The one-year spot rate is currently 4 percent; the one-year spot rate one year from now...

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?

please show in excel

Expert Solution

Sol:

One-year spot rate = 4%

One-year spot rate one year = 3%

One-year spot rate two years from now = 6%

Period (n) = 3 years

As per unbiased expectation theory three year spot rate is = Geometric average of the spot and forward one-year interest rates.

Three-year spot rate = (1+One-year spot rate) x (1+One-year spot rate one year) x (1+One-year spot rate two years from now)^1/3 - 1

Three-year spot rate = (1+ 0.04) x (1+0.03) x (1+0.06)^1/3 - 1

Three-year spot rate = (1.04 x 1.03) x 1.06)^1/3 - 1 = 4.3259%

Excel calculation below

One year spot rate	1.04
One-year spot rate one year from now	1.03
One-year spot rate two year from now	1.06
1/n	0.333333
Three year spot rate	4.3259%

Therefore three-year spot rate be = 4.33%

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