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%
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 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%
Which of the following would be most likely to lead to a higher level of interest rates in the economy?
Corporations step up their expansion plans and thus increase their demand for capital.
The four most fundamental factors that affect the cost of money are (1) production opportunities, (2) time preferences for consumption, (3) risk, and (4) the skill level of the economy's labor force.
False
Assume that the rate on a 1-year bond is now 6%, but all investors expect 1-year rates to be 7% one year from now and then to rise to 8% two years from now. Assume also that the pure expectations theory holds, hence the maturity risk premium equals zero. Which of the following statements is CORRECT?
The interest rate today on a 3-year bond should be approximately 7%.
If the pure expectations theory is correct (that is, the maturity risk premium is zero), which of the following is CORRECT?
The yield curve for corporate bonds may be upward sloping even if the Treasury yield curve is flat.
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 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%
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%
Which of the following statements is CORRECT?
The yield on a 2-year corporate bond should always exceed the yield on a 2-year Treasury bond.
If investors expect a zero rate of inflation, then the nominal rate of return on a very short-term U.S. Treasury bond should be equal to the real risk-free rate, r*.
True
One of the four most fundamental factors that affect the cost of money as discussed in the text is the risk inherent in a given security. The higher the risk, the higher the security's required return, other things held constant.
True
The "yield curve" shows the relationship between bonds' maturities and their yields.
True
The Federal Reserve tends to take actions to increase interest rates when the economy is very strong and to decrease rates when the economy is weak.
True
The risk that interest rates will decline, and that decline will lead to a decline in the income provided by a bond portfolio as interest and maturity payments are reinvested, is called "reinvestment rate risk."
True