One-year Treasury securities yield 4%. The market anticipates that 1-year from now 1-year Treasury securities will yield 2.1%. If the pure expectations theory is correct, what should be the yield today for 2-year Treasury securities? Write your answer as a percentage, i. e. for example write 8% as 8.

3.05%

Explanation:

According to Pure Expectation Theory, the future short term interest rates are actually the forward rates.

Mathematically,

(1 + r2,0) ^2 = (1 + r1,0) ^1 * (1 + r1,1) ^1

Here,

r2,0 is the rate of interest for 2 year treasury security from today

r1,0 is the rate of the interest for 1 year treasury security from today

r1,1 is the rate of the interest for 2 year treasury security from Year 1

By Putting Values, we have:

(1 + r2,0) ^2 = (1 + 0.04) ^1 * (1 + 0.021) ^1

(1 + r2,0) ^2 = 1.06184

By taking square-root on both sides, we have:

(1 + r2,0) = 1.0305

r2,0 = 3.05%