Question

Quantitative Problem: An analyst evaluating securities has obtained the following information. The real rate of interest is 2.6% and is expected to remain constant for the next 5 years. Inflation is expected to be 2.3% next year, 3.3% the following year, 4.3% the third year, and 5.3% every year thereafter. The maturity risk premium is estimated to be 0.1 x t-1 %, where t number of years to maturity. The quidity premium on relevant 5-year securities is 0.5% and the default sk premium on relevant 5-year securities is 1%. a. What is the yield on a 1-year T-bill? Round your intermediate calculations and final answer to two decimal places b. What is the yield on a 5-year T-bond? Round your intermediate calculations and final answer to two decimal places c. What is the yield on a 5-year corporate bond? Round your intermediate calculations and final answer to two decimal places

Answer 1

a. Yield on 1 year T- Bill will be Nominal interest rate that is real imterest rate + Inflation .

    As in 1 year T- Bill, Inflation for this year not given , therefore real = Nominal.

    Therefore, yield on 1 Year T- Bill is 2.6%.

b. Nominal interest rate for 5 year T - Bond = 2.6% x 1.023 x 1.033 x 1.043 x 1.053 = 3.018%

    + Maturity risk premium of [0.1 x (5-1)%] = 0.4%

    T- Bond is not having liquidity risk and default risk because these government bonds are free from these risks.

Therefore, interest rate for 5 year T - Bond = 3.018% + 0.4% = 3.418%

c. Yield on a 5 year corporate bond = Yield on T - Bond + Liquidity risk premium + default risk premium

                                                         = 3.418% + 0.5% + 1%

                                                         = 4.918%