1. Compare a two-year bond with two successive one-year bonds in a situation in which an investor buys a one year bond today and then another one-year bond when the first matures. Suppose that the two-year bond has an interest rate of 8 percent each year. a. Now 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 he has at the end of the two years. In each case, how much would an investor have at the end of two years if he invested $1,000 today? i. The one-year interest rate today is 7 percent; the one-year interest rate will be 9 percent one year from now. ii. The one-year interest rate today is 5 percent; the one-year interest rate will be 11 percent one year from now. iii. The one-year interest rate today is 3 percent; the one-year interest rate will be 13 percent one year from now. iv. The one-year interest rate today is 0 percent; the one-year interest rate will be 16 percent one year from now. b. From these results, is it reasonable to compare the average interest rates on alternative financial investments? (In other words, how reasonable is the assumption that we can compare average interest rates on short-term bonds with the interest rate on long-term bonds instead of using the exact method?)

2. If the interest rate on a one-year bond today is 5.0 percent, the expected interest rate on a one-year bond one year from now is 7.0 percent, and the expected interest rate on a one-year bond two years from now is 7.5 percent. According to the expectations theory of the term structure of interest rates, what is the interest rate on a two-year bond today?

3. Compare a two-year bond with two successive one-year bonds, in which an investor buys a one-year bond today, then another one-year bond when the first matures. Suppose the two- year bond has an annual interest rate of 4 percent.

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; that is, she is risk neutral. In each case, how much would an investor have at the end of two years if she invested $1000 today? In each case, which bond would the investor buy today? Show your work. a. The one-year interest rate today is 1 percent; the one-year interest rate will be 8 percent one year from now. b. The one-year interest rate today is 2 percent; the one-year interest rate will be 6 percent one year from now. c. The one-year interest rate today is 3 percent; the one-year interest rate will be 5 percent one year from now. d. The one-year interest rate today is 5 percent; the one-year interest rate will be 3 percent one year from now.

4. Suppose that a risk-neutral investor has a choice between buying a one-year bond paying 5 percent today, a two-year bond paying 5.4 percent today, a three-year bond paying 5.8 percent today, or a four-year bond paying 6.2 percent today, if a one-year bond purchased one year from now is expected to have an interest rate of 6 percent, a one-year bond purchased two years from now is expected to have an interest rate of 7 percent, and a one- year bond purchased three years from now is expected to have an interest rate of 8 percent. Arrange the sequence of bonds giving the interest rate from highest to the lowest. Which bond would the investor buy? Show your work.

5. Consider the bond market to be in equilibrium according to the complete theory of the term structure of interest rates. The current interest rate on one-year bonds is 2 percent, and you believe, as does everyone in the market, that in one year the interest rate on one-year bonds will be 3 percent, and in two years, the interest rate on one-year bonds will be 4 percent. That is, using the standard notation, i 0 = 2%, i1 = 3%, and i 2 = 4%. Assume that there is no term premium on a one-year bond. a. According to the expectations theory of the term structure of interest rates, what will the interest rate be today on a two-year bond and a three-year bond? That is, what are i 0 and i0 ?

Suppose the term premium equals 0.75 percent the number of years to maturity, for the 2- year bond and the 3-year bond. b. Calculate the interest rate today on the two-year bond and the three-year bond, incorporating the term premium.

6. Consider the bond market to be in equilibrium according to the complete theory of the term structure of interest rates. The current interest rate on one-year bonds is 3.0 percent, and you believe, as does everyone in the market, that in one year the interest rate on one-year bonds will be 3.5 percent. Assume that there is no term premium on a one-year bond. Suppose the term premium equals 0.75 percent the number of years to maturity, for the two-year bond. What is the interest rate on the two-year bond today?

7. Consider the bond market to be in equilibrium according to our complete theory of the term structure of interest rates. You observe the following interest rates available today on bonds with differing times to maturity. (You may ignore transactions costs.) Time to maturity Yield to maturity 1 year 5.0% 2 years 7.0% 3 years 7.5% The term premium for the two-year bond is the extra yield to maturity paid on a two-year bond compared with buying two separate one-year bonds (one today and another after one year). You believe that the term premium on the two-year bond is 0.5 percent. The term premium for the three-year bond is the extra yield to maturity paid on a three-year bond compared with buying three separate one-year bonds (one today, another after one year, and another after two years). You believe that the term premium on the three-year bond is 1.0 percent. Given your beliefs about the term premiums on two-year and three-year bonds, calculate the interest rates on one year bonds that you expect to prevail one year from now and two years from now. In other words, what do you expect to be the yield to maturity on a one-year bond one year from now and what do you expect to be the yield to maturity on a one-year bond two years from now? Explain and show all your work.