EXPECTATIONS THEORY Interest rates on 4year Treasury securit

EXPECTATIONS THEORY Interest rates on 4-year Treasury securities are currently 5.7%, while 6-year Treasury securities yield 7.95%. If the pure expectations theory is correct, what does the market believe that 2. year securities will be yielding 4 years from now? Calculate the yield using a geometric average. Do not round your intermediate calculations. Round your answer to two decimal places.

Solution

1.) 4-year Rate = 5.7%

6-year Rate = 7.95%

Let the yield for 2-year security 4 years from now be \'r\'.

According to pure expectation theory,

(1.0795)⁶ = (1.057)⁴ (1 + r)²

(1.0795)⁶ / (1.057)⁴ = (1 + r)²

1.582471 / 1.248245 = (1 + r)²

1.267757 = (1 + r)²

(1.267757)^1/2 = 1 + r

1.125947 - 1 = r

r = .125947 or 12.59%

2.)  r = Real risk-free rate + Inflation premium + Default risk premium + Liquidity premium + Maturity Risk premium

As it is a treasury security therefore, DRP & LP must be 0.

Real risk-free rate = 2.7% [given]

Average Inflation or Inflation premium = (2.15% + 3.9% + 2.9% + 2.9% + 2.9% + 2.9% + 2.9%) / 7 = 2.935714%

Maturity risk Premium = 0.05 x (t - 1)% = 0.05 x (7 - 1)% = 0.30%

Rate of treasury security = 2.7% + 2.935714% + 0.30% = 5.935714% or 5.94%