A thirty-year 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 percent points over the next ten years.
a. Estimate the expected real rate of return on the ten-year U.S. Treasury bond.
b. If the 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 the thirty-year bond.
a. To estimate the expected real rate of return on the ten-year U.S. 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 percent over the next ten years. Therefore, the estimated expected real rate of return on the ten-year bond would be:
Real rate of return = Nominal interest rate - Expected inflation rate
Real rate of return = 2.5% - 1.5%
Real rate of return = 1.0%
Therefore, the expected real rate of return on the ten-year U.S. Treasury bond is 1.0%.
b. If the real rate of return is expected to be the same for the thirty-year bond as for the ten-year bond, we can estimate the average annual inflation rate expected by investors over the life of the thirty-year bond.
The nominal interest rate on the thirty-year bond is 4.0%, and the expected real rate of return is 1.0%. To estimate the average annual inflation rate expected by investors over the life of the thirty-year bond, we can subtract the expected real rate of return from the nominal interest rate to get the expected inflation rate.
Expected inflation rate = Nominal interest rate - Real rate of return
Expected inflation rate = 4.0% - 1.0%
Expected inflation rate = 3.0%
Therefore, if the real rate of return is expected to be the same for the thirty-year bond as for the ten-year bond, investors expect an average annual inflation rate of 3.0% over the life of the thirty-year bond.
To estimate the expected real rate of return on the ten-year U.S. Treasury bond, we need to calculate the nominal interest rate and then subtract the expected inflation rate.
a. The nominal interest rate on the ten-year Treasury bond is 2.5 percent. The expected inflation rate is 1.5 percent. Therefore, the expected real rate of return can be calculated as follows:
Expected Real Rate of Return = Nominal Interest Rate - Expected Inflation Rate
= 2.5% - 1.5%
= 1.0%
Therefore, the expected real rate of return on the ten-year U.S. Treasury bond is 1.0%.
b. If the real rate of return is expected to be the same for the thirty-year bond as for the ten-year bond, we can use the same expected real rate of return of 1.0% in our calculation. The thirty-year bond has an interest rate of 4.0% and a maturity risk premium of 0.2 percentage points.
Expected Nominal Interest Rate on Thirty-year Bond = Nominal Interest Rate on Ten-year Bond + Maturity Risk Premium
= 2.5% + 0.2%
= 2.7%
To estimate the average annual inflation rate expected by investors over the life of the thirty-year bond, we need to subtract the expected real rate of return from the estimated nominal interest rate.
Average Annual Inflation Rate = Expected Nominal Interest Rate on Thirty-year Bond - Expected Real Rate of Return
= 2.7% - 1.0%
= 1.7%
Therefore, the average annual inflation rate expected by investors over the life of the thirty-year bond is 1.7%.