Question

Suppose we observe the three-year Treasury security rate (1R3) to be 5.3 percent, the expected one-year rate next year—E(2r1)—to be 6.1 percent, and the expected one-year rate the following year—E(3r1)—to be 6.5 percent. If the unbiased expectations theory of the term structure of interest rates holds, what is the one-year Treasury security rate? (Do not round intermediate calculations. Round your percentage answer to 2 decimal places. (e.g., 32.16))

Answer 1

3.33%

Step-by-step explanation:

Determine the one-year treasury security rate

using this relation below

= ( 1 + 1R3 )^2 / [ ( 1 + E2r1 ) * ( 1 + E3r1 ) ] - 1

= ( 1 + 5.3% )^2 / [ ( 1 + 6.1% ) * ( 1 + 6.5% ) ] - 1

= ( 1 + 0.053 )^2 / [ ( 1 + 0.061 ) * ( 1 + 0.065 ) ] - 1

= 0.0333

= 3.33%