Question

4. Right now, one-year bonds are paying a rate of return of 2%, while two-year bonds pay a rate of return of 4%. The US government issues 2-year bonds to borrow. The US treasury secretary decides to save money by shortening the term of the debt, issuing two one-year bonds in succession rather than a two-year bond. This year, he or she reasons, interest payment each year will be lower by (.04 -.02)*D, where D is the level of the debt. If pure expectations theory is correct, will the Secretary’s plan work? Explain why or why not. Suppose, on the other hand, that preferred-habitat theory is correct so that two-year rate include a term premium of .005 (half a percent). Can the secretary save money? How much?

Answer 1

forecasting the interest rate of a future one-year bond using pure expectation theory :

• The first step is to add 1 to the two-year bond’s interest rate i.e. 1+.04 = 1.04
• The next step is to square the result or (1.04)^2 = 1.0816.
• Now divide the result by the current one-year interest rate and add one or ((1.0816 / 1.02) = 1.060).
• Subtract one from the result or (1.060-1 = .060 or 6.0%).

the interest rate for the future one year bond is 6% which is more than the 2 year bond therefore, the secretary's plan will not work.