Question

An investor in Treasury securities expects in ation to be 2.5 % in Year 1, 3.2 % in Year
2, and 3.6 % each year thereafter. Assume that the real risk free rate is 2.75 % and that this rate
will remain constant. Three-year treasury securities yield 6.25 %, while 5-year Treasury securities
yield 6.8 %. What is the dierence in the maturity risk premiums (MRPs) on the two securities;
that is MRP5 ?MRP2

Answer 1

Average inflation over three years, IP3 = (2.5% + 3.2% + 3.6%) / 3 = 3.10%

Average inflation over five years, IP5 = (2.5% + 3.2% + 3.6% + 3.6% + 3.6%) / 5 = 3.30%

Treasury security yield = the real risk free rate + IP + MRP

Three-year treasury securities yield = 2.75% + IP3 + MRP3 = 2.75% + 3.10% + MRP3 = 6.25%

Five-year treasury securities yield = 2.75% + IP5 + MRP5 = 2.75% + 3.30% + MRP5 = 6.80%

Take the difference to get:

MRP5 - MRP3 + 0.20% = 0.55%

Hence, the dierence in the maturity risk premiums (MRPs) on the two securities = MRP5 - MRP3 = 0.55% - 0.20% = 0.35%