FIN 3403 Chapter 6

Suppose 10-year T-bonds have a yield of 5.30% and 10-year corporate bonds yield 6.65%. Also, corporate bonds have a 0.25% liquidity premium versus a zero liquidity premium for T-bonds, and the maturity risk premium on both Treasury and corporate 10-year bonds is 1.15%. What is the default risk premium on corporate bonds?

1.10% Default risk premium = Corporate yield - T bond yield - Liquidity premium = 6.65% - 5.30% - 0.25% = 1.10%

Kelly Inc's 5-year bonds yield 7.50% and 5-year T-bonds yield 5.80%. The real risk-free rate is r* = 2.5%, the default risk premium for Kelly's bonds is DRP = 0.40%, the liquidity premium on Kelly's bonds is LP = 1.3% versus zero on T-bonds, and the inflation premium (IP) is 1.5%. What is the maturity risk premium (MRP) on all 5-year bonds?

1.8% Maturity Rate Premium (MRP) MRP = rT.bond − r* − IP MRP = 5.80% - 2.5% - 1.5% MRP = 1.8%

5-year Treasury bonds yield 4.4%. The inflation premium (IP) is 1.9%, and the maturity risk premium (MRP) on 5-year T-bonds is 0.4%. There is no liquidity premium on these bonds. What is the real risk-free rate, r*?

2.10% Real risk free rate= Nominal risk free rate (bonds yield) - Inflation premium - Maturity risk premium = 4.4% - 1.9% - 0.4% = 2.1%

Suppose the interest rate on a 1-year T-bond is 5.00% and that on a 2-year T-bond is 4.10%. Assume that the pure expectations theory is NOT valid, and the MRP is zero for a 1-year T-bond but 0.40% for a 2-year bond. What is the yield on a 1-year T-bond expected to be one year from now? Round the intermediate calculations to 4 decimal places and final answer to 2 decimal places.

2.42 yield on t.bond without MRP = 2 yr T.bond - MRP for 2 yr bond = 4.10% - 0.40% = 3.7% yield on a 1-year T-bond expected to be one year from now = [(1 + yield on t.bond w/out MRP)^yr / (1 + interest rate on a 1 yr T.bond)^yr ] - 1 = ( (1 + 3.7%)^2 / (1 + 5%)^1 ) - 1 = ( (1.037)^2 / (1.05)^1 ) - 1 = (1.075 / 1.05) - 1 = .0242 = 2.42%

Kop Corporation's 5-year bonds yield 6.50%, and T-bonds with the same maturity yield 5.90%. The default risk premium for Kop's bonds is DRP = 0.40%, the liquidity premium on Kop's bonds is LP = 0.20% versus zero on T-bonds, the inflation premium (IP) is 1.50%, and the maturity risk premium (MRP) on 5-year bonds is 0.40%. What is the real risk-free rate, r*?

4% Real Risk free rate = Nominal risk free rate (bonds yield) - Inflation Risk Premium - Default Risk Premium - Maturity Risk Premium - Liquidity Premium = 6.50% - 1.50% - 0.40% - 0.40% - 0.20% = 4%

Suppose the rate of return on a 10-year T-bond is 6.90%, the expected average rate of inflation over the next 10 years is 2.0%, the MRP on a 10-year T-bond is 0.9%, no MRP is required on a TIPS, and no liquidity premium is required on any Treasury security. Given this information, what should the yield be on a 10-year TIPS? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average.

4% yield be on a 10-year TIPS = rate of return on a 10 year T.bond - Average Inflation -MRP = 6.90% - 2% - 0.9% = 4%

Suppose 1-year T-bills currently yield 7.00% and the future inflation rate is expected to be constant at 2.00% per year. What is the real risk-free rate of return, r*? The cross-product term should be considered , i.e., if averaging is required, use the geometric average. (Round your final answer to 2 decimal places.)

4.9% Real risk free rate of return = ((1 + yield) / (1 + Inflation rate)) -1 = ((1 + 7%) / (1 + 2%)) - 1 = (1.07 / 1.02) - 1 = .049 = 4.9%

Suppose the real risk-free rate is 4.20%, the average expected future inflation rate is 2.50%, and a maturity risk premium of 0.10% per year to maturity applies, i.e., MRP = 0.10%(t), where t is the number of years to maturity, hence the pure expectations theory is NOT valid. What rate of return would you expect on a 4-year Treasury security? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average.

7.10% rate on return = real rate + inflation rate + per yr. maturity risk premium * T yrs. of maturity rate of return = 4.20% + 2.50% + (.10% * 4) rate of return = 6.80% * 4 rate of return = 7.10%

Suppose the real risk-free rate is 3.00%, the average expected future inflation rate is 4.00%, and a maturity risk premium of 0.10% per year to maturity applies, i.e., MRP = 0.10%(t), where t is the years to maturity. What rate of return would you expect on a 1-year Treasury security, assuming the pure expectations theory is NOT valid? Include the cross-product term, i.e., if averaging is required, use the geometric average. (Round your final answer to 2 decimal places.)

7.22% rate of return = (1 + real risk-free rate) * (1 + inflation rate) - 1 + maturity risk premium RoR = (1 + 3%) * (1 + 4%) - 1 + 0.10% RoR = 1.03 * 1.04 - 1 + .001 (solve in order left to right) RoR = .0722 = 7.22%

The real risk-free rate is 3.55%, inflation is expected to be 3.60% this year, and the maturity risk premium is zero. Taking account of the cross-product term, i.e., not ignoring it, what is the equilibrium rate of return on a 1-year Treasury bond? (Round your final answer to 3 decimal places.)

7.278% Equilibrium rate of return = ((1 + Real risk-free rate) * (1 + Inflation rate)) -1 = ((1 + 3.55%) * (1 + 3.60%)) - 1 = ( 1.0355 * 1.0360 ) - 1 = 1.0715 - 1 = .07278 = 7.278%

Suppose the real risk-free rate is 2.50% and the future rate of inflation is expected to be constant at 7.00%. What rate of return would you expect on a 5-year Treasury security, assuming the pure expectations theory is valid? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average.

9.50% rate of return on a 5-yr Treasury security = risk-free rate + expected future rate of inflation 2.50% + 7.00% = 9.50%