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.