Question

An investor in Treasury securities expects inflation to be 2.4% in Year 1, 3.2% in Year 2, and 4.25% each year thereafter. Assume that the real risk-free rate is 1.95% and that this rate will remain constant. Three-year Treasury securities yield 5.80%, while 5-year Treasury securities yield 7.00%. What is the difference in the maturity risk premiums (MRPs) on the two securities; that is, what is MRP5 - MRP3? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

SOLUTION :

Yield on 3 years bond = rF + (IF1 + IF2 + IF3) / 3 + MRP3

=> 5.80 = 1.95 + (2.4 + 3.2 + 4.25) / 3 + MRP3

=> 5.80 = 5.23 + MRP

=> MRP3 = 5.80 - 5.23

=> MRP3 = 0.57% 

Yield on 5 years bond = rF + (IF1 + IF2 + IF3 + IF4 + IF5) / 5 + MRP5

=> 7.00 = 1.95 + (2.4 + 3.2 + 4.25*3) / 5 + MRP3

=> 7.00 = 5.62 + MRP5

=> MRP5 = 7.00 - 5.62

=> MRP3 = 1.38% 

So, difference between MRP5  and MRP3 = 1.38 - 0.57 = 0.81% (ANSWER)

Answer 2

Step 1 - Inflation risk premium for 3 year and 5 year:

 Inflation premium (3 year) = = 3.28% 

Inflation premium (5 year) =  (2.4+ 3.2+ 4.25x 3)/5  = 3.67%

The real risk free rate is 1.95%

MRP3 = 5.80% - 3.28% - 1.95% = 0.57%

MRP5 = 7.00% - 3.67% -1.95% = 1.38%.

So, MRP5 - MRP3 = 0.81%