# finance

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.

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1. 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.

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2. 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)

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