Question

The real risk-free rate is 2.05%. Inflation is expected to be 3.05% this year, 4.75% next year, and 2.3% thereafter. The maturity risk premium is estimated to be 0.05(t- 1)%, where t=5 number of years to maturity. What is the yield on a 7-year Treasury note?

Answer 1

The yield on a 7-year Treasury note is 5.11%.

Step-by-step explanation:

Given

Real risk-free rate = r* = 2.05%. Inflation Rate = 3.05% this year, 4.75% next year, and 2.3% thereafter.

Time = 7 years

Maturity risk premium, MRP = 0.05(t- 1)%

First, we'll calculate the average inflation rate for the next 7 years.

This is given by:

((3.05% * 1) + (4.75% * 1) + (2.3% * (7-2)))/7

This is so, because the Inflation Rate is 3.05% this year (1 year), 4.75% next year (1 year), and 2.3% thereafter (7-2=5 years).

So, we have

(3.05% + 4.75% + 11.5%)/7

= 19.3%/7

= 2.757142857142857%

= 2.76%

So, IP7 = 2.76%

The yield on a 7-year Treasury note is calculated by

r* + IP7 + MRP

Yield = 2.05% + 2.76% + 0.05(t- 1)% where t = 7

Yield = 4.81% + 0.05(7-1)%

Yield = 4.81% + 0.05*6%

Yield = 4.81% + 0.3%

Yield = 5.11%