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

An investor holds a long position in an FRA with 30 days to expiration. The FRA is on the 90-day rate, has a notional principal of 20,000,000 and a contract rate of 2.50%. Current market rates (360-day year, simple interest) are 2.80% for 30 days and 3.00% for 120 days. The current value of the FRA to the long position is closest to:

The long FRA is worth about 27,700. The implied forward rate is about 3.06%, which exceeds the 2.50% contract rate, giving a payoff of roughly 27,980 at day 120. Discounting it over 120 days at 3.00% gives about 27,703 today.

  1. A27,700Correct
  2. B27,920
  3. C27,980

Explanation

Current forward rate = [(1 + 0.03×120/360)/(1 + 0.028×30/360) − 1] × 4 = (1.01/1.0023333 − 1) × 4 ≈ 3.06%. Payoff at day 120 = (0.030596 − 0.025) × 0.25 × 20,000,000 ≈ 27,980. Discount for the full 120 days at 3.00%: 27,980/1.01 ≈ 27,703. The 27,980 choice is undiscounted; 27,920 discounts only for 30 days at 2.80%.

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