Danish Government Borrowing and Debt

10.1 Summary

In recent years international focus on risk management within government debt management has sharpened. Government debt management in Denmark has also worked extensively with risk management for a number of years.

Risk management is applied to the overall central-government debt. The predominant risk to which the Danish government debt is subject is the interest‑rate risk on re‑financing the debt at unknown future interest rates. A low interest‑rate risk typically entails higher costs. It is therefore necessary to weigh expected costs against risks. Government Debt Management has developed a quantitative model for identification of expected costs and risks that can be applied to this weighing (Cost‑at‑ Risk, CaR). The chosen trade‑off between costs and risk is hereafter managed on a continuous basis by applying strategic benchmarks/focal points to the distribution of borrowing on various maturities, the duration of the central-government debt, and the size of the annual redemptions.

Internationally, in a more academic perspective, there has been increased focus on the potential derived effects of costs and on the interaction with the macroeconomy. Here, the interest‑rate risk is related to the central government's budgetary position in order to achieve "budget smoothing".

10.2 Interest-rate risk in brief

In relation to government debt management, interest‑rate risk can be defined as the risk of refinancing the debt at unknown future interest rates. A debt portfolio where redemptions are spread smoothly across a relatively long horizon will be associated with a low interest‑rate risk. This is because the refinancing requirement will be smoothly distributed, while the interest payments on a larger proportion of the debt are fixed for a longer period. This limits the risk of a sudden increase in the interest costs on the debt. A low interest‑rate risk can, however, entail higher average costs, since long‑term borrowing is typically relatively expensive. The interest‑rate risk must therefore be weighed against the interest costs.

10.3 Choice of risk-management framework

In the management of the central government's exposure to market developments it is appropriate as a general principle to consider the central government's financial portfolios on a consolidated basis. This makes it possible to compile the overall exposure of the central government in accordance with the principles for asset liability management, cf. Box 10.1. On defining the interest‑rate risk, cf. Section 10.2, it can thus be relevant to set off any income and financial assets.

Asset Liability Management

Box 10.1

Asset Liability Management (ALM) is a risk‑management principle that is often applied in private financial institutions. ALM states that, as far as possible, the entire balance sheet, i.e. both assets and liabilities, should be included in the risk analysis, in order to compile the overall exposure. This makes it possible to limit the risk by matching the financial characteristics of respectively assets and liabilities, so that one side of the balance sheet hedges the other.

This principle is applied to the exchange‑rate risk on the foreign government debt and Danmarks Nationalbank's foreign‑exchange reserve. The central-government's foreign debt, which is raised in order to finance the foreign‑exchange reserve, is exclusively exposed in euro. At the same time, the currency exposure on Danmarks Nationalbank's foreign‑exchange reserve is predominantly in euro. The objective is to avoid raising loans in one currency and thereafter placing the proceeds in another currency. This reduces the exchange‑rate risk on the central-government debt, and on Danmarks Nationalbank's foreign‑exchange reserve, taken as one.

The ALM approach also comprises matching of portfolios without explicit financial characteristics. Life assurance companies can e.g. reduce the risk by investing in financial assets with a payment profile that reflects the expected obligations as determined by actuarial tables of expected mortality.

In Danish government debt management , the interest‑rate risk on the overall central-government debt, comprising the domestic and foreign debt, less the assets of the Social Pension Fund and the balance of the central government's account with Danmarks Nationalbank, is managed. The central government's assets from re‑lending are also included in the portfolio management by Government Debt Management. The net debt approach entails a more comprehensive assessment of the central government's exposure to fluctuations in interest rates in accordance with the ALM principles.

10.4 Quantification of trade-off between costs and risk

The basis for determining an ongoing strategy for the government debt policy is an analysis of the trade‑off between expected costs and risks for various strategies. This enables the central government to choose a strategy that entails an appropriate weighing of costs against risk.

Analyses of various profiles of costs and risk require scenarios to be set up for the expected development in interest rates. Based on the expected future financing requirement, the expected costs for a given strategy can hereby be calculated. The risk entailed by the strategy can be compiled as the potential increases in interest costs measured in relation to the interest costs in the expected or most probable scenario.

Within government debt management various approaches and models are applied to this analysis. Often, relatively simple models are used, based on a few deterministic scenarios. The central scenario can be based on a simple assumption of e.g. unchanged interest rates, or the starting point may be implicit forward interest rates. The central scenario can then be compared to ad‑hoc adjustments or historical series.

In Danish government debt management, deterministic scenario analyses are applied to e.g. stress tests of the development in costs. However, for the actual analysis of the trade‑off between expected costs and risk, Government Debt Management has developed a stochastic simulation model, the Cost‑at‑Risk (CaR) model. In the CaR model, 2,500 scenarios for the development in interest rates are simulated for each quarter within a 10‑year horizon, so that probability distributions of costs can be set up. The advantage is that actual quantification of the risk requires assignment of different probabilities to the cost scenarios.

So far, the CaR calculations have only been applied to the domestic debt, which constitutes the greater part of the debt, and the central government's asset portfolio from re‑lending. The other portfolios of the government debt will be implemented in 2003. This makes it possible to quantify the trade‑off between costs and risk for the overall government debt.

The Cost-at-Risk-model
The structure of the CaR calculations is illustrated in Chart 10.4.1. The basis is information on the existing portfolio (outstanding amount in all government securities and the swap portfolio) and the central government's expected future budget surplus. In addition to this comes input concerning the strategic arrangement of the government debt policy, including the distribution of future borrowing on various maturity segments, the frequency at which new securities series are opened, and the volume of future swaps and buy‑backs of government securities.

Structure of CaR calculations	Chart 10.4.1

All in all, this information gives the central government's current borrowing requirement, the distribution of new borrowing on various securities and the central government's interest-rate exposure. New redemptions and interest payments are subsequently included in the future borrowing requirement.

The interest costs are calculated on the basis of simulated zero-coupon-yield curves. The yield curves are applied in the model to determine coupon rates for new loans, the swap interest rates, and prices for bonds subject to buy-back.

The calculations are made for 2,500 scenarios. Each describes a particular development in interest rates on a quarterly basis over 10 years, and thereby a specific scenario for the development in the interest costs on the debt.

On the basis of the 2,500 scenarios, a probability distribution for the annual interest costs during the simulated period can be determined. The expected future annual costs of a given strategy are calculated as the mean value of the calculated costs. The risk is summarised in two measures: absolute CaR and relative CaR. Absolute CaR for a given year states the maximum costs with a probability of 95 per cent. Relative CaR is the difference between absolute CaR and the mean value. Relative CaR is thus a measure of the maximum increase in costs from the mean value for a given year, with a probability of 95 per cent. The quantification of risk in CaR is methodologically related to Value‑at‑Risk (VaR), cf. Box 10.2.

CaR Versus VaR

Box 10.2

In methodological terms, CaR is related to VaR, which is a risk‑management instrument that is much used by asset portfolio managers. VaR expresses the maximum loss in a portfolio's market value with a given probability over a given – typically short – horizon. CaR expresses the maximum increase in the annual interest payments on the debt with a given probability in the medium and long term.

Both CaR and VaR entail quantification of the risk, depending on the probability distribution of the future market development. In CaR, the time horizon is relatively long. The purpose of the CaR analysis is to assess the differences between various strategies in the longer term, i.e. the strategies' average characteristics. The risk related to short‑term fluctuations in market interest rates is countered by e.g. spreading borrowing across the year. This reduces the central government's exposure to short‑term volatility.

In the CaR model, a number of other useful key figures are also calculated, e.g. the central government's annual borrowing requirement, the size of the government debt, the redemption profile of the debt, the outstanding volume in various securities, and the duration of the central-government debt.

Use of CaR to determine strategy
The results of the CaR model are used as a strategic reference when planning the government debt policy. The reference contains an analysis of the profile for the expected costs and risks (absolute and relative CaR), subject to various assumptions concerning the government debt policy.

Chart 10.4.2 illustrates the trade‑off between costs and risk in the medium term for the domestic government debt according to the CaR model. The calculations are based on the existing government debt portfolio and the assumption of a current budget surplus. It is also illustrated how the trade‑off changes if a larger budget surplus is assumed.

Trade-off between interest costs and risk, 2003-05	Chart 10.4.2

The Chart shows the relation between average relative CaR and the average interest costs in the period 2003‑05 for various distributions of borrowing on the 2‑, 5‑ and 10‑year segments. The various borrowing strategies result in various profiles of the duration of the debt.

It follows that issuance only in 2‑year bonds gives the lowest average costs, but also the highest risk. On the other hand, issuance in 10‑year bonds gives the highest costs, but also the lowest risk.

Borrowing in short‑term bonds entails a larger interest‑rate risk than borrowing in long‑term bonds for two reasons. Issuance of short‑term bonds gives a higher degree of refinancing. This means that, on average there is more re‑financing at future unknown interest rates, leading to a higher interest‑rate risk. Moreover, the volatility of interest rates at the short end of the yield curve is relatively high. The expected interest costs on short‑term borrowing, on the other hand, are lower than on long‑term borrowing as the yield curve is typically upward-sloping.

The Chart also indicates that issuance solely in 5‑year securities is not advantageous in relation to the CaR analysis, since the trade‑off between costs and risk for this strategy lies above the dashed line. By spreading the issues across several points of the yield curve instead, it is possible to achieve an equivalent risk profile with slightly lower expected costs. This result is achieved because the yield curve is often concave, i.e. the average costs of distributing the borrowing on 2‑year and 10‑year securities are often lower than when borrowing is concentrated in the 5‑year segment.

As the Chart illustrates, the trade‑off changes on assuming a larger budget surplus. A larger budget surplus reduces the central government's borrowing requirement, and thereby both the expected interest costs and the interest‑rate risk.

Model uncertainty
The calculation of CaR figures is sensitive to the assumptions made. First, the risk analysis is sensitive to the choice of interest‑rate model used to generate the future interest rates, and the estimation basis chosen to estimate the parameters of the interest‑rate model. The interest input to the CaR model has so far been simulated using the CIR model^[1]. The CIR model is prominent in the finance literature, and can be implemented in practice. However, the model has difficulty in replicating certain empirical characteristics of the historical course of interest rates. For example, there is a tendency for the CIR model to underestimate the volatility of the long‑term interest rates. The CIR model is also subject to certain limitations of its ability to generate various yield curves. In the light of the CaR results' sensitivity to the choice of interest‑rate model, work is ongoing on modelling alternative interest-rate input to the CaR model. The first stage of this work was presented in Chapter 9 of Danish Government Borrowing and Debt 2001.

Second, the calculation of the risk is significantly influenced by assumptions concerning the development in the central-government budget, which entails great uncertainty. The CaR calculations are therefore made for various budget scenarios in order to illustrate the robustness of the results.

10.5 Management of costs and risk by use of strategic benchmarks

The CaR analysis is used to support the setting of so-called strategic benchmarks. Strategic benchmarks are key portfolio figures that summarise the desired cost and risk profile and are used as guiding points in the ongoing management. CaR supports the setting of strategic benchmarks for the distribution of domestic borrowing on various maturities, the duration of the central-government debt and the profile of the future redemption payments.

Duration is a key risk management measure for many government debt managements. Duration is a measure of the portfolio's average fixed interest period. Long duration means that, in average terms, a longer period will pass before the debt is to be re‑financed at unknown interest rates. This reduces the probability of a sudden increase in interest costs in the short term. As an average measure, duration does not, however, contain information on the distribution of the payments. A portfolio in which the redemption payments are concentrated in the medium‑term segment can thus have the same duration as a portfolio where the redemptions are distributed over a longer horizon, cf. Chart 10.5.1. In order to avoid the interest‑rate uncertainty related to refinancing a large proportion of the debt in particular years, the duration target is therefore combined with an objective of a certain smoothing of the redemption profile.

Redemption profiles with same duration	Chart 10.5.1

In Danish government debt management duration is managed by transacting interest‑rate swaps. Interest‑rate swaps make it possible to achieve a different interest‑rate exposure to that determined by the maturity distribution of the government securities issues. The redemption profile is smoothed via buy‑backs and the issuance policy. Since both interest‑rate swaps and buy‑backs are modelled in the CaR model, it is possible to quantify the risk for various levels of duration and objectives for the annual redemptions, in addition to the analysis of various issuance policies.

Benchmarking and performance measurement
Within private portfolio management, benchmarks are also applied as a measure of the desired exposure, and used to guide the ongoing management. Here, the strategic benchmark is often accompanied by a certain scope for tactical positions. Tactical positions are deviations from the strategic benchmark on the basis of certain expectations of e.g. the development in interest rates. Typically, portfolio management is subject to ongoing evaluation by comparing the result of the tactical positions with the result that would have been achieved had the manager followed the strategic benchmark.

A mandate, as a strategic benchmark, for a bond portfolio manager of an asset portfolio can e.g. be that the portfolio must consist of 30 per cent long‑term mortgage‑credit bonds, 30 per cent medium‑term government bonds, and 40 per cent long‑term government bonds. If the portfolio manager has certain expectations that mortgage‑credit bonds will e.g. perform better than government bonds, or that yields will be higher at the long end of the yield curve, tactical positions can be taken by changing the distribution of securities within certain limits.

An equivalent application of strategic benchmarks to performance measurement of tactical positions has so far only been used by a few government debt managements, and typically only applied to foreign debt. In Denmark, performance measurement was previously used in the management of the net foreign-exchange exposure of the foreign debt and Danmarks Nationalbank's foreign‑exchange reserve.

Two factors in particular make it problematic to apply benchmarks to performance measurement as regards the government debt management's domestic portfolios. First, it must be assumed that the central government as a portfolio manager is a small player in a large market, and therefore takes prices as given. Otherwise, the portfolio manager could influence the market prices and the benchmark. Secondly, it must be ensured that market participants do not gain the incorrect impression that the central government takes tactical positions in relation to the strategic benchmark based on privileged information, including information concerning the future fiscal policy.

With the introduction of the euro and the establishment of a large single market for financial services, the domestic financial markets in the euro area member states are less influenced by the transactions of the government debt managements. This improves the opportunities for use of benchmarking and performance measurement. At the same time, it is possible that the establishment of independent government debt managements will lead to increased use of benchmarking and performance measurement. A benchmark can clarify the government debt management's mandate, and make it possible for the portfolio owner to evaluate the manager's performance.

10.6 Management of costs and risk in a macroperspective

The government debt managements' portfolios are typically substantial. There may thus be significant potential negative spill‑over effects from cost development to the rest of the economy via the government budget in the event of turmoil on the financial markets. Budget smoothing is a risk‑management approach within government debt management that is based on planning government debt policy on the basis of overall macroeconomic considerations. In recent years, certain countries have put stronger emphasis on this approach.

Budget smoothing entails an alternative definition of costs and risk, and thereby a different approach to risk management. Here, the costs of the debt are related to the government budget, so that the "real" costs depend on both the size of the interest costs and the budget position. The less favourable the budget, the greater the "real" costs. Budget smoothing is therefore intended to establish a debt structure that ensures that the probability of high debt servicing costs is reduced in situations where the budget is tight.

The rationale behind this approach is that there can be important negative derived effects from cost shocks to the budget. In the literature on budget smoothing, the starting point is thus typically that a sudden increase in the costs of the debt can create a need for political initiatives such as tax increases or a reduction of government expenditure, and possibly default on the government's redemption payments.

Implementing budget smoothing can impose methodological difficulties. This is because the majority of the budget items, e.g. taxes and duties, do not have explicit financial characteristics which can be immediately matched to the financial characteristics of the debt.

It is thus relevant to know whether the economy is primarily affected by demand or supply shocks. In the event of a negative demand shock, there will be a tendency for inflation to decline, simultaneously with budget deterioration. In this case index‑linked debt will alleviate the consequences of budgetary deterioration. If there are supply shocks instead, where the budget deteriorates while inflation and interest rates are rising, the nominal fixed-rate debt would be preferred, according to the budget‑smoothing approach. It can be difficult to identify the various shocks to the economy, and therefore also to implement a suitable strategy.

The idea of budget smoothing is of particular interest if there are significant potential derived effects from a sudden increase in the debt servicing costs, and if it is possible to identify important shocks to the economy that can be hedged via a particular debt structure. Limited spillovers from the debt to the rest of the economy can be the reason to focus on the financial risks of the debt.