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 2.25%, a maturity premium of 0.08% per year to maturity applies, i.e., MRP = 0.08%(t), where t is the years to maturity.

Suppose also that a liquidity premium of 0.5% and a default risk premium of 0.85% applies to A-rated corporate bonds.

How much higher would the rate of return be on a 5-year A-rated corporate bond than on a 5-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

Real risk-free rate, r*

r* = 3.5%

IP = 2.25%

MRP, 5 year T-bond = 0.4% (0.08% per year x 5)

MRP, 10 year corporate = 0.8% (0.08 per year x 10)

LP = 0.5%

DRP = 0.85%

k = r* + IP + MRP

T-Bond Rate = 3.5 +2.25 + 0.4

= 6.15%

k = r* + IP + MRP + LP + DRP

A Bond Yield = 3.5 + 2.25 + 0.8 + 0.5 + 0.85

= 7.9%

Difference = 7.9 – 6.15

= 1.75%

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