Question

The one-year spot rate is currently 4 percent; the one-year spot rate one year from now will be 3 percent; and the one-year spot rate two years from now will be 6 percent. Under the unbiased expectations theory, what must today's three-year spot rate be?

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Answer 1

We know that,

1 + F(1,2) = (1+spot rate for two year )^2/(1+ spot rate for one year)

One year spot rate = 4%

F(1,2) = 3%

1.03 = (1+spot rate for two year )^2/(1+ 0.04)

spot rate for two year = (1.03 * 1.04 )^0.5 -1 = 3.5%

1 + F(2,3) = (1+spot rate for three year )^3/(1+ spot rate for two year)^2

F(2,3) = 6%

Two year spot rate = 3.5%

(1.06 * 1.035^2 )^(1/3) - 1 = Three year spot rate

Three year spot rate = 4.33 % Answer

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