The Wall Street Journal reports that the rate on fouryear Tr

The Wall Street Journal reports that the rate on four-year Treasury securities is 2.3 percent and the rate on five-year Treasury securities is 3 percent. According to the unbiased expectations hypotheses, what does the market expect the one-year Treasury rate to be four years from today, E(5r1)? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) Expected one-year Treasury rate %

Solution

(1+1R5)⁵ = (1+1R4)⁴ + (1+E(5r1))

1R5 = Rate on five year treasury = 3% or 0.03

1R4 = Rate on Four year treasruy = 2.3% or 0.023

E(5r1) = Expected rate ...........one year treasury rate in 5th year

(1.03)⁵ = (1.023)⁴ * ( 1 + E(5r1) )

1.1592740743 = 1.095222947841 * ( 1 + E(5r1) )

( 1 + E(5r1) ) = 1.1592740743 / 1.095222947841 = 1.058482272

E(5r1) = 1.058482272 - 1 = 0.058482272

= 5.85 % ................... Final answer