An investor in Treasury securities expects inflation to be 2.45% in Year 1, 3% in Year 2, and 4.25% each year thereafter. Assume that the real risk-free rate is 2.25%, and that this rate will remain constant. Three-year Treasury securities yield 6.20%, while 5-year Treasury securities yield 7.65%. What is the difference in the maturity risk premiums (MRPs) on the two securities; that is, what is eqMRP_5 – MRP_3 /eq?

Yields on bonds are determined by a variety of factors. The real risk free rate is the compensation for the pure time value of money. The risk premium is the additional return required by investors for the bearing of additional risks.

The difference in maturity risk premiums is 1.04%.

We can use the following formula to compute implied maturity risk premium for each bond first, and then compute the difference. Bond yield could be decomposed as follows:

For 3-year bond, the average inflation = (2.45% + 3% + 4.25%) / 3 = 3.23%. Real interest rate is 2.25%, and the bond yield is 6.20%. Therefore we have:

For 5-year bond, the average inflation = (2.45% + 3% + 4.25% * 3) / 5 = 3.64%. Real interest rate is 2.25%, and the bond yield is 7.65%. Therefore we have:

Therefore, the difference in maturity risk premium = 1.76% – 0.72% = 1.04%.

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