FRM Part II · FRM Exam Part II · Expectations, Risk Premium, Convexity and the Shape of the Term Structure
A trader notes that the 1-year spot rate is 2.00% and the 1y1y forward rate is 3.00% (annually compounded). Historical analysis shows the one-year rate one year ahead has on average been 2.60%. Which interpretation is most consistent with a positive risk premium?
A forward rate of 3.00% above an expected future spot rate of 2.60% indicates a positive risk premium of about 0.40%. Investors holding longer bonds were compensated for term risk, so the pure expectations hypothesis does not hold exactly.
- AThe forward rate exceeds the average realized future spot rate, so investors demanded compensation for bearing term riskCorrect
- BThe forward rate is below the realized rate, so the expectations hypothesis holds exactly
- CThe forward rate equals the spot rate, so no premium exists
- DThe realized rate exceeding the forward rate shows a convexity effect
Explanation
Forward 3.00% minus expected future spot 2.60% gives a 0.40% premium embedded in the forward. This means forward rates overstate expected rates, consistent with a positive term premium. The expectations hypothesis would require equality.
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