Issuance of Long-Term Government Bonds

During 2005, several government issuers resumed or commenced the issuance of ultra-long fixed-rate nominal or inflation-linked government bonds with maturities of 30 years or more.

Issuance of ultra-long bonds should be viewed against the background of falling interest rates and flattening yield curves in several countries in recent years.

Some market participants have indicated that the life insurance sector and pension funds have underpinned the structural demand for ultra-long government bonds, which may have contributed to the flattening of the yield curve.

In view of the very low borrowing requirement, Government Debt Management has no current plans to change its issuance strategy to include more instruments with longer maturities.

9.1 NEW TRENDS IN GOVERNMENT BORROWING

During 2005, several government issuers resumed or commenced the issuance of ultra-long fixed-rate nominal or inflation-linked government bonds. Ultra-long government bonds have maturities of 30 years or more.

In February 2005, France issued the longest government bond in the euro area so far^[1], maturing in 2055, cf. Table 9.1.1. Several issuers resumed or continued issuing in the 30-year segment, while Greece issued in this segment for the first time in March 2005.

Outside the euro area, the UK issued a fixed-rate 50-year government bond in May and an inflation-linked 50-year government bond in September. The US has indicated that it plans to resume issuance of 30-year bonds in 2006 after being absent from this maturity segment for several years.

Investors and price formation in long-term government bonds
Several of the countries mentioned have held consultations with primary dealers and investors prior to their decision to resume or commence issuance of ultra-long securities.

Generally, the market participants consulted have indicated that particularly the life insurance and pension sector (L&P) has contributed to increasing the structural demand for ultra-long government bonds. The L&P sector is mainly characterised by its long-term obligations such as guaranteed pension payments, and in step with the ageing of the population, private contributions to pension schemes are expected to rise substantially.^[2]

Several countries are introducing – or have already introduced – legislative requirements for hedging of pension obligations. In addition, there is an increasing tendency to introduce market valuation of both assets and liabilities.^[3] These principles are already applied in Denmark .

The transition to market valuation entails that the sector's solvency fluctuates with the level of interest rates to a far greater extent than before. For instance, a fall in interest rates will lead to an increase in the market value of liabilities as a result of the long duration of the obligations. To the extent that the duration of the assets is shorter than the duration of the liabilities, the increase in the market value of the assets will not match the increase in liabilities. This reduces solvency. Ultra-long fixed-rate bonds contribute to alleviating this problem by lengthening the duration of the assets. Inflation-linked bonds are particularly suitable if the liabilities include obligations that are linked to the level of prices or wages.

Ultra-long bonds can also be attractive to speculative investment managers, e.g. hedge funds, due to the high positive convexity of long-term bonds. Convexity is a measure of the interest-rate sensitivity of a bond's duration, cf. Box 9.1 . Interest from this investor category was clearly apparent on the issue of the 50-year French government bond, when hedge funds took up a significant share of the initial offering. This emphasises that it can be difficult to target issues at specific investor segments with particular requirements. In addition, investors in large government issues will typically show a broad geographical distribution, entailing that the issue cannot be placed exclusively with national investors.

CONVEXITY	Box 9.1
Convexity of a bond is defined as the second derivative of the price in relation to the yield, i.e. the interest-rate sensitivity of duration. 1 An increase in term to maturity increases convexity relatively more than duration, cf. the Chart, which shows the relationship between duration and convexity for bullet loans. For instance, the krone duration increases from 8.1 to 21.5, equivalent to 165 per cent, when term to maturity is increased from 10 to 50 years, while convexity increases from 0.8 to 7.4, equivalent to 811 per cent.
CONVEXITY AND DURATION, BULLET LOANS
Note: The calculations were made on the basis of a flat term structure and 4 per cent coupon rates. Krone duration is calculated as the change in the price on a parallel shift to the term structure of 100 basis points. Convexity is calculated as the change in the krone duration on a parallel shift to the term structure of 100 basis points.
Positive convexity of a bond means that the value of the bond increases more on a given fall in interest rates than it declines on an equivalent rise in interest rates. All other things being equal, positive convexity thus increases the return on a bond, irrespective of the direction of any fluctuations in interest rates. On the basis of a flat yield structure of 4 per cent, a 10-year bond e.g. increases 10 per cent more in market value on a fall in interest rates of 1 per cent than it decreases in market value on an equivalent rise in interest rates. For a 50-year bond, the price increase is 40 per cent greater than the price decrease, which can be attributed to the greater convexity. The more the level of interest rate fluctuates, the greater the increase in return as a result of positive convexity. Bonds with high positive convexity are therefore particularly attractive if higher volatility is expected in the interest-rate market. The contribution from increased convexity means that the yield spread between long-term and ultra-long bonds is very small.
1 See Christensen, M., 2001, Bond investments, Theoretical considerations and practical use (in Danish only), DJØF Publishing.

During 2005, the average spread between 10-year and 30-year euro yields was around 45 basis points, cf. Chart 9.1.1. In other words, an extension of the term to maturity from 10 to 30 years entails a yield premium of around 45 basis points for a government issuer in the euro area. Against this background, it should be noted that the 50-year French issue was priced 3 basis points above a French 30-year issue. In the UK , the 50-year bond yield is lower than the 30-year bond yield, and the yield curve is thus inverted for longer maturities.

The difference between the 10/30-year yield spread and a 30/50-year yield spread in the euro area is partly attributable to the high convexity of 50-year bonds, cf. Box 9.1 . In addition, several market participants indicate that the – expected or actual – hedging requirements of the L&P sector are an additional explanatory factor behind the very flat yield curve for longer maturities.

Swap spreads for ultra-long bonds
Euro-denominated interest-rate swaps with maturities of 30 and 50 years have been traded for several years. The spread between the 30-year and 50-year French government bonds is close to the 30/50-year spread in the European swap market, which indicates that the bond market has used the swap market as the basis for pricing the French 50-year issue, cf. Chart 9.1.2. On the other hand, the 10/30-year spread in the swap market is around 6 basis points higher than the 10/30-year government yield spread. By and large this implies that a government issuer wishing to swap the cash flow on a fixed-rate bond for a variable-rate cash flow can save 6 basis points by issuing in the 30-year rather than the 10-year segment. This saving is not increased by issuing 50-year bonds, which indicates that the government's comparative advantage relative to the swap market does not increase further for maturities exceeding 30 years.

9.2 CONSIDERATIONS BEHIND LONG-TERM ISSUES

The overall objective of the government debt policy is typically to cover the central government's financing requirement at the lowest possible borrowing costs, subject to a prudent degree of risk. In addition, the government debt policy is often designed to ensure well-functioning capital markets.

Costs and risk
The yield curve, i.e. the relationship between the yield to maturity and the term to maturity of a bond, has a positive slope in most countries. This means that the interest costs of short-term borrowing are typically lower than for long-term borrowing. On the other hand, the risk increases for short-term borrowing relative to long-term borrowing since the debt must be refinanced more frequently at unknown future interest rates.

In recent years, the absolute level of interest rates has fallen substantially, and the spread between long-term and short-term interest rates has narrowed considerably, cf. Chart 9.2.1.

The decline in interest rates and the narrowing of the spread between short-term and long-term interest rates imply that the costs of increasing duration have fallen. In other words, it has become relatively less expensive to reduce risk by locking in interest rates for a longer period. Thus, the trade-off between costs and risk has changed.

According to AFT (the French government debt management office), the demand for long duration has contributed to the decision to issue ultra-long bonds.^[4] Likewise, the UK Debt Management Office has indicated that the issuance of ultra-long bonds is consistent with an objective of minimising debt costs over the long term while taking account of the degree of risk.^[5]

Well-functioning capital markets
A very flat or inverted yield curve may indicate that investors require long-term instruments that are currently not offered, or are only offered to a limited extent.^[6] On the basis of an analysis of the trade-off between costs and risk, a government issuer may in this case supplement the market by issuing long-term bonds.

The demand for long-term bonds is difficult to estimate. Based on assumptions of portfolio restructuring in the L&P sector, it is estimated that the potential demand from this sector is around twice the circulating volume of long-term government and corporate bonds in the UK , and around three times the circulating volume in the US .

Government issuers with limited borrowing requirements cannot be expected to cover total demand on this scale. Nevertheless, the establishment of a credit-risk-free reference yield curve through issuance of ultra-long bonds would be important. The reason is that it would subsequently be possible to price long-term bonds from non-government issuers as well as other financial instruments on the basis of the government yield curve.

Historically, central-government issuers have played an important role in the establishment of a liquid yield curve without any credit risk. Given the development of liquid markets for interest-rate swaps, which are often used as alternatives to government bonds when pricing non-government issues, this role has, however, become somewhat less significant.

For smaller government issuers with limited borrowing requirements, an expansion of the issuance universe entails conflicting considerations. The reason is that governments generally achieve a liquidity premium by issuing large bond series. The liquidity premium helps to reduce the borrowing costs. Firstly, the introduction of long-term bonds would, all other things being equal, increase the costs of issuing in existing maturity segments by diluting the liquidity premium. Secondly, liquidity supports a well-functioning capital market.

Since the introduction of the euro, small government issuers in the euro area have taken these considerations into account by focusing on a few, highly liquid benchmark bonds in certain maturity segments. Other countries with limited borrowing requirements, e.g. New Zealand^[7] , plan to issue long-term government bonds in connection with government financing of infrastructure projects. Long-term government issues can be natural instruments for financing infrastructure projects with a long investment horizon since the nominal interest-rate risk can be hedged over the entire horizon. In the same way, long-term inflation-linked issues are suitable for financing projects of which the current revenue correlates with inflation and where it is desirable to hedge the real interest-rate risk.

Large government issuers have been able to maintain several different borrowing programmes while also introducing new instruments.

9.3 THE DANISH PERSPECTIVE

In view of the very low borrowing requirement, Government Debt Management has no current plans to change its issuance strategy to include more instruments with longer maturities, cf. Chapter 4. On the contrary, the future strategy focuses on maintaining liquidity in fewer, core maturity segments.

Since the government debt is declining, it is not deemed appropriate to introduce ultra-long bonds instead of the existing benchmark bonds in the 10-year maturity segment. The longest Danish government security is 7-per-cent bullet loans 2024, where issuance ceased in 2001 in order to concentrate liquidity in the 10-year maturity segment.

Cost-at-Risk simulations indicate that the duration of the central-government debt can be reduced in the long term, cf. Chapter 8. Issuance of long-term bonds would therefore have to be counterbalanced by means of interest-rate swaps, whereby the overall duration contribution from the government to the market would be neutralised. The reason is that the government would have to pay a long-term fixed bond yield and at the same time receive a long-term swap rate. The recipient of the long-term bond yield, e.g. a pension fund, would to a large extent be able to receive the long-term swap rate as a direct substitute. In addition, the fixed-exchange-rate policy allows Danish market participants to hedge positions as required in euro area government securities with a very limited exchange-rate risk.