Question

Interest rates on 4-year Treasury securities are currently 6.9%, while 6-year Treasury securities yield 7.8%. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the question below.

Open spreadsheet

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.

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Answer 1

(1+yield on n-year security)ⁿ*(1+yield on r-year security after n-years)^r = (1+yield on r+n year-security)^r+n

n-year security is the 4-year Treasury security and r-year security is the 2-year security.

(1+0.069)⁴*(1+yield on r-year security after n-years)² = (1+0.078)²⁺⁴

1.069⁴*(1+yield on r-year security after n-years)² = 1.078⁶

(1+yield on r-year security after n-years)² = 1.078⁶/1.069⁴ = 1.569323814085808704/1.305902703121 = 1.2017157253256723684379981281186

(1+yield on r-year security after n-years) = 1.2017157253256723684379981281186^1/2 = 1.2017157253256723684379981281186^0.5 = 1.0962

yield on 2-year security after 4-years = 1.0962- 1 = 0.962 or 9.62%

the market believes that 2-year securities will be 9.62% yielding 4 years from now.