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 percent, ₁R₂ = 4.75 percent, ₁R₃ = 5.25 percent, ₁R₄ = 5.95 percent
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

According to the unbiased expectations theory, the one-year forward rate on a zero-coupon bond for a specific year is equal to the market's expectation of the spot rate for that year plus the risk premium. The risk premium is assumed to be zero.

Using this theory, we can calculate the one-year forward rates as follows:

- Year 2: (1 + 0.0475)^2 / (1 + 0.0455) - 1 = 6.26%
- Year 3: (1 + 0.0525)^3 / (1 + 0.0455)^2 - 1 = 8.08%
- Year 4: (1 + 0.0595)^4 / (1 + 0.0455)^3 - 1 = 9.68%

Therefore, the best choice is A.

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