1. Compare a two-year bond with two successive one-year bonds in a situation in which an investor buys a one 3-year bond when the first matures. Suppose that the two-year bond has an interest rate of 8 percent each year. A. Consider the pattern of interest rates on the one-year bonds listed below and explain whether an investor should buy the two-year bond or the one-year bond today, assuming that the only thing that matters to the investor is the amount of money she has at the end of the two years. In each case, also indicate how much she would have at the end of two years if she invested $1,000 today.
(i) The one-year interest rate today is 7 percent; the one-year rate will be 9 percent one year from now. Should she buy the 1 or 2-year bond? ______________________ How much would she have after 2 years? ____________________
(ii) The one-year interest rate today is 5 percent; the one-year interest rate will be 11 percent one year from now. Should she buy the 1 or 2-year bond? ______________________ How much would she have after 2 years? ____________________
(iii) The one-year interest rate today is 3 percent; the one-year interest rate will be 13 percent one year from now. Should she buy the 1 or 2-year bond? ______________________ How much would she have after 2 years? ____________________
(iv) The one-year interest rate today is 0 percent; the one-year interest rate will be 16 percent one year from now. Should she buy the 1 or 2-year bond? ______________________ How much would she have after 2 years? ____________________
B. In our text it was suggested that a reasonable estimation technique would be to compare the average short-term (one-year) rate with the longer-term (two-year) rate.
Do you get the same decision in each of the above scenarios with this simpler technique? Yes, or No: ______________
2. Suppose that the interest rate on a one-year bond is 7 percent today and the interest rates expected on one-year bonds in the future are 6 percent in one year, 5 percent in two years, and 4 percent in three years.
A. According to the expectations theory of the term structure, what are the interest rates today on a two-year bond, a three-year bond, and a four-year bond? Rate on a two-year bond _____________% Rate on a three-year bond ____________ % Rate on a four-year bond _____________% B. If the term premium is equal to 0.5 times the number of years to maturity of a bond for times to maturity of two, three, and four years, what are the interest rates today on a two-year bond, a three-year bond, and a four-year bond?
Assume no term premium on one-year bonds. Rate on a two-year bond _____________% Rate on a three-year bond ____________ % Rate on a four-year bond _____________%