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

Under the pure expectations hypothesis, if the spot rate curve is upward sloping, which conclusion follows?

Investors expect short-term rates to rise. Under the pure expectations hypothesis, forward rates equal expected future short rates, and on an upward-sloping spot curve forwards lie above spot rates. The slope therefore reflects only rate expectations, not risk premiums or convexity.

  1. AInvestors expect short-term rates to riseCorrect
  2. BInvestors require a negative risk premium on long bonds
  3. CForward rates must lie below spot rates
  4. DConvexity makes the long end lower than expected rates

Explanation

With no risk premium, an upward-sloping spot curve means forward rates exceed spot rates, and forwards equal expected future short rates. So expected short rates rise. Forwards lie above spot rates on a rising curve, ruling out the third option.

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