Suppose in the Wall Street Journal you see the following current (spot) interest rates for Treasury bonds on January 7, 2021 with an upward sloping yield curve:

?10-year bond rate =1.08%; 20-year bond rate = 1.64%  

a)Under the expectations theory, what is the expected 10-year bond rate (forward rate) 10 years from now? Based on your answer, what are rates expected to do (rise/fall/stay the same)? Explain why

 Expected 10-year bond rate 10 years from now = _________________

(Be sure to show your work here).

Rate are expected to ___________ because ________________________

 

b)  For the same above if there is a liquidity premium of 0.08% for a 10-year bond and 0.20% for a 20-year bond, under the liquidity premium theory (adjusting for liquidity premiums incorporated in bond rates) what is the new expected 10-year bond rate 10 years from now? Based on your answer, what are rates expected to do (rise/fall/stay the same)? Explain why.

Expected Rate with LP __________ Rates Expected to __________________

(Be sure to show your work here).

c) Explain how interest rates are determined under the market segmentation theory What is the flaw in this theory?

Hope this helps. Thank you!

Step-by-step explanation

a. 10 years rate 10 years from now = ((1+1.64%)^20/(1+1.08%)^10)^(1/10)-1 = 2.20%

Rates are expected to rise

b. Yield on 20 year bond with liqudity premium = 1.64%+0.2% = 1.84%

Yield on 10 years bond with liquidity premium = 1.08%+0.1% = 1.18%

10 years rate 10 years from now = ((1+1.84%)^20/(1+1.18%)^10)^(1/10)-1 = 2.50%

Rates Expected to Rise

c.  Market Segmentation theory of interest Rate:

As per market segmentation theory, interest rate of bonds with different maturity length is not related to each other.
As per market segmentation theory of interest rate, bond market is segmented based on term structure of bond and each segment operates independently with each other. Interest rate on a bond with specific term structure is only dependent on supply and demand of that bond. It is not impacted by interest rate of other bonds with different term structure.
 

As per the theory, market participants have different return requirements. So, they deal with bonds which matches their return requirements. For example, banks usually deal in short term bonds, whereas pension funds usually deal in long term bonds.
Hence, long term and short-term bonds has basically different demand and supply agent and can their interest rate be not related.

Flaws of Market Segmentation Theory:

The theory is based on investors and borrowers demand for a specific maturity of bond in order to hedge their position. However, in practical investor change their preference based on available yield. So, if investors are compensated with sufficient yield then, they can move out of their preferred segment. The theory fails to consider it, which is considered under Preferred Habitat theory.