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CFA Level I · CFA Level I Exam · Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities

The 90-day Libor is 4.0% and the 180-day Libor is 4.4%, both quoted on a 360-day year with simple interest. The no-arbitrage fixed rate on a 3x6 FRA (a 90-day rate starting in 90 days) is closest to:

The 3x6 FRA rate is about 4.75%. It is found by dividing the growth factor of the 180-day rate, 1.022, by the growth factor of the 90-day rate, 1.010, subtracting one, and annualizing by multiplying by four. Simple extrapolation to 4.80% ignores the correct compounding.

  1. A4.40%
  2. B4.75%Correct
  3. C4.80%

Explanation

FRA rate = [(1 + 0.044×180/360) / (1 + 0.040×90/360) − 1] × 360/90 = (1.022/1.010 − 1) × 4 = 0.011881 × 4 = 4.75%. The 4.80% choice comes from simple linear extrapolation (2×4.4% − 4.0%), which ignores compounding of the first-period rate.

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