Question

An analyst evaluating securities has obtained the following information. The real rate of interest is 2.4% and is expected to remain constant for the next 5 years. Inflation is expected to be 2.2% next year, 3.2% the following year, 4.2% the third year, and 5.2% every year thereafter. The maturity risk premium is estimated to be 0.1 × (t – 1)%, where t = number of years to maturity. The liquidity premium on relevant 5-year securities is 0.5% and the default risk premium on relevant 5-year securities is 1%.

a. What is the yield on a 1-year T-bill? Round your answer to one decimal place.
b. What is the yield on a 5-year T-bond? Round your answer to one decimal place.
c. What is the yield on a 5-year corporate bond? Round your answer to one decimal place.

Answer 1

To calculate the yield on a 1-year T-bill, add the real rate of interest and the inflation rate. To calculate the yields on a 5-year T-bond and a 5-year corporate bond, add the real rate of interest, inflation rate, maturity risk premium, liquidity premium, and default risk premium.

Step-by-step explanation:

To calculate the yield on a 1-year T-bill, we need to consider the real rate of interest and inflation. The real rate is 2.4%, and inflation is expected to be 2.2% next year. Using the formula:

Yield on T-bill = Real rate of interest + Inflation rate

Yield on 1-year T-bill = 2.4% + 2.2% = 4.6%

To calculate the yield on a 5-year T-bond and a 5-year corporate bond, we need to consider the maturity risk premium, liquidity premium, and default risk premium. The maturity risk premium is calculated as 0.1 × (t – 1)%, where t is the number of years to maturity.

Yield on 5-year T-bond = Real rate of interest + Inflation rate + Maturity risk premium + Liquidity premium + Default risk premium

Yield on 5-year T-bond = 2.4% + 2.2% + 0.1 × (5 – 1)% + 0.5% + 1% = 7.2%

Yield on 5-year corporate bond = Yield on 5-year T-bond + Default risk premium

Yield on 5-year corporate bond = 7.2% + 1% = 8.2%