Fourth OECDChina Forum on Public Debt Management and Government Securities markets The Yield Curve f

1
Fourth OECD-China Forum on Public Debt Management
and Government Securities marketsThe Yield Curve
for Government SecuritiesSeptember 13-14, 2007

• Ove Sten Jensen
• Head of Government Debt Management
• Danmarks Nationalbank

2
Definition of a yield curve

• A yield curve shows a relation between the
  interest rate and the time to maturity
• This relation is also called the term structure
  of interest rates

3
Characteristics of the yield curve

• A yield curve can be constructed for various
  financial instruments
• Requirements
• Belong to the same asset class
• Are liquid and inconvertible
• Prices are not influenced by taxation effects
• Contain the same credit risk
• Cover a wide spectrum of maturities

4
Construction of the yield curve

• The yield curve is only known with certainty for
  a few specific maturity dates, the other
  maturities are calculated by interpolation
• There exists different interpolation techniques,
  that are used for determining prices for
  different products

5
Different ways to intrapolate

• Pure mathematical models
• Nelson-Siegel Extended (nice forward curves)
• Spline-functions (flexible, based on polynomials)
• Bootstrapping (linear interpolation)
• Based on financial theory
• CIR (Cox-Ingerslev-Ross)
• Different characteristics
• Bootstrapping gives per construction theoretical
  price observed price
• Nelson-Siegel Extended may give better
  out-of-sample prices (relevant when opening new
  bonds)
• Choice should be based on empirical evaluation
  (we mainly use Nelson-Siegel Extended)

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Uses of the yield curve

• Benchmark for pricing of bonds, futures and many
  other fixed income instruments
• Benchmark for pricing in issuance, buy-backs and
  re-lending
• Indicator for future interest rates
• Predictor of future economic activity. The slope
  of the yield curve is one of the variables in
  leading indicators

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Uses of the yield curve

• A government debt management office can use
  another countrys yield curve as a reference in
  price discovery if the spread is stable

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On-the-run/Off-the-run

• Electronic trading has decreased the yield spread
  between on-the-run and off-the-run bonds
• Electronic trading ensures that tradable prices
  are quoted on both on-the-run and off-the-run
  papers
• The result is that the curve is defined and
  updated throughout the maturities

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Moves in the yield curve

• Shift in expectations on monetary policy
• Markets reaction to news
• Shift in investors preferences for maturity
  segments

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Shapes of the yield curve

• The normal shape
• Upward sloping, since bond yields usually rise as
  the maturity extends
• Investors require additional compensation for the
  risk of holding long-term instruments, a term
  premium

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Shapes of the yield curve

• Flat yield curve
• The yield curve can flatten when central bank
  raises interest rates
• Bonds of different terms are not substitutable
• Investor preferences affect the shape of the
  curve
• Preference for guaranteed longer term yields from
  i.e. the pension funds lowers the long-term
  yields

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Shapes of the yield curve

• Inverted yield curve
• Downward sloping
• If investors expect the economic activity to slow
  down in future requiring monetary policy easing,
  they will mark down their projected path of
  future spot interest rates causing the yield
  curve to flatten or even invert
• Slope of the yield curve tends to decline
  significantly in advance of recessions
• The yield curve does not usually stay inverted or
  flat for long

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Illustration Pricing of a bond

• A price of a new bond of a certain maturity (here
  12 years) can be found using the estimated yield
  curve