The Wall Street Journal reports that the rate on 4-year Treasury securities is 1.60 percent and the rate on 5-year Treasury securities is 2.15 percent. According to the unbiased expectations theory, what does the market expect the 1-year Treasury rate to be four years from today, E (5r1)

Treasury rate

4.38 ± 0.01%

Explanation:

1 + 1R5 = { (1 + 1R4) ^4 (1 + E (5r1)) }^1/5

1.0215 = { (1.016) ^4 (1 + E (5r1)) }^1/5

(1.0215) ^5 = (1.016) ^4 (1 + E (5r1))

(1.0215) ^5 / (1.016) ^4 = 1 + E (5r1)

1 + E (5r1) = 1.0438

E (5r1) = 4.38%

The Treasury rate

4.18 ± 0.01%

Explanation: The solution to the problem is given below

1 + 1R6 = { (1 + 1R4) 4 (1 + Expectation (4r2)) 2}1/6 = 1.0225 = { (1 + 0.0130) 4 (1 + Expectations (4r2)) 2}1/6

This implies that we going to have

=> Expectation (4r2) = { (1.0225) 6 / (1 + 0.0130) 4}1/2 - 1 = 4.18%

So the answer to this solution is 4.18%