A thirty year US Treasury bond has a 4.0% interest rate.In contrast a ten year treasury bond has an interest rate of 3.7%. If inflation is expected to average 1.5% points over both the next ten years and thirty years, determine the maturity risk premium for the thirty year bond over the ten years bond.
nominal risk free rate for 10 years = 3.7 + 1.5 = 5.2
nominal risk free rate for 30 years = 4.0 + 1.5 = 5.5
Thus maturity risk premium is 5.5 - 5.2 = 0.3%
It is basically premium for holding bond for longer duration.
r = RR + IP + DRP + MRP + LP or RR + IP + DRP + MRP + LP = r
30 year bond 10 year bond
r = 4.0% r = 3.7%
IP = 1.5% IP = 1.5%
4.0 + 1.5 = 5.5% 3.7 + 1.5 = 5.2%
= 0.3%
30 year
= (1 + 0.04)*(1 + 0.015) - 1
1.04 * 1.015 = 1.0556
1.0556 - 1 = 0.0556 or 5.56%
= 5.56% for nominal risk free interest rate
10 year
= (1 + 0.037)*(1 + 0.015) - 1
1.037 * 1.015 = 1.0525
1.0525 - 1 = 0.05255 or 5.26%
= 5.26% for nominal risk free interest rate
5.56% - 5.26% = 0.3000 or 0.3% (maturity risk preimum)
n,m
To determine the maturity risk premium for the thirty-year bond over the ten-year bond, we need to calculate the difference between the yields of the two bonds.
First, we calculate the yield of the thirty-year bond after accounting for expected inflation.
Yield of thirty-year bond = Interest rate of the thirty-year bond - Expected inflation for thirty years
= 4.0% - 1.5%
= 2.5%
Next, we calculate the yield of the ten-year bond after accounting for expected inflation.
Yield of ten-year bond = Interest rate of the ten-year bond - Expected inflation for ten years
= 3.7% - 1.5%
= 2.2%
Finally, we calculate the maturity risk premium by subtracting the yield of the ten-year bond from the yield of the thirty-year bond.
Maturity risk premium = Yield of thirty-year bond - Yield of ten-year bond
= 2.5% - 2.2%
= 0.3%
Therefore, the maturity risk premium for the thirty-year bond over the ten-year bond is 0.3%.