Question

Unbiased Expectations Theory The Wall Street Journal reports that the rate on four-year Treasury securities is 1.60 percent and the rate on five-year Treasury securities is 2.15 percent. According to the unbiased expectations theory, what does the market expect the one-year Treasury rate to be four years from today, E(5r1)? (LG6-7)

Answer 1

Explanation: Unbiased Expectations Theory states that current long-term interest rates contain an implicit prediction of future short-term interest rates. More specifically, the theory states that an investor should earn the same amount of interest from an investment in a single two-year bond today as that person would with two consecutive investments in one-year bonds.

From the above question:

1 + 1R5= {(1 + 1R4)4(1 + E(5r1))}1/51.0215

= {(1.016)4(1 + E(5r1))}1/5(1.0215)5

= (1.016)4(1 + E(5r1))(1.0215)5 / (1.016)4

= 1 + E(5r1)1 + E(5r1)

= 1.0438E (5r1) = 4.38%