Question

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1. Assume that the current 1-year interest rate is 3%, the expected 1-year rate next year is 2%, and the expected 1-year rate in the following year (3^rd year) is 4%.

1. Calculate the 2-year interest rate and the 3-year interest rate based on the expectations theory. (Show calculations)
2. Draw the yield curve based on your data above. Label your axis and mark the numbers along the axis, so you can read the actual interest rates in your graph. (This doesn’t need to be 100% precise, but your graph should look consistent with the numbers. Sloppy graphs will lose points.)
3. Assume that investors want a liquidity premium with a higher compensation for holding long-term bonds. Add the liquidity premium in your graph above. Make clear which curve is based only on the expectations theory and which takes into consideration the liquidity premium.
4. Based on this yield curve: What do you think market participants expect from future inflation and the economy (Write brief answers.)

1. in the next 2 years?
2. From year 3?

Answer 1

a) 2-year interest rate y(2)

(1+y(2))^2 = (1+y(1))*(1+y(1,1))

y(2) = (((1+y(1))*(1+y(1,1)))^0.5) -1

y(2) = (((1+0.03)*(1+0.02))^0.5) -1 = 0.0249878048

y(2) = 2.50%

2-year interest rate y(3)

(1+y(3))^3 = (1+y(2,1))* (1+y(2))^2

y(3) = ((1+y(2,1))* (1+y(2))^2 )^(1/3) -1

y(3) = (1.04*1.025*1.025)^(1/3) -1 = 0.02997580613

y(3) = 3.00%

b)

Year	Rate
1	3%
2	2.50%
3	3%

c)

We add a liquidity premium for bonds with higher year to maturity

Year to maturity	Expectation theory rates	Liquidity premium	Rate with Liquidity premium
1	3%	0.50%	3.50%
2	2.50%	0.75%	3.25%
3	3%	1.00%	4.00%

d) Based on this yield curve in the next 2 years - We expect inflation to be less for the next 2 years and the economic growth to be low in the next 2 years. This is evidend as the interest rates are falling in year 2 as compared to year 1.

Based on this yield curve From year 3 - Here, we expect inflation to start rising and economic growth to start rising. This is evidend as the interest rates are starting to rise in year 3 as compared to year 2.