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.