Questions: Question 7 Multiple Choice Chapter 5-2 - Suppose today's yields are 3.9%, 3.6% and 3.4% on 1-year, 2-year and 3-year bonds. According to ET, what does market expect 1-year bond will pay two years from now? - A) 3.5% - B) 3.63% - C) 3.0% - D) 2.7%

Solution Steps

To solve this problem, we can use the Expectations Theory (ET) of the term structure of interest rates. According to ET, the yield on a long-term bond is an average of the short-term interest rates that people expect to occur over the life of the long-term bond. We can use the given yields to calculate the expected 1-year bond yield two years from now.

1. Calculate the average yield for the 2-year bond.
2. Calculate the average yield for the 3-year bond.
3. Use these averages to solve for the expected 1-year bond yield two years from now.

Given the yields: \[ \text{yield}_{1\text{ year}} = 0.039 \] \[ \text{yield}_{2\text{ year}} = 0.036 \]

The average yield for the 2-year bond is: \[ \text{average\_yield}_{2\text{ year}} = \frac{\text{yield}_{1\text{ year}} + \text{yield}_{2\text{ year}}}{2} = \frac{0.039 + 0.036}{2} = 0.0375 \]

Given the yields: \[ \text{yield}_{3\text{ year}} = 0.034 \]

The average yield for the 3-year bond is: \[ \text{average\_yield}_{3\text{ year}} = \frac{\text{yield}_{1\text{ year}} + \text{yield}_{2\text{ year}} + \text{yield}_{3\text{ year}}}{3} = \frac{0.039 + 0.036 + 0.034}{3} = 0.03633 \]

Using the Expectations Theory formula: \[ \text{expected\_yield}_{1\text{ year, 2 years from now}} = (3 \times \text{average\_yield}_{3\text{ year}}) - (2 \times \text{average\_yield}_{2\text{ year}}) \]

Substituting the values: \[ \text{expected\_yield}_{1\text{ year, 2 years from now}} = (3 \times 0.03633) - (2 \times 0.0375) = 0.109 - 0.075 = 0.034 \]

Final Answer