June 8, 1999
The Ministry of Finance
103 33 STOCKHOLM
Methods for analysing the structure of the central government debt
In 1998, the Riksdag decided on certain amendments to the Act (1988:1387) on Government Borrowing and Debt Management. Pursuant to the new rules, the government was, following proposals from the Swedish National Debt Office, to establish fixed guidelines for the management of the central government debt. The government, in its directive for 1999, instructed the Debt Office to develop simulation methods for analysing the costs and risks associated with alternative debt structures. The proposal shall be drawn up in consultation with the Ministry of Finance (Financial Markets Department). The result of this assignment is presented in this memorandum in the form of a concrete proposal for a model for analysing the structure of the central government debt and for drawing up proposals for guidelines. This memorandum also includes a discussion of what definitions of cost and risk should be used as a basis for making decisions on the structure of the debt.
1.2Points of departure
The purpose of this memorandum is, in the first instance, to describe how a decision-support model for the preparations of guidelines should be designed. On the basis of the directives included in the government’s guidelines for the current year, the main task at this stage is to develop a model that is directed towards analysing the debt portfolio at a level corresponding to the government’s decision on guidelines, i.e. the overall structure of the debt in terms of instrument and maturity. Questions concerning benchmarks and relevant definitions of risk also have a natural place within the framework of the description of the model. Once this general framework is in place it is, however, desirable to use the same principles and models as instruments for the design of sub-benchmarks, and in the day-to-day management of the debt. However, this requires further study and is not addressed in this report.
It should also be emphasised that the model outlined in this report is an expression for long-term goals with regard to modelling. In the short term, i.e. in the preparations for the guidelines for 2000, the work on the model is to some extent constrained by lack of time. The Debt Office is currently engaged in procuring consultancy services for:
a)Drawing up a report based on a model constructed in accordance with the ideas outlined in this memorandum.
b)Support with the development of an in-house model for the Debt Office, in accordance with the ideas outlined in this memorandum.
As it is of the greatest importance that a quantitative background is available before the guidelines are decided for 2000, it will, in all probability, be necessary to make certain adjustments to the standard solutions that the consultants in question can have at their disposal. The aim is to create a model based on the Debt Office’s specific requirements, as soon as possible. It will, however and in all probability, be difficult to achieve this in time for this year’s benchmark proposal.
It should also be emphasised that the purpose is to develop a model that will serve as a basis for decision; not an instrument that more or less automatically creates an optimal government debt portfolio that can be translated into a concrete decision on guidelines. A model can be used to derive a debt portfolio which, from given assumptions regarding the characteristics of the economy, the connection between interest rates, exchange rates, and inflation, etc., has optimal qualities. Uncertainty concerning the conformity of the model with the real world in which the result shall be applied means, however, that it cannot be applied mechanically. Decisions on guidelines for debt management must, therefore, be made on the basis of assessments of a qualitative nature, where quantitative results from simulation models form part of the background material.
As an introduction to the description of how the model and the work it involves are to take shape, the overall requirements and principles that should serve to guide the quest for a suitable model are outlined below.
a) An intuitive, creative instrument
A model for analysis of the debt management shall, above all, be capable of serving as a creative instrument. A properly designed instrument support the discussions conducted between the Debt Office and the Ministry, between the Debt Office’s board and its management, and also for the operative internal work at department level.
One basic requirement, therefore, is that the model be so simple that it offers a clear intuition. A model that recommends a counter-intuitive debt structure and management will not be accepted as a guideline for deciding on benchmarks. In the procurement of consultancy services it is essential to assure that the Debt Office acquires an instrument over which it has complete control.
b) The right degree of precision
It is important that the target variables set up for the model actually correspond to the goals stipulated in the act on the management of the central government debt. The choice of cost definition is far from self-evident. Market valuation is a straightforward method that fails, however, to take proper account of the risks associated with central government debt management, as the risks largely consist of refinancing risk and cash flow risks, rather than a straightforward market risk. It is more important that the definition is correct rather than that it is precise, as a precise definition that includes the wrong elements, gives rise to false precision and can also lead to decisions that reduce the probability of achieving the actual goals. Agreat deal of attention should therefore be given to finding a goal and definition of this goal with a realistic degree of precision and that is closely connected to the conditions for debt management.
1.3The organisation of the report
The main parts in the decision-support model are described in brief in the section below. The individual aspects are described in greater detail in the sub-sections that follow, where ideas and considerations relating to each building block in the model are examined in more detail.
The model, in its simplest version, consists of three building blocks:
- A description of possible portfolio strategies.
- A simulation of possible interest rate, exchange rate and inflation scenarios.
- A quantification of the average costs and risks for each portfolio strategy based on the simulated scenarios.
The idea is that the search for an optimal debt portfolio should start with a number of stylised debt portfolios defined on the basis of a limited set of strategies. These strategies include a so-called status quo-portfolio, which describes the characteristics that the central government debt has today, i.e. before any decision on an alternative direction has been made. By strategy is meant a pattern of issues that gives rise to a certain distribution by types of debt (nominal, inflation-linked, and currency debt) and a certain maturity by within each type of debt. In principle, each strategy gives rise to a benchmark candidate.
The average costs and risks associated with each strategy can be quantified by applying these strategies in a large number of interest rate scenarios. The quantification is made by estimating for each strategy the cost and risk definition that reflects the various dimensions of risks that debt management involves; see also section 4.
These exercises then lead to changes in the set of portfolio strategies, where strategies with unfavourable characteristics (high cost and/or high risk) are eliminated and the remainder are examined in more detail. The new strategies are then applied to the interest rate scenarios in an iterative process. Finally, it is hoped, one obtains a set of strategies that reflect the costs and risks associated with a status quo-strategy, as well as with a range of strategic changes in the direction of the debt management. These options, which have been worked out in detail, then serve as a basis for the Debt Office’s recommendation and the government’s decision on guidelines.
In the following sections, the different building blocks are discussed in greater detail; the first point is how the various interest rate scenarios are intended to be formulated (Section 2). The points discussed in this section are, for example: What role should forecasts of macro-economic developments play? What variables must be simulated so that we will have a reasonably complete picture of the risks involved in the management of the central government debt? What processes can it be assumed that these variables follow? How can the dependence between interest rates and exchange rates be modelled? How are these scenarios finally converted into yield curves?
Section 3 deals with questions that arise in the process of formalising the various portfolio strategies. How are the different borrowing/management strategies described in a reasonable way so that they fit into the framework of the model? What degree of precision is needed, and what simplified assumptions can be made?
Section 4 looks in more detail at the issue of what the relevant definition of cost should be for the debt management. Which definition corresponds best to the goals laid down in the Act on government borrowing and debt management? To what extent is a market valuation relevant, and what role does the cash flow risk play?
The final section covers the implications for and the work involved in arriving at new and modifying existing definitions of risk for the Debt Office’s debt management activities.
2Simulation of scenarios
It is impossible to discuss an optimal portfolio structure for the central government debt without having some idea about future changes in interest rates. One alternative is to make explicit predictions of future interest rates on the basis of a detailed macro-economic forecast. The result will then be a model whose success will depend on the ability to predict the future. The long-term character of debt management activities would make such forecasts particularly uncertain. The result could consequently be high costs and high risks. A more robust approach is therefore to be preferred.
One possible alternative is to acknowledge the difficulties involved in predicting the future and, as far as possible, to refrain from doing so. An extreme starting point could then be to create interest rate and exchange rate models in the form of a random walk, i.e. to assume that the changes in these variables are independent of other variables and their own historical development. There is, however, a risk that such an approach would lead to uncertainty being overestimated, which would tend to favour more risk-averse strategies.
A reasonable middle way is to attempt to incorporate information that is available with a fair degree of certainty. Views on where in the business cycle the Swedish economy at present is could be a good starting point. We also have some idea about how interest rates exchange rates and the borrowing requirement behave during recessions and booms. If the model is used to roughly describe these conditions and then, using stochastic methods, to simulate changes in interest rates over an extended period of time, one should obtain a fairly accurate picture of future interest rates, upon which the various portfolio strategies can be tested.
It should be noted that the intention is not to produce a forecasting model. The model simulates economic recessions and booms, and the interest rates associated with these conditions, but does not take a stand on the timing of a change in the direction of the economy. One approach with theoretical characteristics that correspond to those mentioned above, and which has also turned out to be empirically successful, is so called regime-switching models. The following section explains how this approach could be used for the application in question.
2.2The business cycle model
There are several stages to a simulation of interest and exchange rates: In the first stage a regime-switching model simulates switches between economic upswings and downturns. Depending on whether the economy is in a boom or a recession, the model then simulates time series for a number of variables that are of interest. These variables are then used as direct input data for cost and risk calculations, and they also serve as a base for the creation of yield curves, which in turn serve as input data for cost and risk calculations.
The core of the simulation model is thus a regime-switching model that determines the swings between economic recessions and boom conditions. This type of model was first proposed by Hamilton (1988) and has gained widespread acceptance in empirical macro-economic applications. The basic idea is that observable variables, such as growth, inflation and interest rates can be characterised by one model during boom periods and by a different model during recessions. A variable, which is not directly observable, that can only assume two values (i.e. boom and recession) then determines which of the regimes is currently in effect.
The result is a model that is non-linear and also rather difficult to handle. However, by assuming that the probability of being in a certain regime in the next period is solely determined by which regime is in effect during the current period, the problem becomes much more manageable. The non-observable variable is then said to follow a Markov chain. A typical parameterisation of such a model could be to state that there is a 90 per cent probability that one quarter of boom in Sweden will be followed by another quarter of boom.
The probability stated corresponds to the observation that on average a period of high growth lasts for ten quarters (1/[1-0.9] = 10), which is an empirically testable implication. Slightly simplified, this is also what happens when the model is estimated. This estimation gives the probability parameter a value that means that the two regimes’ separate models together give model values for the observable variables which ends up as close as possible to the data we actually observe.
For simulation purposes, models of this type are particularly useful. By starting Markov chains in the regime we currently observe, and then allowing them to develop on the basis of a stochastic pattern over time, we obtain chains with values that are, on average, similar to historically observed ones. However, we will also obtain individual chains with values that imply economic growth periods and recessions of significantly longer or shorter duration than average.
The mainspring of the simulation model is, therefore, the stochastic shift between boom and recession. It is, however, important to emphasise that this is not a forecasting model. The model says nothing about when the economic cycle will change direction, merely that it will, and what is the period of time which, on average, passes between these changes. It is the inherent random factor in this process that determines the variance simulated by the model and that is then used to quantify the risk in any given portfolio strategy.
2.3Simulation of individual variables
The simulation model includes a number of equations for certain variables, such as short-term interest rates in Sweden and abroad, exchange rates, inflation and the borrowing requirement. All variables are provided with two equations, one for each regime. In their simplest form, these could be an unconditional expected value for each regime. In addition, a variance-covariance matrix is estimated for the processes involved. This can also be allowed to be regime dependent.
The design of the model will in this respect initially depend on the choice of partner in the current procurement process. Exactly which specification the model should have for each variable and regime, is an empirical question. The two criteria that should be used are, in all circumstances, a parsimonious parameterisation and the requirement that the parameters included in the model are constant over time. The first criterion is of particular importance in this application as it is essential to ensure robust results rather than a high explanatory power from each individual model.
When it comes to changes in short-term interest rates, it could be desirable to use a well established theoretical model, such as that developed by Cox, Ingersoll and Ross (1985). The essential difference in relation to the original approach is that the parameters would change with the regime.
A model for exchange rates will most likely be based on a equilibrium rate given by along-term purchasing power parity condition. One may add to this long-term equilibrium rate toward which the exchange rate is assumed to converge the relative regime position and the international long-term yield spread. There is a risk that this partial model could quickly become extremely complex, particularly if the number of countries included is large. To the extent that an existing model structure is not already available, but has to be developed together with the external consultant, it is desirable to keep the number of countries limited to ensure that the model as a whole remains transparent.