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FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage

The zero curve is upward sloping at all maturities. For a given maturity such as 5 years, which ordering of the forward rate for the final year, the 5-year zero (spot) rate and the 5-year coupon par yield is correct?

The final-year forward rate is highest, then the spot rate, then the par yield. On an upward-sloping curve, forwards lie above spot rates. The par yield blends the lower, shorter-maturity spot rates because coupons arrive earlier, so it sits below the spot rate.

  1. AFinal-year forward rate > spot rate > par yieldCorrect
  2. BSpot rate > final-year forward rate > par yield
  3. CPar yield > spot rate > final-year forward rate
  4. DFinal-year forward rate > par yield > spot rate

Explanation

On an upward-sloping curve, each forward rate exceeds the spot rate of the same maturity, because the longer-dated spot rate is an average of earlier, lower forwards. The par yield is a weighted average of spot rates up to that maturity, so it falls below the final spot rate. The ordering is therefore forward > spot > par.

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