The Risk and Term Structure of Interest Rates

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Chapter 7

• The Risk and Term Structure of Interest Rates

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The Questions

• 1. Why do different bonds have different yields
  or interest rates?
• 2. What information is there in the relative
  yield of different bonds?

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What do different bonds have different interest
rates?

• Risk of default
• Tax
• Maturity

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Bond Ratings and RiskImpact of Ratings on Yields

• Risk ? Bond Demand?
• Bond Price ?
• Bond Yield or interest rate ?
• Riskier bonds have higher interest rates

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Bond Ratings

• Bond Ratings -
• Moodys, Standard and Poors, Fitch
• Ratings Groups
• Investment Grade --- risk is low
• Non-Investment --- risk is high
• Speculative Grade
• Highly Speculative

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Bond RatingsInvestment Grade
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Bond RatingsSpeculative Grades
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Bond Yield and Default Risk

• Bond Yield U.S. Treasury Yield Default
  Risk Premium(Default risk premium sometimes
  called risk spread or the spread over
  Treasuries.)

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Bond Ratings and RiskRisk Structure of Interest
Rates
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Information Content of Interest RatesRisk
Structure

• Default risk premium Bond yield
• U.S. Treasury Yield
• The bigger the yield spread, the bigger the
  default risk.
• The yield spread (the difference between bond
  yield and U.S. Treasury yield) is an excellent
  indicator of financial distress.

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Default risk premiums andthe business cycle
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Default risk premiums and the business cycle

• When the economy starts to slow, it puts a strain
  on private firms.
• A slower economy means a higher default
  probability
• Increased default risk is different across firms
• Firms already doing poorly, do even worse

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Commercial Paper

• An important source of short-term funds for
  businesses is the commercial paper market.

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Default risk premium in the financial crisis

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Default risk premiumanother example
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Tax Status and Bond Prices

• Interest income on Municipal Bonds are exempt
  from Federal Tax Payments.
• Other things being equal, municipal bonds have
  higher price, lower interest rate than Treasury
  bonds.
• Tax-Exempt Bond Yield
• (Taxable Bond Yield) x (1- Tax Rate).
• Municipal bonds are worth holding if your tax
  rate is high enough.

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Term Structure of Interest Ratesdefinitions

• Definition of the Term StructureThe
  relationship among bonds with the same risk
  characteristics but different maturities is
  called the term structure of interest rates.
• Yield Curve
• A plot of the term structure, with the yield
  to maturity on the vertical axis and the time
  to maturity on the horizontal axis.

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Interest Rates on the U.S. Treasury Securities

• Maturity 1month to 30 years

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Term Structure of Interest Rates
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Term Structure of Interest RatesYield Curve
The U.S. Treasury Yield Curve October 12, 2006.
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Term Structure of Interest RatesFacts to Explain

• Interest Rates of different maturities tend to
  move together
• Interest rates on short-term bond are more
  volatile than interest rates on long-term bonds
• Long-term interest rates tend to be higher than
  short-term interest rates.
• But sometimes, short-term interest rates are
  higher than long-term interest rates.

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Term Structure of Interest RatesExpectations
Hypothesis

• AssumptionBonds of different maturities are
  perfect substitutes for each other.
• Implies Investor w/ a two-year horizon
  indifferent between
• 1. A 2 yr bond for 2 yrs
• 2. A 1 yr bond and a second 1yr bond in 1 yr.

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Term Structure of Interest RatesExpectations
Hypothesis

• 1. Total return from 2 year bonds over 2 years

2. Total return from 1 yr bond and then another
1 yr bond
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Term Structure of Interest RatesExpectations
Hypothesis

• If one and two year bonds are perfect
  substitutes, then

or Long-term interest rate average of
expected future short-term interest rates
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Term Structure of Interest RatesExpectations
Hypothesis
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Term Structure of Interest RatesExpectations
Hypothesis
General formula
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Why the yield curve slopes downwards?

• According to the expectation theory
• If the yield curve slopes downwards, that is
  i1,t gt i2,t gt ,
• i1,t is expected to decrease in the near future,
  
• or ie1,t1 lt i1,t
• If the yield curve is flat, that is i1,t i2,t
  
• i1,t is not expected to change in the near
  future, or i1,t ie1,t1
• If the yield curve slopes upwards, that is
  i1,t lti2,t lt
• i1,t is expected to increase in the near future,
  or ie1,t1 gt i1,t

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Term Structure of Interest RatesExpectations
Hypothesis

• Explains
• Interest Rates of different maturities tend to
  move together
• Yields on short-term bond are more volatile than
  yields on long-term bonds
• BUT NOT
• 3. Long-term yields tend to be higher than
  short-term yields.

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Term Structure of Interest RatesLiquidity
Premium Theory

• The yield curves upward slope is explained by
  the fact that long-term bonds are riskier than
  short-term bonds. Bondholders face both
  inflation and interest-rate risk. The longer the
  term of the bond, the greater both types of risk.

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Term Structure of Interest RatesLiquidity
Premium Theory

• Explaining the fact that the yield curve normally
  slopes up
• Bondholders face both inflation and interest-rate
  risk.
• The longer the term of the bond, the greater both
  types of risk.
• The bigger the risk, the higher the risk premium

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Term Structure of Interest RatesLiquidity
Premium Theory

• General Formula

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Information in the yield curve according to the
expectation theory
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Information Content of Interest RatesTerm
Structure

• When the yield curve slopes down, it is called
  inverted
• An inverted yield curve is a very valuable
  forecasting tool.
• It predicts that interest rates are likely to
  decrease in the near future.

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U.S. Interest Rates during 09/2000 and 01/2001
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The yield curve and economic recessions

• Since we know interest rates fall during economic
  recessions.
• Since we also know that an inverted yield curve
  predicts that interest rates are likely to
  decrease in the future.
• An inverted yield curve signals an economic
  downturn in the near future.

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Business Cycles and Interest Rates
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The yield curve and economic recessions
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Information Content of Interest RatesTerm
Structure