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FRM Part II · FRM Exam Part II · Expectations, Risk Premium, Convexity and the Shape of the Term Structure

A risk analyst observes a one-year spot rate of 3.00% and a two-year spot rate of 4.00%, both annually compounded. Under the pure expectations hypothesis (ignoring risk premium and convexity), what is the market's implied expectation of the one-year rate one year from now?

The implied one-year rate one year ahead is about 5.01%. It comes from dividing the two-year growth factor of 1.0816 by the one-year factor of 1.03. Simple averaging gives 3.50% but is wrong because spot rates compound from successive forward rates.

  1. A3.50%
  2. B5.01%Correct
  3. C4.00%
  4. D5.00%

Explanation

The forward rate satisfies (1.04)^2 = (1.03)(1+f). So 1+f = 1.0816/1.03 = 1.05010, giving f = 5.01%. The 3.50% option is the simple average of the two spot rates, which ignores compounding and the way spot rates are built from forwards.

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