1 Debt Stock Database
Information on the instruments of the current debt portfolio is held in this database. Each
strategy simulation starts with the actual bond portfolio reading from the database, which
contains detailed records of the bonds and bills issued by the Treasury in local and
international markets.
The configuration of the database reflects the structure of Turkeyâ€™s central government gross
debt stock that has changed considerably over the last ten years. At the end of 2002, local
currency debt represented only about 42% of total debt stock and consisted mainly of short-
term zero coupon instruments, including treasury bills and floating rate notes. The foreign
currency-denominated/indexed debt included bonds and bills issued in local markets,
Eurobond issuances in international markets, and a substantial external loan portfolio
(multilateral agency, bilateral lender, and other creditor debt). In line with the governmentâ€™s
strategic goals, and developments in the Turkish economy, the risk profile of public debt has
improved significantly, with increasing maturities in local markets and reduced reliance on
18
foreign currency debt. The share of local currency debt is over 70% now, as of end-2011.
Eighty-eight percent of total liabilities are in the form of securities or bonds issued in local
and international markets, in contrast with 77% at the end of 2002. The remainder includes
external loans.
Given the change in the portfolio structure, the debt database primarily accounts for securities.
Each security is represented with an MS Access Database record with identifying attributes
such as instrument type, currency, coupon rate etc. The database is updated at the end of each
month by using designated queriesâ€”delete overdue bonds, add new issuances, and update
coupon payment datesâ€”in order to calculate key debt structure metrics.
At the start of the simulation procedure, the debt stock database is checked to ensure that it
reflects recent issuances and redemptions, and adjusted if needed. This data is fed into the
cash-flow engine module to calculate the debt redemptions arising from outstanding bond
issues.
The cash-flow characteristics of the non-securitized loans are not standard and differ
significantly from market instruments such as bond and bills. There are also considerable
differences among the many loans with regard to their amortization and interest payment
schemes. From a modeling perspective, and in terms of a cost-benefit analysis, the time and
other resources required to emulate the cash-flows of the loan portfolio in detail would not be
justified by their diminishing share in the governmentâ€™s debt stock. Therefore, a different
approach is adopted and the cash flows of loans are computed outside the Debt Database and
aggregated into clusters of two main foreign currencies: US Dollar (USD) and Euro. The
loans denominated in other currencies are represented in the USD cluster using prevailing
cross currency rates. The computed payments for each currency group are then fed to the
â€•Cash-Flow Engineâ€– as underlying assumptions.
4.2 Financial Scenario Generation
The cost and risk distributions of alternative strategies depend entirely on the scenario paths
created for financial variables. As discussed in Section 2, the general approach in creating
these scenarios is to use statistical or structural models. In either case, the scenario generators
are calibrated by time series analysis, and therefore the process of creating financial scenarios,
is heavily influenced by the quality of the historical data. In countries where the value of past
data is questionable from a modeling perspective, one can consider adopting flexible
approaches that allow using several models interchangeably, as model performance can vary
19
depending on macroeconomic circumstances. In Turkeyâ€™s case, the financial scenario
generator is constructed as a stand-alone module, so that it is possible to shift conveniently
between different approaches without the need to adapt the remaining parts of TDSM.
Financial crises, regime changes and the significant market volatility that Turkey faced before
2002 create stationarity problems in retrospective time-series analysis. Since the country
entered a new economic policy environment after the beginning of the millennium, it is
difficult for any econometric model, based on long-term historical data, to reasonably
describe future financial outcomes. In order to address this problem, the starting point of the
historical financial data in input modeling was restricted to the beginning of 2002.
Additionally, a forward-looking simulation tool that allows for user calibration was
constructed. Another possible solution could be to adopt a deterministic approach and work
with user-provided scenarios.
The variety of instruments in multiple currencies poses an additional challenge in scenario
generation. The module is extended to cover yield curves not only for local currency bonds,
but also for USD- and Euro-denominated international bond issuances.
The financial scenario generator makes use of time-series analysis and imposes random
shocks to generate correlated paths for financial variables such as interest and exchange rates.
In this module, the main objective is to forecast and simulate variables that directly affect
Treasury debt dynamics and thus produce relevant scenario paths.
The variables that are forecasted and simulated in the Cost-at-Risk framework are as follows:
1. Term structure of interest rates
TRY yield curve
USD yield curve
Euro yield curve
2. Exchange rates
TRY/USD
TRY/Euro
3. Inflation rate (consumer price index)
20
A fixed and exogenous set of assumptions are used for other macroeconomic variables such
as GDP growth and primary balance based on medium-term program9 targets of the
government.
4.2.1 Model Selection10
Short-term interest rates are modelled by using Cox Ingersoll and Ross (CIR, 1985) and Chan,
Karolyi, Longstaff and Sanders (CKLS, 1992) models both with mean reversion properties.
The risk neutral interest rate process via CIR model can be described as follows:
dr ï€½ ï?« (ï?± ï€ r )dt ï€« ï?³ r rï?§ dZ (1)
where
r: Interest rate level
ï?« : Speed of return to the average (Speed of Adjustment)
Î¸ : Average long-term interest rate
Ïƒr: Interest rate volatility
dZ: Wiener process
ï?§ : 0.5
The CKLS model is the generalized version of the CIR model. In other words, in the CKLS
model the parameter ï?§ also needs to be estimated whereas in the CIR model this parameter is
restricted to 0.5.
CIR and CKLS models are mainly risk-neutral short-term interest rate models, and forecasting
and simulating long-term interest rates by using solutions of these models may be misleading.
Indeed, the solution of the CIR model proved to understate the term structure in the
experiments performed. Particularly, the CIR model is successful in capturing short-term
dynamics, but it performs relatively weakly for longer-terms. In order to address this issue, a
hybrid model with both mean reversion and dynamic term-structure fitting features is used to
estimate and forecast yield curves for TRY, USD and EUR interest rates.
9
Medium-term program of Turkey shapes public policies and operations on the basis of strategic objectives and
directs the resource allocation. Macroeconomic targets of the government are included in this program for the
upcoming three years.
10
The model parameters for short-term interest rates, exchange rates, and inflation rate are estimated by
employing the Generalized Method of Moments (Hansen, 1982).
21
As for the term structure part of the hybrid model, the approach developed by Diebold and Li
(2006) is used. The Diebold and Li model uses variations on Nelson-Siegel (1987)
exponential components framework to model the term structure of interest rates as a three-
dimensional designâ€”level, slope and curvatureâ€”evolving dynamically. In the model, yield
curves are fitted using the following functional form:
1ï€ e
ï€ ï?¬ï?´
t
1ï€ e
ï€ ï?¬ï?´
t
ï€ ï?¬ï?´)
yt (ï?´ ) ï€½ ï?¢1t ï€« ï?¢ 2t ( ) ï€« ï?¢ 3t ( ï€e t
(2)
ï?¬tï?´ ï?¬tï?´
where
t: time
ï?´ : time to maturity
The parameter ï?¬t in the above equation governs the exponential decay rate; small values of
ï?¬t produce slow decay and can fit the curve better at long maturities, while large values of ï?¬t
produce fast decay and can better fit the curve at short maturities. ï?¢1t , ï?¢ 2t and ï?¢ 3t are
interpreted as three latent dynamic factors where ï?¢1t governs the level of yield curve, ï?¢ 2t
governs its slope and ï?¢ 3t is closely related to the yield curve curvature (Diebold and Li, 2006).
To implement the hybrid model, the parameters ï?¢1 , ï?¢ 2 and ï?¢ 3 are estimated first based on
historical data, which constitutes the formation period. The second step involves forecasting.
ï?¢ 2t and ï?¢ 3t parameters are fixed to ï?¢ 2 and ï?¢ 3 based on their estimated values from the
formation period. ï?¢1t , the variable related to the level, becomes the only varying parameter in
generating forecasts and adjusted values for ï?¢1t are calculated from the short-term interest rate
level forecasts of CIR and CKLS models. The process for calculating adjusted ï?¢1t can be
described as follows:
1 ï€ e ï€ï?¬ï?´ 1 ï€ e ï€ï?¬ï?´
ï?¢1't ï€½ Lt ï€ ï?¢ 2 ( ) ï€ ï?¢3 ( ï€ e ï€ï?¬ï?´ ) (3)
ï?¬ï?´ ï?¬ï?´
where
ï?¢1t : Adjusted ï?¢1t
'
Lt : Simulated forecast level for short term at period t
22
After ï?¢1t is calculated using equation (3), this value is plugged into equation (2) as the new
'
ï?¢1t so as to estimate interest rates for all maturity segments. An out-of-sample forecasting
experiment displayed that combined hybrid model (CIR or CKLS with Diebold and Li) has
superior fit particularly for the longer terms compared to the stand-alone application of CIR
and CKLS models.
Dramatic changes in the slopes and curvatures of the term structure of interest rates (from
upward sloping to inverted yield curves etc.) due to macroeconomic environment may be the
dominant case for some bond markets across the globe. However, the upward sloping yield
curves with generally parallel shifts is a more common case for the securities issued by the
Turkish Treasury (Graph 1) and thus, level effect is a much more important determinant of the
term structures.
Graph 1: Evolution of TRY Yield Curves
10
20
y
10
ar
nu
20
Ja
ay
10
M
20r
11
be
20
m
te
y
ep
11
ar
nu
S
20
Ja
ay
11
M
20r
be
m
te
ep
S
Therefore, the hybrid model applied in yield curve estimation is designed to address primarily
the level effect. However, in this approach fixing the parameters governing slope and
curvature to the estimated values based on the formation period restricts the variety of slope
and curvature changes that may be witnessed in bond markets. For this reason, possible
changes in the slope of term structure of interest rates are analyzed with a supplemental
scenario called â€•yield curve shifting scenario.â€–11 This scenario is used within the simulation
framework and a discussion on this issue is provided in the following part.
It is a common view in financial markets that the information useful for exchange rate
forecasting tends to arrive randomly under a floating exchange rate regime and thus exchange
11
The experiments performed suggested that the curvatures of the yield curves were quite stable and designing
curvature scenarios from formation period had limited effect on yield curves. Hence, this scenario is structured
to include only slope changes. However, algorithms can be easily adjusted to cover curvature shocks as well, if
needed.
23
rates follow a random walk.12 Geometric Brownian motion is a stochastic process based on
random walk. In addition, the model specification is consistent with our multivariate
simulation setting. The process of a geometric Brownian motion is given below:
dS ï€½ ï?Sdt ï€« ï?³ e SdZ (4)
where
S: Exchange rate level
Âµ: Drift level
Ïƒe: Exchange rate volatility
dZ: Wiener process
It is assumed that the price index also follows a geometric Brownian motion. This is also a
consistent approach within the context of multivariate simulation setting since price level has
an important interaction with interest and exchange rates. When pricing inflation-linked debt,
the estimations of the Consumer Price Index level from the geometric Brownian motion
model is used together with the with real coupon rate estimations. Real coupon rates are
estimated via a simple regression model based on the historical relationship between real
returns and nominal returns of the comparable maturity fixed-coupon bonds. The estimates
from the regression analysis are compared with the real return estimations calculated by using
nominal interest rate and inflation rate estimations of the model for a consistency check.
The models used in the scenario generator were chosen among alternatives tested, including
other continuous time interest rate models and vector autoregressive approaches.
Performances of alternative models are compared on a regular basis. Should there be any
structural changes in the macroeconomic environment, the models can be improved or
replaced based on performance tests.
4.2.2 Simulation Framework
A key element in debt simulation is to ensure that risk factors (macroeconomic/financial
variables) are correlated in each scenario. This requires creating correlated random numbers.
For example, if the correlation between changes in exchange rates and price level is 0.8, one
would expect that when the exchange rate rises, the price level will rise 80% of the time. The
12
Meese and Rogoff (1983) showed in their seminal paper that main empirical exchange rate models have
inferior out-of-sample forecasting ability compared to models such as a random walk. These results have been
confirmed by a large number of studies.
24
focus here is to create random scenarios that would properly capture this relationship. Since
there are more than two risk factors in this simulation framework, the correlation is created by
decomposing the covariance matrix using Cholesky decomposition.
In the Cholesky decomposition method, a new upper triangular matrix, A, is found such that
the transpose of A times A equals the covariance matrix of financial variables. Then, random
numbers are drawn from a chosen distribution to create a random vector, Z. If A is multiplied
by Z, a vector of random risk factors that are correlated according to the original covariance
matrix is reached (Marrison, 2002). This vector is subsequently used to create simulation
paths that are consistent with historical correlations between financial variables. In TDSM,
the decomposition of the covariance matrix and the process of random number generation are
handled using built-in functions in the modeling platform.
TDSM provides flexibility to produce scenario paths based on different approaches: normal
distribution scenarios, fat tail scenarios, asymmetric shocks, yield curve shifting scenarios and
bootstrapping. Normal distribution scenarios are the default case, in other words normally
distributed errors form the benchmark stochastic environment. In addition to scenarios based
on normal distribution, the stochastic environment is enriched to cover extreme cases with
regard to the realizations of financial variables. In these alternative scenario generation
methods, only the error term distributions are changed in the process of random number
generation, while underlying stochastic model parameters remain as is.
The main elements of scenario generation options can be detailed as follows:
- Normal distribution scenarios: Produces simulation paths by using random shocks
drawn from standard normal distribution (N (0,1)).
- Fat tail scenarios (error shock): Fat tails are represented via t-distribution. This uses a
combination of random numbers from t-distribution with selected degrees of freedom
and standard normal distribution and provides the user with the flexibility to choose an
error shock based on future views. For example, if one chooses 10% as the shock
scenario ratio and 100 as the number of simulation paths, then 10 of the scenarios are
formed via random numbers from the t-distribution and the remaining 90 scenarios
from standard normal distribution.
- Asymmetric Shocks (Directed Error): This scenario option can be considered as a
subset of fat tail scenarios with one significant exception. In this case, the user can
25
select whether the random numbers from the t-distribution are generated from the right
tail or left tail.
- Yield curve shifting scenarios (beta shock): As discussed in the previous section, this
option is designed to cover potential slope changes of the yield curves. Selecting yield
curve shifting scenario gives shocks to the slope of the term structure based on the
historical minimum and maximum calculated in the formation period.
- Bootstrapping: This option follows a classical bootstrapping methodology for scenario
generation in which historical changes are used.
The financial scenario generator is run through a graphical user interface (GUI) created on the
Matlab platform. The GUI enables the user to select the variables to be simulated, the number
of scenario paths, forecast horizon (in months) together with methods to be used for
generating the random shocks. Relevant parameters, such as drift and volatility, are then
produced for the selected variables, based on historical data. A print screen of this interface is
presented below for illustrative purposes (Figure 2).
Figure 2: The Graphical User Interface for the Simulation Framework
An important feature of the scenario generation module is that it allows decision maker (DM)
interference to the process. A DM may believe that historical data will not fully reflect the
improvement (or deterioration) in the fundamentals of the country or the world economy over
26
time. In this case, after the model parameters of the financial variables are computed
internally, the DM can use the manual estimation option to produce financial scenarios based
on his/her future views or current market based data, considering that estimations based on
historical data are not â€•desiredâ€– reflectors of the future state of the economy. Forward looking
scenarios can be generated based on medium-term program targets of the government, central
bank inflation targets, or market expectations such as forward rates and implied option
volatilities. For example, in exchange rate scenario generation, one can adjust the drift term in
line with rate of increase implied by forward rates. Once the â€•estimatedâ€– or â€•user calibratedâ€–
parameters are determined for all financial variables, these are used to create final simulation
paths.
The simulation algorithms then produce the summary statistics (mean, 70th percentile, etc.)
regarding the distributions of financial variables. The DM can also interfere at this stage if the
summary statistics of these simulated paths reveal that the estimations based on historical data
deviates significantly from his/her market expectations. The DM could then calibrate the
model parameters by â€•trial-errorâ€– method until he/she reaches the desired distributions.
Even though, the â€•manualâ€– option provides additional flexibility, in the implementation of
TDSM, scenario generation based on automatic model estimation is considered as the default
case. In practice, no user calibration is performed without taking into account the scenario
trees generated by using the selected financial models described in section 4.2.1.
Once the simulation paths are generated, they are exported to MS Excel platform 13
automatically, where monthly forecasts are converted to quarterly14â€”granularity of the
modelâ€”data and then these quarterly paths are fed into the cash-flow engine module of
TDSM in order to estimate cost and risk profiles of alternative debt strategies.
4.3 Cash-Flow Engine
The cash-flow engine is where computations are carried out with regard to the borrowing
requirement, the bonds issued, the payments and finally the output metrics, given the scenario
paths. The central feature of the engine is the debt-stock matrix. This is a matrix where each
row represents a different financing instrument (i.e., Treasury bill, coupon bond, floating-rate
note, etc.) and each column represents a different attribute of the corresponding financing
13
Using MS Excel platform to transfer simulation paths to Matlab enables users to create their scenarios
manually (deterministic scenarios) and feed them easily to the Cash Flow Engine.
14
Although, TDSM performs mainly on quarterly granularity, financial scenario generator is based on monthly
historical data and subsequently provides monthly forecasts. Since historical financial data was restricted to the
beginning of 2002, this approach enables to extend the length of data set.
27
instrument. These attributes include the coupon rate, payment frequency, currency, issue date,
and maturity date among others.
At the inception of each simulation and at the beginning of the simulation horizon, the debt-
stock matrix provides a description of the initial debt stock. The first task performed by the
model involves, in fact, the initialization of this debt-stock matrix using the actual debt stock
from the debt stock database. The majority of subsequent operations in the model are
performed by either updating the debt stock matrix or by using the information embedded in
the matrix to perform an ancillary calculation. In summary, the debt stock matrix, by virtue of
the fact that it represents a description of the entire debt stock at any given point of time, is
the central element of the TDSM implementation.
The principal application of any debt strategy model is the computation of the cost-risk
distributions for a number of alternative financing strategies over a pre-defined time horizon.
In the model, this is accomplished by a nested loop. The loop has three layers. The first layer
loops over the number of financing strategies. The second layer loops over the number of
stochastically generated interest and exchange rate outcomes. The third and final layer loops
over each of the time steps across the simulation horizon.
The bulk of the computation occurs at each quarterly time step. At each of these quarterly
time steps, a sequence of stages is performed.
- The first stage in this sequence is the computation of cash flows, performed by
screening the debt stock matrix using the attributes corresponding to the instruments,
kept in each row.
- Consequently, the matrix is updated by deletion of maturing bonds/bills.
- The next stage is the computation of the gross funding requirement, which equals the
net cash flow at that time step. The inflows are determined by the assumptions
regarding the primary surplus, privatization revenues, etc. for each quarter. These
quantities are fed into the model at inception and assumed to remain fixed across all
scenarios and financing strategies. The outflows are given by redemptions calculated
in the first stage plus some pre-fixed payments of the government, also fed during
initialization.
- The fourth stage involves applying the financing strategy, represented as a vector of
weights, to compute the amount of issuance in the current time step. TDSM uses a
flow-based rule to determine the issuance and meet the gross funding requirement.
28
Each individual element of the vector corresponds to a bond or bill and denotes the
proportion to be issued in that security to meet the funding requirement. The user
chooses from a pre-defined set of bonds and decides on the ratio of each instrument in
the incumbent strategy. The borrowing composition is fixed for each quarter of a
given year, while it may change from year to year in the decision horizon.
- In the fifth stage, the debt-stock matrix is updated based on instruments issued.
The above quarterly approach is repeated for all time steps, scenarios and strategies. Finally,
the expected cost and risk indicators of alternative strategies are generated as outputs. The
analysis of the outputs is discussed in the following section. The general framework of the
stochastic simulation algorithm and the summary of the previously discussed sequences are
presented below (Figure 3)15.
Figure 3: Stochastic Simulation Algorithm of TDSM
Enter the number of strategy alternatives to be tested
Enter the number of scenarios (Simulation paths)
Enter the forecast horizon (in quarters) Repeat for each alternative
strategy to be tested
Run the DebtSim
1. Select the first financing strategy
2. Select the first simulation path
3. Select the first time step
Calculate debt payments arising from existing debt stock (Initialize Debt-Stock Matrix)
Update debt-stock matrix by deleting maturing instruments Repeat for
Calculate financing requirement each
Issue new debt simulation
Update debt-stock matrix by adding new issuances path
Repeat Step 3 for each time step
Iterate Step 3 with the next simulation path
Compute and save debt-cost distributions for given strategy
Compute and save debt structure metrics for given strategy
Select second financing strategy and repeat Steps 2 and 3
Repeat for each step
in the forecast horizon
5. Experimental Framework: Runs and Analysis
Simulation models are developed to experiment with alternative policy designs. Once the
coding process, i.e., representing the behavior of the system in a computer language is over,
the analystsâ€™ next task is to develop an experimental framework that includes several steps
from checking the accuracy of the system representation to designing policy inputs, running
the model and analyzing the outputs.
Similar to other simulation analyses, experimenting with TDSM involves the following steps:
15
Figure 3 is adopted from â€•Stochastic Simulation Algorithmâ€– in Bolder and Deeley (2011, p.7) due to
similarities of simulations frameworks.
29
5.1 Verification and Validation
After completing the coding, the first stage is to ensure that the computer program performs
properly. This â€•verificationâ€– process includes debugging and ensuring that the code produces
correct computations. The verification of TDSM involves checking the cash-flow
calculations, i.e., interest and principal payments for different types of bonds and ensuring
that the borrowing requirement and the issuance amounts are correctly computed in the model
given a certain scenario and a borrowing strategy. This process is crucial after the
construction of the model and should be repeated following modifications such as adding new
instruments to the model.
The â€•Validationâ€– stage is about testing the consistency of the model and determining that the
model is a correct representation of the real system as far as the modellersâ€™ purposes are
concerned. The TDSM is validated by analyzing the financial scenarios generated to ensure
that they are justifiable given the current macroeconomic outlook and future possibilities. At
this stage, one can rely on expert judgement regarding economic fundamentals and/or market
based forecasts with regard to the span of the scenario tree. For example, one should not
expect to have negative inflation rates in an environment of depreciating local currency if the
price level is heavily influenced by prices of imported goods. In such a case, the model
specification should be re-visited.
The cost and risk metrics are also analyzed, depending on the decision makersâ€™ choices and
characteristics of the instruments added to the model. These two steps together make sure that
the right model is built rightly.
5.2 Experimental Design
Experimental design involves determining the policy alternatives to be tested in the model.
Risk managers in charge of model building are responsible for determining which strategy
alternatives are worth considering and whether the alternatives are applicable given the
market constraints. At this stage, coordination with the front-office may also be required to be
able to incorporate their views about market conditions.
In designing strategy alternatives, maximum issuance limits are set for some particular
borrowing instruments based on historical and expected market demand, i.e., constraints are
imposed. An issuance floor is set for some securities across the yield curve in line with the
objective of developing and maintaining an efficient and liquid market for government
30
securities. In addition, if the market appetite for a type of security is expected to increase in
the future, this is reflected through the increasing issuance amounts over time, within the
decision horizon.
The strategy alternatives are chosen to ensure that each alternative represents a specific policy
direction (with a story behind it) that can be pursued by DMs. Some of the alternatives tested
previously include strategies with regard to â€•cost minimization,â€– â€•moderate risk reduction,â€–
â€•currency risk reduction,â€– â€•ambitious risk reduction,â€– and â€•maintain current profile.â€–
Alternatives based solely on a single borrowing instrument are also tested to identify the
different cost and risk characteristics of the securities (for example, 100% CPI-indexed bonds
vs. 100% floating-rate notes). The strategy alternatives are designed by plugging in the
appropriate weights in the financing strategy vector, described in section 4.3. For example,
weights of local currency instruments are increased in the vector to develop a â€•currency risk
reductionâ€– strategy.
5.3 Runs and Analysis of Results
Following the creation of simulation paths and selection of alternative strategies to be tested,
TDSM then calculates the cash flows associated with each strategy. This module also
compiles summary statistics (mean, conditional-at-risk values for different percentiles, etc.) of
the distributions for these strategies with respect to the measures discussed in Section 3.1. The
future levels of debt structure metrics discussed in Section 3.3 is calculated for each strategy
tested. As the model is capable of producing interest and principal payments and future debt
stock levels for each strategy under each simulation path, other cost and risk indicators can
easily be calculated.
Each alternative strategy following a different policy direction is then numerically presented
in terms of the debt structure metrics. For example, the share of local debt will be higher for a
â€•currency risk reductionâ€– strategy compared to a â€•maintain current profileâ€– strategy. Debt
structure metrics for alternative strategies is then reported to senior management together with
the expected cost and risk levels of these strategies for each year in the decision horizon. An
illustrative result for the distribution of cash-based interest costs under 5,000 simulation paths
for a strategy tested is presented in Graph 2.
31
Graph 2: Distribution of Interest Costs
Frequency
Since the first cost metric is based on cash-based interest payments and the other two metrics
are based on debt stock levels, different measures may give different rankings of the
strategies. In particular, alternative strategies assuming a higher share of foreign currency-
denominated and/or inflation indexed debt in the future may provide the best rankings in
terms of cash-based interest cost, while they may rank differently with respect to debt stock
related measures. Therefore, a comprehensive analysis on rankings of different strategies is
provided for strategy formulation process. In many multiple criteria cases, there is not a single
choice that is best for all criteria. Usually, one needs to give up in some criteria in order to
improve in others. In general, if we have more than one decision criteria, a solution (a strategy
in our case) is said to be â€•inefficientâ€– or â€•dominatedâ€– if there exists another solution that is
equally good in all objectives, and better in at least one measure. Some of the strategies tested
in the simulation model may be dominated by other strategies, and these are then excluded
from the analysis. The DMs then evaluate the efficient solutions and decide on one strategy
depending on their preferences. The risk management team also presents its strategy
recommendation with underlying rationales to DMs in order to assist the decision-making
process.
As a complement to the primary outputs of TDSM, analyses with regard to market demand
for government auctions and different securities, volatility and covariance profile of exchange
rates and redemption profile for upcoming years are also reported to DMs in order to enhance
the decision-making process in strategy formulation. This can be supplemented with a stress-
testing component that aims at quantifying and comparing the exposure of public debt
dynamics to different types of shocks such as a depreciation of the exchange rate.
These outputs and analyses are not the sole criteria in making the final decision about the debt
management strategy. Assessments about the macroeconomic environment, the market
32
outlook, the considerations of front offices and other restrictions or objectives arising from the
economic policy framework are also key factors in strategy selection.
6. Concluding Remarks
The paper addresses two main objectives. The first is to share Turkeyâ€™s experiences on the
process of developing a model to support debt management strategy decisions. Model
development for debt managers is especially challenging since the academic literature on this
field and material publicly shared by debt management offices is limited. That said, we
learned much from the examples of countries that were kind enough to disclose the details of
their models, and we hope this paper will provide some insight for debt offices that are
considering, or in the process of building, their own analytical tools. For this reason, we have
described not just the technicalities, but also the conceptual stages of the modelâ€™s
development, which we consider to be crucial in model building. In this sense, this paper also
provides an opportunity to compare the methodology used in Turkey to the approaches
followed by other debt management offices (mainstream applications). The Turkish
Treasuryâ€™s model can be classified in the class of debt management strategy models in which
only financial variables are stochastically simulated and macroeconomic variables are treated
as exogenous. The approach used for modeling the relationship between the financial
variables is based on the statistical analysis of their behavior and correlations.
The second objective in introducing the model is to invite comments on its quantitative
structure to gain insights for further progress. As debt management offices operate in a
dynamic environment, their models also need to cope with altering environmental factors.
Therefore, no model can be used indefinitely with a static form. The TDSM has been in use in
its current structure since 2007, with some modifications required by the debut of new
instruments, such as inflation-linkers. The introduction of new instruments not only
necessitates an adjustment of cash-flow calculations in the engine, but may also necessitate a
reassessment of the cost and risk indicators, as in the case of Turkeyâ€™s cost metric.
The TDSM is actively used in debt management strategy formulation and decision-making
process. The model proved to be quite robust even during the global financial crises. The
scenarios generated were able to cover extreme events, and hence, the tail risk. Nevertheless,
we believe there is room for modifications and improvement, particularly in scenario
generation and future work should focus in this area.
33
References
Anderson P, 2011, â€•Optimal Uses of Risk Management Techniquesâ€–, Presentation at the
Eighth UNCTAD Debt Management Conference,
(retrieved on December 17, 2011).
Balibek E and KÃ¶ksalan M, 2010, â€•A Multi-Objective Multi-Period Stochastic Programming
Model for Public Debt Managementâ€–, European Journal of Operational Research 205:
205-217.
Banks J and Carson SC, 1984, Discrete Event System Simulation, Prentice Hall: Englewood
Cliffs, New Jersey.
BergstrÃ¶m PB, Holmlund A and Lindberg S, 2002, â€•The SNDOâ€™s Simulation Model for
Government Debt Analysisâ€–, Swedish National Debt Office (SNDO),
(retrieved on March 08, 2011).
Bolder DJ, 2002, â€•Towards a More Complete Debt Strategy Simulation Frameworkâ€–, Bank of
Canada, Working Paper 2002-13.
Bolder DJ, 2003, â€•A Stochastic Simulation Framework for the Government of Canadaâ€™s Debt
Strategyâ€–, Bank of Canada, Working Paper 2003-10.
Bolder DJ and Rubin T, 2007, â€•Optimization in a Simulation Setting: Use of Function
Approximation in Debt Strategy Analysisâ€–, Bank of Canada, Working Paper 2007-13.
Bolder DJ and Deeley S, 2011, â€•The Canadian Debt-Strategy Model: An Overview of the
Principal Elementsâ€–, Bank of Canada, Working Paper 2011-3.
Cox JC, Ingersoll JE and Ross SA, 1985, â€•A Theory of Term Structure of Interest Rateâ€–,
Econometrica 53: 385-407.
Chan KC, Karolyi GA, Longstaff FA and Sanders AB, 1992, â€•An Empirical Comparison of
Alternative Models of the Short-Term Interest Rateâ€–, Journal of Finance 47: 1209-1227.
Consiglio A and Stanio A, 2010, â€•A Stochastic Programming Model for the Optimal Issuance
of Government Bondsâ€–, Annals of Operations Research,doi:10.1007/s10479-010-0755-5
Danmarks Nationalbank, 2005, Danish Government Borrowing and Debt,
(retrieved on January 29, 2011).
34
Diebold FX and Li C, 2006, â€•Forecasting the Term Structure of Government Bond Yieldsâ€–,
Journal of Econometrics 130: 337-364.
Granger R, 2005, â€•Risk Management of Government Debt in Portugalâ€–, In: Advances in Risk
Management of Public Debt, Vol.6. OECD Publishing: Paris.
Hansen LP, 1982, â€•Large Sample Properties of Generalized Method of Moments Estimatorsâ€–,
Econometrica 50: 1029-1054.
International Monetary Fund and The World Bank, 2001, Guidelines for Public Debt
Management, International Monetary Fund Publication Services: Washington, D.C.
International Monetary Fund and The World Bank, 2003, Guidelines for Public Debt
Management-Accompanying Document and Selected Case Studies, International
Monetary Fund Publication Services: Washington, D.C.
Jensen OS and Risbjerg L, 2005, â€•Recent Developments in the Management of Market Riskâ€–,
In: Advances in Risk Management of Public Debt, Vol.6. OECD Publishing: Paris.
Kocher PA and NebenfÃ¼hr G, 2005, â€•Risk Management of Government Debt in Austriaâ€–, In:
Advances in Risk Management of Public Debt, Vol.6. OECD Publishing: Paris.
Marrison C, 2002, The Fundamentals of Risk Measurement, McGraw-Hill.
Meese RA and Rogoff K, 1983, â€•Empirical Exchange Rate Models of Seventies: Do They Fit
Out of Sample?â€–, Journal of International Economics 14: 3-24.
Mitchell G, 1993, The Practice of Operational Research, John Wiley and Sons: Chichester,
West Sussex.
Nelson CR and Siegel AF, 1987, â€•Parsimonious Modelling of Yield Curvesâ€–, Journal of
Business 60: 473-489.
Organization for Economic Cooperation and Development (OECD), 2010, Debt Structure and
Risk Metrics â€“ OECD Questionnaire on Debt Portfolio Management.
Organization for Economic Cooperation and Development (OECD), 2005, Advances in Risk
Management of Government Debt, Vol.6. OECD Publishing: Paris.
Pick A and Anthony M, 2006, â€•A Simulation Model for the Analysis of the UKâ€™s Sovereign
Debt Strategyâ€–, UK Debt Management Office Research Paper.
Risbjerg L and Holmlund A, 2005, â€•Analytical Framework for Debt and Risk Managementâ€–,
In: Advances in Risk Management of Public Debt, Vol.6. OECD Publishing: Paris.
35
Silva AC, Carvalho LO and Medeiros OL, 2010, Public Debt: The Brazilian Experience, The
World Bank and National Treasury of Brazil, Brasilia.
The World Bank and International Monetary Fund, 2009, Developing a Medium-Term Debt
Management Strategy (MTDS)-Guidance Note for Country Authorities, Washington,
D.C.
Turkish Treasury, 2004, Public Debt Management Report, February 2004,
(retrieved on February 14, 2011).
Turkish Treasury, 2008, Annual Public Debt Management Report 2008, (In Turkish),
(retrieved on February 17, 2011).
Velandia A, 2002, â€•A Risk Quantification Model for Public Debt Managementâ€–, The World
Bank Working Paper 2002-45233.
36