On May 23, 20XX, the existing or current (spot) one-year, two-year, three-year, and four-year zero-coupon Treasury security rates were as follows: ₁R₁ = 4.55%, ₁R₂ = 4.75%, ₁R₃ = 5.25%, ₁R₄ = 5.95%
Using the unbiased expectations theory, calculate the one-year forward rates on zero-coupon Treasury bonds for years two, three, and four as of May 23, 20XX.

Question

Quizplus · Accepted Answer

The unbiased expectations theory suggests that the forward rates are determined by the expected future spot rates. The one-year forward rate for year two is calculated using the formula: (1+₁R₂)^2 / (1+₁R₁) - 1. Similarly, the forward rate for year three is: (1+₁R₃)^3 / (1+₁R₂)^2 - 1, and for year four: (1+₁R₄)^4 / (1+₁R₃)^3 - 1. Calculating these gives the forward rates as 4.95% for year two, 6.26% for year three, and 8.08% for year four.

On May 23, 20XX, the Existing or Current (Spot) One-Year