4.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.
Need urgent answer
Do your own homework
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 formula to calculate the real rate of return is:
Real Rate of Return = Nominal Interest Rate - Expected Inflation Rate
In this case, the nominal interest rate on the ten-year Treasury bond is 2.5 percent, and investors expect inflation to average 1.5 percentage points over the next ten years.
To find the expected real rate of return:
Real Rate of Return = 2.5% - 1.5% = 1%
Therefore, the expected real rate of return on the ten-year US Treasury bond is 1%.
For part b, to estimate the average annual inflation rate expected by investors over the life of the thirty-year bond, we can use the concept of the maturity risk premium. The maturity risk premium is the additional interest rate compensation that investors demand for holding longer-term bonds.
In this case, the thirty-year bond has a maturity risk premium of 0.2 percentage points. If the real rate of return is expected to be the same for the thirty-year bond as for the ten-year bond (which we estimated to be 1%), the average annual inflation rate over the life of the thirty-year bond can be calculated as:
Inflation Rate = Nominal Interest Rate - Real Rate of Return
In this case, the nominal interest rate on the thirty-year bond is given as 4.0 percent.
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%.