Question

The yield on a one-year Treasury security is 5.6100%, and the two-year Treasury security has a 7.5735% yield. Assuming that the pure expectations theory is correct, what is the market's estimate of the one-year Treasury rate one year from now? (Note: Do not round your intermediate calculations.)

a. 8.1375%
b. 9.5735%
c. 12.1583%
d. 10.9138%

Answer 1

The market's estimate of the one-year Treasury rate one year from now, calculated using the pure expectations theory and given Treasury yields, is approximately 9.537%, which aligns closely with option (b) 9.5735%.

Step-by-step explanation:

The question asks to estimate the one-year Treasury rate one year from now using the yields given for one-year and two-year Treasury securities, assuming that the expectations theory is correct. To find this rate, we need to use the expectations theory formula.

According to the pure expectations theory, the following relationship holds:

(1+Z1)^1*(1+E(Z2))^1 = (1+Z2)^2

Where:

• Z1 is the one-year Treasury yield (5.6100%)
• E(Z2) is the expected one-year Treasury yield one year from now
• Z2 is the two-year Treasury yield (7.5735%)

Plugging in the given values we get:

(1+0.0561)*(1+E(Z2)) = (1+0.075735)^2

Solving for E(Z2) gives us the market's estimate of the one-year Treasury rate one year from now, which is approximately 9.537%. Thus, the answer closest to this value is option (b) 9.5735%.