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FRM Part I · FRM Exam Part I · Interest Rates

Under the pure expectations theory of the term structure, the current one-year spot rate is 3.0% and the two-year spot rate is 3.5% (annual compounding). What is the market-implied one-year rate one year from now?

The implied one-year forward rate is about 4.00%, found by dividing (1.035)^2 by 1.03 and subtracting one. Under pure expectations, this forward equals the expected future one-year spot rate, so the upward-sloping curve signals expected rate increases.

  1. A3.00%
  2. B3.50%
  3. C4.00%
  4. D4.01%Correct

Explanation

Forward rate f satisfies (1.035)^2 = 1.03 x (1+f). 1.035^2 = 1.071225; dividing by 1.03 gives 1.040024, so f is about 4.00%. More precisely 1.071225/1.03 = 1.04002, which is 4.00%, so the closest exact option is 4.00%. Check: 1.03 x 1.04002 = 1.07122.

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