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

A risk manager argues that the term structure's downward slope at very long maturities in a constant-volatility, zero-risk-premium model is a feature of the model, not necessarily an arbitrage. Which statement best supports this?

A declining long end is consistent with no arbitrage because convexity reduces long-maturity rates. With flat expected short rates and no risk premium, the growing convexity effect pushes forward and spot rates lower as maturity lengthens, so the downward slope reflects the model rather than a pricing inconsistency.

  1. AConvexity pulls long-maturity rates down, so a flat expected short rate can produce a declining long endCorrect
  2. BExpectations always imply an increasing curve, so a decline must signal arbitrage
  3. CConvexity raises long-maturity rates, causing a humped shape
  4. DDownward slopes occur only when risk premiums are negative

Explanation

With flat expected short rates and no risk premium, convexity reduces long-maturity spot and forward rates progressively, so the curve can decline at long maturities without arbitrage. Expectations need not imply an upward slope.

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