Problem 1: The following yields on U. S. Treasury securities were taken from a recent financial publication:
Term Rate
6 months 5.1%
1 year 5.5
2 years 5.6
3 years 5.7
4 years 5.8
5 years 6.0
10 years 6.1
20 years 6.5
30 years 6.3
a. Plot a yield curve based on these data.
b. What type of yield curve is shown?
c. What information does this graph tell you?
d. Based on this yield curve, if you needed to borrow money for longer than 1 year, would it make sense for you to borrow short- term and renew the loan or borrow long- term? Explain.
Problem 2: The real risk- free rate is 3%. Inflation is expected to be 3% this year, 4% next year, and 3.5% thereafter. The maturity risk premium is estimated to be 0.05 × ( t - 1)%, where t = number of years to maturity. What is the yield on a 7- year Treasury note?
Problem 3: Due to a recession, expected inflation this year is only 3%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 3%. Assume that the expectations theory holds and the real risk- free rate is r* = 2%. If the yield on 3- year Treasury bonds equals the 1- year yield plus 2%, what inflation rate is expected after Year 1?
Problem 4: A company's 5- year bonds are yielding 7.75% per year. Treasury bonds with the same maturity are yielding 5.2% per year, and the real risk- free rate ( r*) is 2.3%. The average inflation premium is 2.5%; and the maturity risk premium is estimated to be 0.1 × ( t - 1)%, where t ¼ number of years to maturity. If the liquidity premium is 1%, what is the default risk premium on the corporate bonds?
Problem 5: An investor in Treasury securities expects inflation to be 2.5% in Year 1, 3.2% in Year 2, and 3.6% each year thereafter. Assume that the real risk- free rate is 2.75% and that this rate will remain constant. Three- year Treasury securities yield 6.25%, while 5- year Treasury securities yield 6.80%. What is the difference in the maturity risk premiums ( MRPs) on the two securities; that is, what is MRP5 - MRP3?
Problem 6: Assume that the real risk- free rate is 2% and that the maturity risk premium is zero. If the 1- year bond yield is 5% and a 2- year bond ( of similar risk) yields 7%, what is the 1- year interest rate that is expected for Year 2? What inflation rate is expected during Year 2? Comment on why the average interest rate during the 2- year period differs from the 1- year interest rate expected for Year 2.