A thirty-year U.S. Treasury bond has a 4.0 percent interest rate. In contrast, a ten-year treasury bond has an interest rate of 3.7 percent. If inflation is expected to average 1.5 percentage points over both the next ten years and thirty years, determine the maturity risk premium for the thirty-year bond over the ten-year bond.
Compute the MRP for both types of Bonds and subtract the difference.
You get the answer?
To determine the maturity risk premium (MRP) for the thirty-year bond over the ten-year bond, we need to calculate the MRP for each bond and then subtract the difference.
The formula for calculating the MRP is:
MRP = Nominal Interest Rate - Real Interest Rate
1. Calculate the nominal interest rate for each bond:
For the thirty-year bond: Nominal Interest Rate = 4.0%
For the ten-year bond: Nominal Interest Rate = 3.7%
2. Calculate the real interest rate by subtracting the expected inflation rate from the nominal interest rate:
Real Interest Rate = Nominal Interest Rate - Expected Inflation Rate
For both bonds, the expected inflation rate is 1.5%.
For the thirty-year bond:
Real Interest Rate = 4.0% - 1.5% = 2.5%
For the ten-year bond:
Real Interest Rate = 3.7% - 1.5% = 2.2%
3. Calculate the MRP for each bond:
MRP for the thirty-year bond = Nominal Interest Rate - Real Interest Rate
MRP for the thirty-year bond = 4.0% - 2.5% = 1.5%
MRP for the ten-year bond = Nominal Interest Rate - Real Interest Rate
MRP for the ten-year bond = 3.7% - 2.2% = 1.5%
Both bonds have a maturity risk premium of 1.5%.
4. Finally, subtract the MRP of the ten-year bond from the MRP of the thirty-year bond to find the maturity risk premium for the thirty-year bond over the ten-year bond:
Maturity Risk Premium (30-year bond over 10-year bond) = MRP of thirty-year bond - MRP of ten-year bond
Maturity Risk Premium = 1.5% - 1.5% = 0%
Therefore, the maturity risk premium for the thirty-year bond over the ten-year bond is 0%.