A Treasury note with a maturity of four years carries a nominal rate of interest

Question

A Treasury note with a maturity of four years carries a nominal

rate of interest of 10 percent. In contrast, an eight-year Treasury

bond has a yield of 8 percent.

a. If inflation is expected to average 7 percent over the first four

years, what is the expected real rate of interest?

b. If the inflation rate is expected to be 5 percent for the first

year, calculate the average annual rate of inflation for years

2 through 4.

c. If the maturity risk premium is expected to be zero between

the two Treasury securities, what will be the average annual

inflation rate expected over years 5 through 8?

Explanation / Answer

If the maturity risk premium is expected to be zero between the two Treasury securities, what will be the average annual inflation rate expected over years 5 through 8?

Y4 = real rate + Inflation4
10% = real rate +7%
real rate = 3%
=======================================
Y8 =real rate + Inflation8
8% =3% +Inflation8
Inflation8= 5%
=======================================

Inflation8 =average annual inflation rate over years 1 through 4 +average annual
inflation rate expected over years 5 through 8
5% =7% +average annual
inflation rate expected over years 5 through 8
average annual
inflation rate expected over years 5 through 8 = -2%

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