.A thirty year US treasury bond has a 4.0 percent interest rate.In contrast, a ten year Treasury bond has an interest rate of 2.5 percent. A maturity risk premium is estimated to be 0.2 percentage points for the longer maturity bond. Investors expect inflation to average 1.5 percentage points over the next ten years.
a. estimate the expected real rate of return on the ten year US treasury bond.
b. If the thirty year real rate of return is expected to be the same for the thirty year bond as for the ten year bond, estimate the average annual inflation rate expected by investors over the life of thirty year bond.
a. To estimate the expected real rate of return on the ten year US Treasury bond, we need to subtract the expected inflation rate from the nominal interest rate.
The nominal interest rate on the ten year bond is 2.5 percent, and investors expect inflation to average 1.5 percentage points over the next ten years. Therefore, the expected real rate of return can be calculated as:
Real Rate of Return = Nominal Interest Rate - Expected Inflation Rate
Real Rate of Return = 2.5% - 1.5% = 1.0%
Therefore, the expected real rate of return on the ten year US Treasury bond is 1.0%.
b. We can estimate the average annual inflation rate expected by investors over the life of the thirty year bond by comparing the nominal interest rate on the thirty year bond with the real rate of return on the ten year bond.
We are given that the nominal interest rate on the thirty year bond is 4.0 percent and the expected real rate of return is the same as the ten year bond, which is 1.0 percent. Therefore, we can calculate the average annual inflation rate as:
Average Annual Inflation Rate = Nominal Interest Rate - Real Rate of Return
Average Annual Inflation Rate = 4.0% - 1.0% = 3.0%
Therefore, the average annual inflation rate expected by investors over the life of the thirty year bond is 3.0%.