The Term Structure of Interest Rates

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The Term Structure of Interest Rates

• Business 3059
• Chapter 12

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K. Hartviksen
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Key Terms

• Term structure of interest rates
• Yield curve
• Spot rate
• Pure yield curve
• Forward interest rate
• Liquidity premium
• Expectations hypothesis
• Liquidity preference theory
• Term premiums

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Useful Links

• Bloombergs Bond Yields
• Bank of Canada Selected Bond Yields

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Term Structure of Interest Rates

• Liquidity preference theory
• Expectations hypothesis
• Segmentation theory
• Inflation Premium theory

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Expectations Theory

• The current spot rate is the geometric average of
  the forward rates expected to prevail over the
  life of the investment.
• R1 spot rate for a one year bond
• R2 spot rate for a two year bond
• f forward rate
• 1f2 forward rate from time 1 to time 2
• (1 R2)2 (1 R1)(1 1f2)
• 1f2 (1 R2)2 / (1 R1)

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Expectations Theory

• Obviously, the 1 year spot rate is made up
  (according to the Fisher Hypothesis) of a real
  rate of return plus an expected inflation
  premium.
• We know the recent rate of inflation (core in the
  past year has been 2.3)
• If the one year spot rate for a zero coupon
  Government of Canada bond is 4.1 then the real
  rate of return is
• Of course, our estimate of the expected rate of
  inflation has been naively estimated as the most
  recent trailing CPI rate of core inflation.
  Investors (the markets may well be using
  something else).

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Expectations Theory

• Example
• The current spot rate for a one year
• R1 spot rate for a one year bond 4.1
• R2 spot rate for a two year bond 3.97
• f forward rate
• 1f2 forward rate from time 1 to time 2
• (1 R2)2 (1 R1)(1 1f2)
• 1f2 (1 R2)2 / (1 R1) - 1
• (1.0397)2 / (1.041) 1.080976 / 1.041 1
• 3.84

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Expectations Theory

• We can find the implied forward rate for year 2
  to 3 as

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Expectations Theory

• We can find the implied forward rate for year 3
  to 4 as

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Expectations TheoryExample
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Expectations TheoryExample
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Expectation Theory

• Sowhy do we care about this theory? How can we
  use this knowledge?
• By imputing the implied forward rates we can
  figure out what the market (the consensus of
  the smart money managers who dominate activity in
  the bond market) is forecasting for spot rates
  and by implication, the markets inflationary
  expectations.
• The market is supposed to give us the best
  unbiased estimate of the future that is the best
  available information that we have today (if you
  believe in EMH)

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Liquidity Preference Theory

• Investors require a premium for tying up their
  investment in bonds over a longer period of time.

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Inflation Premium Theory

• This theory says that risk comes from uncertainty
  associated with future inflation rates.
• Though the market may be the best source of an
  unbiased estimate of future ratesactual rates
  will no doubt differ from these expectations.
• The longer the term to maturity of a bondthe
  greater inflation risk the investor in long bonds
  will bear.
• The longer the term to maturity, the greater the
  inflation riskthe higher the yield to maturity.

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Market Segmentation Theory

• There may be separate supply/demand conditions
  present at the short, intermediate, or long-term
  part of the market.
• These conditions can cause the yield curve to be
  disjoint

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Key Points

• Understanding the term structure of interest
  rates and the theories used to explain them can
  assist you in making a variety of decisions
  including
• Informing bond portfolio strategies
• Decisions regarding retirement
• Choice of mortgage financing options, etc.