Question

1.The yield of a one-year bond this year equals to 6.5%, and people expect the yield of a one-year bond to remain the same on the second year but fall to 5% on the third year. Also, people also require a 0.25% term premium for each additional year of bond maturity.

a.Calculate the yield of a two-year bond and a three-year bond according to the theory of liquidity premium. Compare the yields of the three-year bond, two-year bond, and one-year bond, what does it tell you about the shape of the yield curve? (10 points)

b.Calculate the yield of a two-year bond and a three-year bond according to the expectations theory. Compare the yields of the three-year bond, two-year bond, and one-year bond, what does it tell you about the shape of the yield curve? (10 points)

Answer 1

a) Calculation of the bond according to liquidity premium theory:

2 year bond= [(6.5%+6.5%)/2]+0.25%= 6.75%

3 year bond = [(6.5%+5.0%)/2]+0.25%= 6.00%

The yield curve is upward sloping when compared to 1st year 6.5% and 2nd years 6.75% but it slopes downward when compared to 2nd years 6.75% and 3rd years 6.00%.

b) Calculation of bond under expectation theory:

2 year bond= (6.5%+6.5%)/2 = 6.5%

3 year bond =(6.5%+5.0%)/2 = 5.75%

The yield curve is flattish in first two years and has sloped downwards in 3rd years.

In expectation theory, an investor has no preference for bond selection, they will not invest in bonds which are expected to give less return than others. the bond yield is the average of the yield under different maturity. However, investor under liquidity preference theory expects for liquidity premium due to uncertainty towards inflation risk and interest risk. Therefore, a shape of the yield curve under liquidity preference theory will be higher than the expectation theory.