Using the Term Structure to Forecast Interest Rates

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Using the Term Structure to Forecast Interest
Rates
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Interest Rate Forecasts

• Interest rate forecasts are needed when managers
  of financial institutions have to set interest
  rates on loans that are promised to customers in
  the future.
• We also might want to find the implied forward
  rate on a bond originating in the future.
• Specific forecasts of the implied forward
  interest rate can be generated using the term
  structure.

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Expectations Theory

• According to the expectations theory, the
  expected return over two periods from investing
  1 in a two period bond must equal the expected
  return from investing 1 in two one period bonds.
• (1 i2t)(1 i2t) -1 (1 it)(1 iet1) - 1

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The Forward Rate

• (1 i2t)(1 i2t) -1 (1 it)(1 iet1) - 1
• (1 i2t)2 - 1 (1 it)(1 iet1)
  - 1
• Solve for iet1, the forward rate.
• Add 1 to both sides and divide by (1 it)
• 1 iet1 (1 i2t)2 / (1 it)
• Subtract 1 from both sides
• iet1 (1 i2t)2
  
  (1 it)

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Liquidity Premium

• According to the liquidity premium hypothesis,
  investors prefer to hold short-term rather than
  long-term bonds.
• Therefore, long-term rates include a liquidity
  premium to compensate the investor for accepting
  more risk.

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Adjusted Forward Rate Forecast

• To allow for liquidity premiums in our formula,
  we subtract it out.
• iet1 (1 i2t - l2t)2
  
  (1 it)

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Example

• Would you be willing to make a one year loan at
  an interest rate of 8 one year from now? To
  make a profit, you need to charge one percentage
  point more than the expected interest rate on a
  Treasury bond with the same maturity.
• The liquidity premium is 0.4, the one year
  Treasury rate is 6, and the 2 year Treasury rate
  is 7.

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Solution

• iet1 (1 i2t - l2t)2
  
  (1 it)
• iet1 (1 0.07 - 0.004)2
  
  (1
  0.06)
• iet1 7.2
• You would reject the loan.

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