Question

Suppose 2-year Treasury bonds yield 3.3%, while 1-year bonds yield 2.7%. r* is 1%, and the maturity risk premium is zero. Using the expectations theory, what is the yield on a 1-year bond, 1 year from now? Calculate the yield using a geometric average. Do not round intermediate calculations. Round your answer to two decimal places. % What is the expected inflation rate in Year 1? Year 2? Do not round intermediate calculations. Round your answers to two decimal places. Expected inflation rate in Year 1: % Expected inflation rate in Year 2: %

Answer 1

Using the expectations theory, the expected yield on a 1-year bond one year from now is calculated to be 3.90%. The expected inflation rate in Year 1 is 1.70%, and in Year 2 it is 2.30%.

Step-by-step explanation:

The question asks for the expected yield on a 1-year bond one year from now, as well as the expected inflation rates for the first and second years, using the expectations theory. Given a 2-year bond yield of 3.3% and a 1-year bond yield of 2.7%, with an assumed equilibrium short-term real interest rate (r*) of 1%, and a maturity risk premium of zero, we can calculate the expected future interest rate.

To calculate the yield one year from now we can use the formula:

(1 + two-year yield)^2 = (1 + current one-year yield) * (1 + next one-year yield)

Solving for the next one-year yield gives us a geometric mean of the interest rates:

(1.033)^2 = (1.027) * (1 + next one-year yield)

1.067089 = 1.027 * (1 + next one-year yield)

Therefore, next one-year yield = (1.067089/1.027) - 1 = 0.039 or 3.90%.

The expected inflation rate in each year can be inferred from the nominal interest rates. Given the real interest rate (r*), we can subtract it from the nominal rate to find the expected inflation:

Expected inflation rate in Year 1 = 2.7% - 1% = 1.70%.

Expected inflation rate in Year 2 = 3.3% - 1% = 2.30%.

Answer 2

3.90%

1.7%

2.9%

Step-by-step explanation:

Give the following :

Yield on 2 years Treasury bond (Y2) = 3.3% = 0.033

Yield on 1 years Treasury bond (Y1) = 2.7% = 0.027

r* = risk free rate = 1%

Yield on 1 year bond, 1 year from now :

Compounded yield on yield 1 at 2.7% + Interest on return = compounded yield on 2 years bond :

(1 + 0.027) = yield on year 1

(1 + y) = yield one year from now

(1 + 0.027)¹ + (1 + y)¹ = (1 + 0.033)²

1 + y = (1 + 0.033)² / (1 + 0.027)¹

1 + y = 1.067089 / 1.027

1 + y = 1.0390350

y = 1.0390350 - 1

y = 0.03903

Yield = 0.039 * 100% = 3.90%

Inflation premium = yield rate - Risk free rate - maturity risk premium

Maturity risk premium = 0%

Hence,

For year 1

Inflation premium = 2.7% - 1% - 0% = 1.7%

For year 2:

Inflation premium = 3.9% - 1% - 0% = 2.9%