Question

3. 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 (3rd year) is 4%. a. Calculate the 2-year interest rate and the 3-year interest rate based on the expectations theory. (Show calculations) b. 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.) 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. d. Based on this yield curve: What do you think market participants expect from future inflation and the economy (Write brief answers.) (i) in the next 2 years? (ii) From year 3?

Answer 1

2. To calculate the 2-year interest rate and 3-year interest rate, we will use the below formula -

[ {1 + r (n+1)}^(n+1) / (1 + rn)^n] - 1

Plugging in the values, 2-year interest rate =

{(1+2%)^2 / (1+3%)^1} - 1

= {(1 + 0.02)^2 / (1 + 0.03)^1} - 1

= (1.02^2 / 1.03) - 1

= 1.0404 / 1.03 - 1

= 1.01 - 1

= 0.01

= 1%

Similarly, 3-year interest rate =

{(1 + 4%)^3 / (1 + 2%)^2} - 1

= (1.04^3 / 1.02^2) - 1

= (1.124864 / 1.0404) - 1

= 1.0811 - 1

= 0.0811

= 8%

b. Yield curve -

Interest Rates 8077 + = 1.01 1+0.2 3 Borroicing Period

c) Liquidity Premium

Interest Rates Liquidity TE presninar 61+ 4% + > Expectations theory ito.2 3 Borrowing Period

d) In the next two years, the interest rate is falling to 1% according to expectations theory. In general, a fall in interest rates would mean that borrowing is cheap and people will borrow more and have more money. Thus, they will spend more on goods and services, consumption would go up, and it would lead to an increase in inflation.

In the next three years, the interest rate is rising to 8% according to expectations theory. In general, a rise in interest rates would mean that borrowing is expensive and people will borrow less. Thus, consumption will fall and it would lead to a fall in inflation. But, because of higher interest rates, savings would increase.