Question

1. Interest rates on a 4-year Treasury security are currently 7%, while 6-year Treasury securities yield 7.5%. If the pure expectations theory is correct, what does the market believe that 2-year securities will be yielding 4 years from now?

Answer 1

Answer:

The market believes that 2-year securities will be yielding 4 years from now is 8.51%

Explanation:

The pure expectations theory tries to predict what short-term interest rates will be in the future based on current long-term interest rates.

Given data;

Interest rate on 4-year treasury security = 7%

Interest rate on 6-year treasury security = 7.5%

The pure expectation theory explains  that the 6-year rate is the geometric average of the 4-year rate and the 2-year rate 4 years from now.

The 2-year rate in 4 years is represented by r

We solve;

(1  +  7.5%)⁶ =  (1  +  7%)⁴ ×  (1  +  r)²

(1 + 0.075)⁶  = (1. 0.07)⁴ ×  (1  +  r)²

1.543301526  =  1.31079601  ×  (1  +  r)²

1  +  r  =  1.08507020

r  =   1.08507020 - 1

r = 0.08507020

r = 8.51%

Therefore, the market believes that 2-year securities will be yielding 4 years from now is 8.51%.