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FRM Part I · FRM Exam Part I · Properties of Interest Rates

Under a normal upward-sloping zero curve with continuous compounding, how does the forward rate for a period beginning at T1 and ending at T2 compare with the zero rates?

With an upward-sloping zero curve, the forward rate lies above the longer-maturity zero rate. The formula adds a positive amount, (R2-R1) times T1 divided by (T2-T1), to R2. So the forward rate is higher than both zero rates, not in between.

  1. AIt lies above the T2 zero rateCorrect
  2. BIt lies below the T1 zero rate
  3. CIt equals the T2 zero rate
  4. DIt lies between the T1 and T2 zero rates

Explanation

The forward rate equals R2 + (R2-R1)T1/(T2-T1). When the curve slopes upward (R2 > R1), the added term is positive, so the forward rate exceeds R2. It therefore does not lie between the two zero rates, and it cannot be below R1 or equal to R2.

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