Suppose we observe the three-year Treasury security rate (1R3) to be 5.2 percent, the expected one-year rate next year—E(2r1)—to be 6.2 percent

  1. Suppose we observe the three-year Treasury security rate (1R3) to be 5.2 percent, the expected one-year rate next year—E(2r1)—to be 6.2 percent, and the expected one-year rate the following year—E(3r1)—to be 6.8 percent. If the unbiased expectations theory of the term structure of interest rates holds, what is the one-year Treasury security rate?

 

Answer

Based on unbiased expectations theory,

Save your time - order a paper!

Get your paper written from scratch within the tight deadline. Our service is a reliable solution to all your troubles. Place an order on any task and we will take care of it. You won’t have to worry about the quality and deadlines

Order Paper Now

(1 + 3 Yr Rate)3 = (1 + 1 Yr rate) * (1 + 1 Yr rate 1 Yr from now) * (1 + 1 Yr rate 2 Yr from now)

(1 + 5.2%)3 = (1 + 1 Yr rate) * (1 + 6.2%) * (1 + 6.8%)

1.164253 = (1 + 1 Yr rate) * (1.062) * (1.068)

1.164253 = (1 + 1 Yr rate) * 1.134216

(1 + 1 Yr rate) = 1.0265

1 Yr rate = 0.0265 = 2.65%