Question

You can calculate the yield curve given inflation and maturity-related risks. Looking at the yield curve, you can use the information embedded in it to estimate the market's expectations regarding future inflation, risk, and short-term interest rates. The Expectations theory states that the shape of the yield curve depends on investors' expectations about future interest rates. The theory assumes that bond traders establish bond prices and interest rates strictly based on expectations for future interest rates and that they are indifferent to maturity because they don't view long-term bonds as being riskier than short-term bonds. For example, assume that you had a 1-year bond that yields 2% and a 2-year bond that yields 4%. From this information, you could determine what the yield on the 1-year bond one year from now would be. Investors with a 2-year horizon could invest in the 2-year bond or they could invest in a 1-year T-bond today and a 1-year bond one year from today. Both options should yield the same result if the market is in equilibrium; otherwise, investors would buy and sell securities until the market was in equilibrium.

Quantitative Problem: Today, interest rates on 1-year bonds yield 2.9%, interest rates on 2-year T-bonds yield 4%, and interest rates on 3-year bonds yield 2.96%.
a. If the pure expectations theory is correct, what is the yield on 1-year bonds one year from now? Be sure to use rounded intermediate calculations. Round your answer to four decimal places.
b. If the pure expectations theory is correct, what is the yield on 2-year bonds one year from now? Be sure to use geometric average in your calculations. Round your answer to four decimal places.
c. If the pure expectations theory is correct, what is the yield on 3-year bonds two years from now? Be sure to use geometric average in your calculations. Round your answer to four decimal places.

Answer 1

The yield on 1-year bonds one year from now is 5.77%. The yield on 2-year bonds one year from now is 3.47%. The yield on 3-year bonds two years from now is 2.96%.

Step-by-step explanation:

The yield on 1-year bonds one year from now can be calculated using the pure expectations theory. According to this theory, the yield on a 1-year bond one year from now is equal to the geometric average of the yields on the 1-year bond and the 2-year bond today. So, the yield on 1-year bonds one year from now would be ((1 + 0.029) * (1 + 0.04))^(1/2) - 1 = 0.0577 or 5.77%.

The yield on 2-year bonds one year from now can also be calculated using the pure expectations theory. According to the theory, the yield on a 2-year bond one year from now is equal to the geometric average of the yields on the 2-year bond today and the 3-year bond today. So, the yield on 2-year bonds one year from now would be ((1 + 0.04) * (1 + 0.0296))^(1/2) - 1 = 0.0347 or 3.47%.

The yield on 3-year bonds two years from now can be calculated using the pure expectations theory. According to the theory, the yield on a 3-year bond two years from now is equal to the yield on the 3-year bond today. So, the yield on 3-year bonds two years from now would be 0.0296 or 2.96%.