Suppose that the current one-year rate (one-year spot rate) and expected one-yea

Question

Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows:

Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year maturity Treasury securities?

Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows:

Explanation / Answer

One year rate = 0.4%

Two year rate = (((1+0.4%)*(1+1.4%))^0.5) -1 = 0.90%

Three year rate = (((1+0.4%)*(1+1.4%)*(1+10.6%))^(1/3)) -1 = 4.03%

Four year rate = (((1+0.4%)*(1+1.4%)*(1+10.6%)*(1+10.95%))^(1/4)) -1 = 5.72%

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