CHAPTER 10

Management of the Central Government's Interest-Rate Risk

Government Debt Management manages the interest-rate risk on central-government assets and liabilities on a consolidated basis. Interest-rate risk is established on the basis of an analysis of the central government's interest-rate exposure and the trade-off between interest costs and interest-rate risk according to the Cost-at-Risk (CaR) model. The central gov ern ment's budget risk is assessed through stress testing of future budget deficits.

Analyses of interest-rate fixing and the trade-off between interest costs and interest-rate risk in the CaR model show that it will be expedient to trans act interest-rate swaps in the coming years. Interest-rate swaps result in a more even distribution of interest-rate fixing across maturity seg ments. At the same time, the analyses in the CaR model show that the transaction of interest-rate swaps contributes to reducing the central government's interest costs without increasing the risk of higher future interest costs.

Against this background, Government Debt Management has chosen to continue to use interest-rate swaps in risk management, conditional on well-functioning swap markets.

Consolidated Risk Management 10.1

The overall objective is to achieve the lowest possible long-term bor row ing costs, while taking the degree of risk into account. Consequently, Government Debt Management considers an appropriate trade-off between costs and risk in its medium-term planning of the government debt policy.

The financial risk on the central-government debt is managed on a consolidated basis, i.e. according to the Asset Liability Management (ALM) principle, cf. Danish Government Borrowing and Debt 2008, Chapter 11. Government Debt Management thus manages the total net exposure of the government debt portfolio. The risk management is based on a trade-off between costs and risk measured by nominal accrued costs, reflecting the cost concept of the central-government accounts.

Portfolios in the central government's risk management
Central-government debt consists of both assets and liabilities. The li abil ities comprise domestic and foreign debt, while the assets comprise the balance of the central government's account at Danmarks Nation albank and the portfolios of three government funds, cf. Table 10.1.1.

Risk management is based on the central-government debt adjusted for re-lending and refinancing of subsidised housing. Adjustment is made for re-lending because the central government has a claim in connection with re-lending to government-guaranteed companies. As a result, the central-government's net interest costs do not increase in connection with re-lending, since the interest costs are borne by the recipients. Refinancing of subsidised housing is also included, as the central government is exposed to interest-rate risk in connection with its financing of the subsidised hous ing sector. In 2008, it was decided to hedge this interest-rate risk by let ting the Social Pension Fund invest in the corresponding mortgage bonds. Refinancing of subsidised housing is therefore included in the cen tral government's risk management.

Separation of Issuance Strategy and Risk Management 10.2

Government Debt Management uses interest-rate swaps in connection with its management of the central government's interest-rate and refi nancing risk, thereby enabling separation of the issuance and buy-back strategy from risk management. The advantage is that the issuance strategy can be targeted at building up large, liquid bond series, thereby reducing the central government's borrowing costs.

The separation of the issuance strategy and risk management makes it easier to stick to the issuance strategy in connection with minor or tem por ary changes in the borrowing requirement. The separation thereby sup ports a transparent issuance strategy, which contributes to reducing investors' risk. Consequently, the central government's buy-back strategy is able to support the build-up of key on-the-run securities and can be used to smooth the redemption profile.

The use of interest-rate swaps in risk management reduces the central government's refinancing risk compared with increasing short-term borrowing, as the principal in the interest-rate swap is not refinanced, cf. Box 10.1. In connection with refinancing of debt, the central government is exposed to the possibility that in a single year it may be particularly difficult to issue government securities. On the other hand, the use of interest-rate swaps increases the central government's instrument risk, i.e. the risk that the floating interest rate in the interest-rate swap, which de pends on the interbank lending rate, and the corresponding government yield will show diverging development patterns. The financial crisis has dem on strated that the normal close link between short-term swap rates and short-term government yields can be broken during periods charac terised by a high degree of uncertainty.

In addition to reducing the central government's refinancing risk, is suance of government bonds with longer maturities has several long-term advantages. This contributes to building up a government yield curve that can be used as a price benchmark for other financial instru ments. It also helps to ensure long-term access to the credit market for the central gov ern ment.

Government Debt Management adjusts the strategy for transaction of interest-rate swaps to the central government's overall interest-rate ex pos ure. Rather than being linked to an individual bond issuance, interest-rate swaps are transacted as portfolio interest-rate swaps when this is deemed to be expedient in relation to risk management of the overall gov ernment debt portfolio.

Interest-Rate Risk 10.3

Interest-rate risk is the risk of higher interest costs as a result of the de vel op ment in interest rates. There is normally a trade-off between interest costs and interest-rate risk, enabling the central government to reduce the expected annual interest costs by assuming a higher interest-rate risk. This is because yields on short-term bonds are normally lower than yields on long-term bonds, corresponding to a positive slope of the yield curve. On the other hand, short-term bonds more frequently entail refinancing at unknown future yields. In addition, short-term yields fluctuate more than long-term yields over time. This may contribute to increasing the risk on government debt.

In an international perspective, Denmark's government debt remains low. The duration of the central-government debt is long compared with those of other countries, which means that the interest-rate risk on gov ernment debt is low. The low interest-rate risk reflects the long duration of the central government's liabilities and the short duration of its assets.

The duration of the government debt portfolio does not include information on the absolute interest-rate exposure or its dispersion over time. The accumulation of assets of short duration and liabilities of long duration has made risk management more complex. An analysis of the central government's interest-rate fixing is important to avoid an uneven distribution of the central government's interest-rate exposure on various maturity segments.

Interest-Rate Fixing 10.4

The annual interest-rate fixing is given by the accrued amount in kroner for which a new interest rate is to be fixed in a given year, cf. Box 10.2. This means that the central government's interest costs in a given year will increase by 1 per cent of the annual interest-rate fixing in the event of a parallel upward shift in the yield curve of 1 percentage point.

Since the central government has net debt, interest-rate fixing will be posi tive overall, cf. Chart 10.4.1. Basically, an even distribution of interest-rate fixing over time and across maturity segments is expedient, and interest-rate fixing should be positive in each maturity segment. Diversified interest-rate exposure along the yield curve means that the central govern ment does not take speculative positions in relation to the future shape of the yield curve.

Interest-rate fixing on maturity segments without conclusion of interest-rate swaps	Chart 10.4.1

Interest-rate fixing without transaction of new interest-rate swaps
With the specified issuance strategy and without the transaction of new interest-rate swaps, short-term interest-rate fixing will be negative in the period 2010 to 2019, cf. Chart 10.4.1. This is primarily due to the large balance of the central government's account at Danmarks Nationalbank. The reason for the increase in negative short-term interest-rate fixing over the period is the gradual expiry of the existing interest-rate swap portfolio of DKK 115 billion.

Interest-rate fixing by annual transaction of interest-rate swaps for DKK 20 billion
The central government's interest-rate exposure can be changed by the transaction of interest-rate swaps. Short-term interest-rate exposure increases on transaction of interest-rate swaps for which the central government pays interest at a floating rate and receives interest on the swap at a fixed rate. The transaction of 10-year interest-rate swaps for an amount of DKK 1 billion, with the central government receiving the fixed 10-year interest rate and paying the floating swap rate, would reduce the central government's long-term interest-rate fixing in the year of transaction by DKK 1 billion and increase the short-term interest-rate fixing by DKK 1 billion annually over the maturity of the swap.

The transaction of interest-rate swaps for a notional amount of DKK 20 billion annually ensures a significantly more even distribution of interest-rate fixing across maturity segments during the period analysed than interest-rate fixing without the transaction of new interest-rate swaps, cf. Chart 10.4.2. However, short-term interest-rate fixing remains low at the beginning of the period.

Interest-rate fixing on maturity segments with annual conclusion of DKK 20 billion interest-rate swaps	Chart 10.4.2

As interest-rate fixing is purely a measure of exposure, it is not possible to assess the expediency of a particular central-government interest-rate fixing scenario solely on the basis of interest-rate fixing. The analysis of the central government's interest-rate fixing is therefore combined with the Cost-at-Risk model that describes the trade-off between interest costs and interest-rate risk.

Cost-at-Risk Model 10.5

The strategy for the central-government debt is determined on the basis of a trade-off between costs and risk. To analyse the risk of a strategy, a baseline scenario for future issuance, buy-back and re-lending is con structed. The baseline scenario is consistent with the expected future financing requirements. Interest-rate risk is then analysed using Govern ment Debt Management's Cost-at-Risk, CaR, model.

The CaR model applies 2,500 interest-rate scenarios. For each interest-rate scenario the central government's costs are calculated given the expected future financing requirements, re-lending, investments of the government funds and the chosen strategy for domestic and foreign issuance and transaction of interest-rate swaps. It is then possible to calculate the central government's expected interest costs and measures of risk in the form of the 5th and 95th percentiles for its annual interest costs. Both measures are relevant as they provide a band for the central government's expected future interest costs.

The input of interest rates is key to the CaR model trade-off between costs and risk. The interest-rate scenarios are calculated based on a two-factor Cox-Ingersoll-Ross (CIR) interest-rate model estimated on Danish government yields for the last 10 years, cf. Danish Government Borrowing and Debt 2005, Chapter 10.

At the outset, the general government yield level is low, and the dif ference between the interest rates in the short and long maturity segments is substantial compared with the average over the last 10 years. The interest-rate model projects generally rising interest rates and a flatter yield curve, cf. Chart 10.5.1.

Average interest rates for selected maturity segments	Chart 10.5.1
Note: Based on the Government Debt Management's 2-factor CIR interest-rate model.

Expected saving without higher risk
In the baseline scenario it is possible to reduce the central government's average expected costs by transacting interest-rate swaps without increasing the risk of higher interest costs. This is because the balance of the central government's account at Danmarks Nationalbank to some extent hedges the floating leg of the interest-rate swap. It is therefore possible to exploit the fact that the interest rate for longer maturities is typically higher, i.e. the yield curve has a positive slope. Thus, the CaR model projects an annual saving by transacting interest-rate swaps for up to DKK 30 billion per year without increasing the risk of higher future interest costs. Moreover, the central government can still benefit from low er interest costs in future, cf. Chart 10.5.2. If interest-rate swaps for more than notionally DKK 30 billion a year are concluded, issuance of the 10-year government bond will no longer hedge the fixed leg of the interest-rate swap.

Expected interest cost and interest-rate risk	Chart 10.5.2
Note: Annual conclusion of 10-year interest-rate swaps for DKK 0, 20 and 30 billion. Risk bands are the 5th and 95th percentiles, respectively.

At the beginning of 2010, the duration of the liabilities in the government debt portfolio was 5.4 years, while the duration of the assets was 1.7 years. This resulted in a duration of the overall government debt portfolio of about 10 years. The long government debt duration reflects the increasing duration of the central government's liabilities over the last two years and the fact that a large balance of the central government's account reduced the duration of its assets.

The long duration of the central-government's liabilities is due to issuance of the 30-year bond at the end of 2008 and the fact that the notional principal of the central government's portfolio of interest-rate swaps has been reduced by DKK 22 billion since 2007 because the central government did not transact any interest-rate swaps in 2007 and 2008. In line with the normalisation of the financial markets, the central govern ment gradually resumed the use of interest-rate swaps for risk manage ment purposes in the 3rd quarter of 2009. At the beginning of 2010, the central government's outstanding interest-rate swaps amounted to notion ally DKK 115 billion, of which DKK 16 billion will expire in 2010.

Budget Risk 10.6

The budget risk is the risk of a different development in the central government's budget than projected. The central government's budget is primarily affected by the economic development. During an economic slowdown, higher unemployment causes social benefit costs to increase and tax revenue to decrease. During periods with shifts in the economic development, budget estimates are more uncertain. In addition, the central government has introduced various stimulus packages in con nection with the financial crisis, which contributes to increasing its future budget risk.

In a situation with a high budget risk it is advantageous for the central government's liabilities to be of long duration, as an increased issuance requirement has less impact on the central gov ern ment's in terest-rate risk. Furthermore, budget risk is accommodated by a large balance of the central government's account at Danmarks Nation albank. The cen tral government's budget risk is assessed through stress testing of future budget deficits.

Stress testing in the Cost-at-Risk model
The greatest risk in relation to the central government's overall interest costs in the coming years is assessed to be the risk of larger budget deficits. The stress tests are based on two alternative scenarios in which government finances deteriorate relative to the baseline scenario, cf. Chart 10.6.1.

Development in central-government debt, ratio of gdp	Chart 10.6.1

In the stress tests, the deterioration of the budget balance is financed by increasing the scope of the T-bill programme and the annual bond issuance according to the 40-20-40 issuance strategy. A deterioration of the central government's budget balance will naturally increase the an nual expected interest costs accordingly. The risk of higher interest costs, measured by the 95th percentile, increases more than the expected interest costs do. This is because the share of government debt for which a new, uncertain interest rate is determined is larger in the stress sce narios, meaning that the future level of interest rates will have a stronger impact on the overall interest costs, cf. Chart 10.6.2.

Expected cost and risk in base and stress scenarios	Chart 10.6.2
Note: Risk bands are the 5th and 95th percentiles, respectively.

The CaR model does not take into account the fact that the central gov ern ment's issuance level may affect the level of interest rates. Accordingly, the stress test does not allow for the fact that a strong increase in annual issuance may affect borrowing conditions and the level of interest rates.

Instrument Risk 10.7

The CaR model does not take into account instrument risk, i.e. the risk that interest rates within the same maturity segment, but on different in struments, show diverging development patterns. Another factor not taken into account is that the central government normally has a com parative advantage in connection with issuance in the long maturity seg ment in view of its high credit standing. Thus, it is assumed that the swap rates equal the corresponding government yields.

The analysis in the CaR model underestimates instrument risk in con nection with interest-rate swaps. For a long time, swap rates and gov ern ment yields have been closely linked. However, the financial crisis has shown that this close link can be broken during periods characterised by a high degree of uncertainty, cf. Chart 10.7.1.

Danish Swap spreads	Chart 10.7.1
Note: In periods in which the 10-year swap spread is higher than the 6-month swap spread, the central-government has a comparative advantage by entering into interest-rate swaps compared to reducing long-term borrowing and increasing short-term borrowing. Source: Bloomberg.

Summary 10.8

Analyses of interest-rate fixing and the trade-off between interest costs and interest-rate risk in the CaR model show that transacting interest-rate swaps will be expedient in the coming years. Interest-rate swaps result in a more even distribution of interest-rate fixing across maturity segments. Basically, an even distribution of interest-rate fixing over time and across maturity segments is expedient, and interest-rate fixing should be positive in each maturity segment. Diversified interest-rate exposure along the yield curve means that the central government does not take speculative positions in relation to the future shape of the yield curve.

At the same time, the analyses in the CaR model show that the trans action of interest-rate swaps contributes to reducing the central government's interest costs without increasing the risk of higher future interest costs. As a result the duration of the overall debt portfolio can be reduced from the current high level without increasing the interest-rate risk.

Against this background, Government Debt Management has chosen to continue to use interest-rate swaps in risk management, conditional on well-functioning swap markets.