Suppose that today the one-year Treasury note yields 0.12% (0.0012 in decimal fo

Question

Suppose that today the one-year Treasury note yields 0.12% (0.0012 in decimal form), the two-year note yields 0.40% (0.0040), the three-year note yields 0.78% (0.0078), the five-year note yields 1.60% (0.0160), the seven-year note yields 2.22% (0.0222) and the ten-year note yields 2.81% (0.0281). Under the pure expectations theory with no maturity risk:

            a) What is the expected yield on a one-year note delivered one year from now?

            b) What is the expected yield on a one-year note delivered two years from now?

            c) What is the expected yield on a three-year note delivered two years from now?

            d) What is the expected yield on a two-year note delivered five years from now?

            e) What is the expected yield on a five-year note delivered five years from now?

            f) What is the expected yield on a seven-year note delivered three years from now?

Note: This concept is discussed in Chapter 3 of the text and in “Lesson 2: More On Yield Curves and Forward Rate Determination” in this week’s online materials.

Explanation / Answer

Year

Yield

1

0.12%

2

0.40%

3

0.78%

5

1.60%

7

2.22%

10

2.81%

Solution-a

Expected Yield = (yield1 * year1 - yield2 * year2) / (year2 - year1)

Expected Yield = (0.40% * 2 - 0.12% * 1) / (2 - 1)

Expected Yield = 0.68%

Solution-b

Expected Yield = (yield1 * year1 - yield2 * year2) / (year2 - year1)

Expected Yield = (0.78% * 3 - 0.40% * 2) / (3 - 2)

Expected Yield = 1.54%

Solution-c

Expected Yield = (yield1 * year1 - yield2 * year2) / (year2 - year1)

Expected Yield = (1.60% * 5 - 0.78% * 3) / (5 - 3)

Expected Yield = 2.83%

Solution-d

Expected Yield = (yield1 * year1 - yield2 * year2) / (year2 - year1)

Expected Yield = (2.22% * 7 - 1.60% * 5) / (7 - 5)

Expected Yield = 3.77%

Solution-e

Expected Yield = (yield1 * year1 - yield2 * year2) / (year2 - year1)

Expected Yield = (2.81% * 10 - 2.22% * 7) / (10 - 7)

Expected Yield = 4.02%

Solution-f

Expected Yield = (yield1 * year1 - yield2 * year2) / (year2 - year1)

Expected Yield = (2.81%*10-2.22%*7) / (10 - 7)

Expected Yield = 4.19%

Year

Yield

1

0.12%

2

0.40%

3

0.78%

5

1.60%

7

2.22%

10

2.81%

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