Suppose the real risk-free rate is 3.50%, the average future inflation rate is 2

Question

Suppose the real risk-free rate is 3.50%, the average future inflation rate is 2.50%, a maturity premium of 0.20% per year to maturity applies, i.e., MRP = 0.20%(t), where t is the years to maturity. Suppose also that a liquidity premium of 0.50% and a default risk premium of 0.80% applies to A-rated corporate bonds. What is the difference in the yields on a 5-year A-rated corporate bond and on a 10-year Treasury bond? Here we assume that the pure expectations theory is NOT valid, and disregard any cross-product terms, i.e., if averaging is required, use the arithmetic average.

Explanation / Answer

step1:

calculate yield on 5-year A=rated bonds

MRP of 5-year bonds = 0.20% * 5 = 1%

yield on A_rated bond = r* + IP + MRP + DRP + LP

= 3.5% + 2.5% + 1% + 0.8% + 0.5%

= 8.3%

step2:

calculate yield on 10-year treasury bonds

MRP on 10-year bonds = 0.20% * 10 = 2%

yield on treasury bond

= r* + IP + MRP

= 3.5% + 2.5% + 2%

= 8%

step3:

calculate difference

difference = 8.3% - 8% = 0.3% .......................ans

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