18 Questions
What is the condition for equilibrium at the aggregate level?
Option A is equal to option B
What is the relationship between the long rate and the short rate of interest in equilibrium?
The long rate plus unity equals the geometric average of each year's expected short rate
What happens to the yield curve if future short rates are expected to rise?
The yield curve will be upwards sloping
What is a limitation of the Expectations Hypothesis?
It assumes that all agents hold the same expectations with certainty
What happens to the long-term rate if future short rates are expected to fall?
The long-term rate will be less than the current short rate
What is the relationship between the slope of the yield curve and the expected change in the short rates?
The slope of the yield curve is directly related to the expected change in the short rates
What is the empirical evidence for the liquidity premium hypothesis?
The upwards slope of the yield curve, especially for short maturities
What is the main challenge in econometric testing of the hypotheses related to the yield curve?
Ex ante expectations need to be specified from ex post data
What is the relationship between real and nominal interest rates according to Fisher?
(1 + 𝜌)(1 + 𝜋) = (1 + 𝑟)
What does the Fisher relation suggest about the real interest rate if money is neutral?
It will be roughly constant
According to Fama (1975), how can short-term interest rates be used to predict inflation expectations?
By using short-term interest rates as a proxy for inflation expectations
What is the main assumption of the expectations hypothesis?
Expectations of future interest rates are reflected in current long-term rates
What is a limitation of the traditional yield curve charts?
They only deal with differences in the maturity of the bonds
What does the expected interest rate one year from now on a two-year bond refer to?
The rate we now expect to exist one year from now on a bond which, if bought at that time, has a term of two years from that date
Which of the following theories of the term structure is considered the most general?
Expectations Hypothesis
What is the primary assumption of the Expectations Hypothesis?
Market participants have different expectations about future interest rates
What is the purpose of interpolation in the traditional yield curve charts?
To fill gaps in the maturity structure
What is the notation for the expected interest rate one year from now on a bond that has a term of two years from that date?
r_t,t+1,1
Study Notes
The Expectations Hypothesis
- The equilibrium is when option A = option B, where 𝑒 𝑒 𝑒 𝑃𝑏 (1 + 𝑅𝑡,𝑛 )𝑛 = 𝑃𝑏 (1 + 𝑅𝑡,1 )(1 + 𝑡𝑟𝑡+1,1 )(1 + 𝑡𝑟𝑡+2,1 ) ….(1 + 𝑡𝑟𝑡+𝑛−1,1 )𝑛
- Cancelling Pb from both sides and rearranging gives: 𝑛 𝑒 𝑒 𝑒 𝑅𝑡,𝑛 = √(1 + 𝑅𝑡,1 )(1 + 𝑡𝑟𝑡+1,1 )(1 + 𝑡𝑟𝑡+2,1 ) ….(1 + 𝑡𝑟𝑡+𝑛−1,1 )𝑛 − 1
The Relationship Between Long and Short Rates
- In equilibrium, there is a specific relationship between the long rate and the short rate of interest: the long rate plus unity equals the geometric average of each year's expected short rate over the period of the long bond.
- If future short rates are expected to be the same in every year as the current long rate, then the yield curve will be horizontal.
- If future short rates are expected to rise, the long-term rate will be greater than the current short rate and the yield curve will be upwards sloping.
- If future short rates are expected to fall, the long-term rate will be less than the current short rate and the yield curve will be downwards sloping.
Limitations of the Expectations Hypothesis
- The Expectations Hypothesis assumes that all agents hold the same expectations with certainty.
- The hypothesis is limited in a practical sense, with two assumptions standing out as particularly impractical.
The Liquidity Premium Hypothesis
- The frequently observed upwards slope of the yield curve, especially for short maturities, is the empirical evidence for the liquidity premium hypothesis.
- Difficulties arise in econometric testing and specification of the various hypotheses.
The Fisher Relation
- The Fisher relation is: 𝜌≅𝑟−𝜋
- If money is neutral, then the real rate will be roughly constant and inflation expectations and nominal interest rates will move together.
- Short-term interest rates may be used to predict inflation expectations.
Theories of the Term Structure
- There are three theories of the term structure: the expectations, segmentation, and liquidity hypotheses.
- The Expectations Hypothesis is the most general, with other models being discussed partly by way of a critique of this model.
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