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The following table gives annual interest rates for the given maturities. Assume that the pure expectations...

The following table gives annual interest rates for the given maturities. Assume that the pure expectations hypothesis holds. 1 Year 1.99% 2 Year 2.12% 3 Year 2.34% 4 Year 2.53% 5 Year 2.98% What is the 1 year rate in 2 years?

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Answer #1

1 Year rate in 2 years is represented as 1f2 which technically means forward rate expected in the third year i.e 1 year rate in two years from now.

Now using the pure expectation theory ......... ( 1 + S2 )2 * ( 1 + 1f2 ) = (1 + S3)3

That means holding period yield shall be same whether we invest for 2 + 1 years or 3 years directly.

Here S2 = Spot rate for two years Investment = 0.0212 ( given) and

S3 is the spot rate of 3 years investment. = 0.0234 ( also given)

( 1.0212 )2 * ( 1 + 1f2 ) = (1.0234)3

( 1 + 1f2 ) = (1.0234)3 / ( 1.0212 )2 = 1.0278

1 + 1f2 = 1.0278

1f2 = 1.0278 - 1 = 0.0278 ........... or 2.78 % ........... is the final answer.

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