Posted by fran taylor on Friday, January 27, 2012 at 7:24pm.
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)
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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