Answer:
The market believes that 2-year securities will be yielding 4 years from now is 8.51%
Explanation:
The pure expectations theory tries to predict what short-term interest rates will be in the future based on current long-term interest rates.
Given data;
Interest rate on 4-year treasury security = 7%
Interest rate on 6-year treasury security = 7.5%
The pure expectation theory explains that the 6-year rate is the geometric average of the 4-year rate and the 2-year rate 4 years from now.
The 2-year rate in 4 years is represented by r
We solve;
(1 + 7.5%)⁶ = (1 + 7%)⁴ × (1 + r)²
(1 + 0.075)⁶ = (1. 0.07)⁴ × (1 + r)²
1.543301526 = 1.31079601 × (1 + r)²
1 + r = 1.08507020
r = 1.08507020 - 1
r = 0.08507020
r = 8.51%
Therefore, the market believes that 2-year securities will be yielding 4 years from now is 8.51%.
