Question

Calculating interest rates

The real risk-free rate (r*) is 2.8% and is expected to remain constant. Inflation is expected to be 7% per year for each of the next four years and 6% thereafter.

The maturity risk premium (MRP) is determined from the formula: 0.1(t – 1)%, where t is the security’s maturity. The liquidity premium (LP) on all Gauge Imports Inc.’s bonds is 1.05%. The following table shows the current relationship between bond ratings and default risk premiums (DRP):

Rating	Default Risk Premium
U.S. Treasury
AAA	0.60%
AA	0.80%
A	1.05%
BBB	1.45%

Gauge Imports Inc. issues 15-year, AA-rated bonds. What is the yield on one of these bonds? Disregard cross-product terms; that is, if averaging is required, use the arithmetic average.

12.32%

11.27%

6.05%

10.92%

Based on your understanding of the determinants of interest rates, if everything else remains the same, which of the following will be true?

A. An AAA-rated bond has less default risk than a BB-rated bond.

B. The yield on U.S. Treasury securities always remains static.

Answer 1

Inflation premium = (7%*4 years + 6%*11 years)/15 years = 6.2667%

Matrurity Risk premium = 0.1*(15-1)% = 1.4%

The liquidity premium (LP) = 1.05%

AA bond default premium = 0.80%

So,

Yield on 15 year AA bonds = 2.8%+6.2667%+1.4%+1.05%+0.80% = 12.31667% or 12.32% (1st option is correct)

All else remaining same, the AAA rated bond has less default risk than a AA rated bond. This statement is true as the bonds are rated based on their default risk (Statement A is true)

The yield on U.S. Treasury securities always remains static. This statement is not correct as yields on US treasury also changes based on decisions of Central bank and market conditions (Statement B is false)