Question

A recent edition of The Wall Street Journal reported interest rates of 7.2 percent, 7.55 percent, 7.85 percent, and 7.95 percent for three-year, four-year, five-year, and six-year Treasury notes, respectively. According to the unbiased expectations theory, what are the expected one-year rates for years 4, 5, and 6 (i.e., what are 4f1, 5f1, and 6f1)? (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

Answer 1

₄f₁ = The expected one-year return on a bond purchased at year 3 along with the three-year bond purchased at Year 0 that gives a total yield equal to that of the four-year bond.

-> (1+r₃)³ (1+₄f₁) = (1+r₄)⁴

-> ₄f₁ = [(1+0.0755)⁴ / (1+0.072)³] - 1

-> ₄f₁ = 8.61%

₅f₁ = The expected one-year return on a bond purchased at year 4 along with the four-year bond that is purcchased at year 0 that gives a total yield equal to that of the five-year bond.

-> (1+r₄)⁴ (1+₅f₁) = (1+r₅)⁵

-> ₅f₁ = [(1+0.0785)⁵ / (1+0.0755)⁴] - 1

-> ₅f₁ = 9.06%

₆f₁ = The expected one-year return on a bond purchased at year 5 along with the five-year bond that is purchased at the Year 0 that gives a total yield equal to that of the six-year bond.

-> (1+r₅)⁵ (1+₆f₁) = (1+r₆)⁶

-> ₆f₁ = [(1+0.0795)⁶ / (1+0.0785)⁵] - 1

-> ₆f₁ = 8.45%