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

An analyst observes that the 1-year spot rate is 2.00% and the 2-year spot rate is 2.60% (annual compounding). She believes the expected 1-year rate in one year is 3.00%. Which conclusion is best supported?

The implied one-year forward rate is about 3.20%, found from 1.026 squared divided by 1.02, minus one. Compared with the analyst's expected rate of 3.00%, about 20 bp is a premium net of convexity, so the expectations hypothesis does not hold exactly.

  1. AThe implied forward rate is about 3.20%, exceeding the expected 3.00% by about 20 bp, which is a one-year-ahead premium (net of convexity)Correct
  2. BThe implied forward rate is 3.30%, so the premium is 30 bp
  3. CThe implied forward rate is 2.30%, so the premium is negative
  4. DThe implied forward rate is 3.00%, so the expectations hypothesis holds exactly

Explanation

Forward = (1.026^2)/1.02 - 1 = 1.052676/1.02 - 1 = 3.2036%, about 3.20%. Comparing with the expected 3.00% leaves roughly 20 bp as premium net of convexity. A simple difference (2×2.6−2=3.2) gives a similar result, but 3.30% and 2.30% arise from errors.

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