Question

Problem 6-8
Expectations Theory

Interest rates on 4-year Treasury securities are currently 6.15%, while 6-year Treasury securities yield 7.85%. If the pure expectations theory is correct, what does the market believe that 2-year securities will be yielding 4 years from now? Round your answer to two decimal places.

Answer 1

According to Pure Expectations Theory of Interest Rates, short term interest rates are indicator of long term interest rates. However, coming to what this theory says using the details in question. According to theory, if you invest in a 6 years treasury or invest ina 4year treasury and the when it matures, invest in a 2 year treasury (so the effective length of investment is 6 years), the amount in both the scenarios would be the same.

Mathematically,

(1 + 6yr Treasury yields)⁶ = (1 + 4yr Treasury yields)^{4 *} (1 + 2yr forward Treasury yields 4 yrs from now)²

(1 + 7.85%)⁶ = (1 + 6.15%)⁴ + (1 + 2yr forward Treasury yields 4 yrs from now)²

2yr forward Treasury yields 4 yrs from now = 7.20%