Question

Given the observed yields below, what is the 1-year forward rate, 4 years from now?

[Hint: This is the 1-year return that will take you from the 4-year average annualized return (yield) to the 5-year average annualized return)

• 4-year yield = 3.5%
• 5-year yield = 4.0%

Forward rate (semi-annual) = [(1 + longer maturity rate/2)^# of periods/ (1 + shorter maturity rate/2)^(# of periods)] - 1

Answer 1

(1 + S5)^5 = (1 + S4)^4 x (1 + 4F1)

where, S5 - Current 4-year rate = 4.0%, S4 - Current 4-year rate = 3.5%, 4F1 - 1-year rate 4-years from now

(1 + 4%)^5 = (1 + 3.5%)^4 x (1 + 4F1)

=> 4F1 = 6.02%