The current one-year Treasury bill rate is 0.40 percent and the expected one-year rate 12 months from now is 1.28 percent

The current one-year Treasury bill rate is 0.40 percent and the expected one-year rate 12 months from now is 1.28 percent. According to the unbiased expectations theory, what should be the current rate for a two-year Treasury security? (Do not round intermediate calculations. Round your percentage answer to 2 decimal places. (e.g., 32.16))

 

Answer

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The current one-year Treasury bill rate, r0 = 0.40% = 0.004

The expected one-year rate 12 months from now, r1 = 1.28% = 0.0128

According to the unbiased expectations theory, the current rate for a two-year Treasury security is given by:

r(0,2) = [(1 + r0) * (1 + r1)]^(1/2) – 1

r(0,2) = [(1 + 0.004) * (1 + 0.0128)]^(1/2) – 1

r(0,2) = [(1.004) * (1.0128)]^(1/2) – 1

r(0,2) = [1.0168512]^(1/2) – 1

r(0,2) = 1.0083904006 – 1

r(0,2) = 0.0083904006

r(0,2) = 0.83904006%

r(0,2) = 0.84%