One-year Treasury bills currently earn 1.85 percent. You expect that one year from now, 1-year Treasury bill rates will increase to 2.05 percent. If the unbiased expectations theory is correct, what should the current rate be on 2-year Treasury securities? (Round your answer to 2 decimal places.)

The answer is: the current rate on 2-year Treasury securities 1.95%.

Explanation:

Under the unbiased expectations theory, the return on holding 2-year T-bill should be equal to the return of holding 1 year T-bill now and then continue holding 1 year T-bill in 12 months time. So, we have:

Interest rate on 2-year Treasury (R02) = [ (1+Interest rate on one-year bill starting from now) * (1+Interest rate on one-year bill starting 12 months later)]^(1/2) - 1 = (1.0185 x 1.0205)^(1/2) -1 = 1.95%

So, the current rate on 2-year Treasury securities 1.95%.  

1.95%

Explanation:

If the unbiased expectations theory is correct, the formula for calculating the current rate on 2-year Treasury securities is as follows:

R2 = {[(1 + current one-year T-bill rate) × (1 + Expected one-year rate 12 months from now)]^1/2} − 1 (1)

Where R2 denotes the current rate on 2-year Treasury securities

Substituting the values from the question into equation (1), we have:

R2 = {[(1 + 0.0185) × (1 + 0.0205)]^1/2} − 1

     = {[1.0186 × 1.0205]^1/2} − 1

     = {1.0394813^1/2} − 1

     = 1.01954955740268  − 1

    = 0.01954955740268

R2 = 0.0195, or 1.95% approximately.

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