CFA Level IDerivativesMedium
An investor enters a 3x9 forward rate agreement (FRA) as the long party with a notional amount of $20 million and an FRA rate of 3.0%. At expiration (3 months from initiation), 6-month LIBOR is observed at 3.5%. Using a 180-day underlying period, what is the approximate payoff to the long party at settlement?
- A$100,000
- B$50,000
- C$25,000
- D$49,140
Show answer & explanationAnswer & explanation
Correct answer: D. $49,140
The undiscounted difference is (0.035 - 0.03) × (180/360) × $20,000,000 = $50,000. Since FRA payoffs are settled at the start of the underlying period, this amount must be discounted: $50,000 / [1 + 0.035×(180/360)] = $50,000 / 1.0175 ≈ $49,140.
Why the other options are wrong
- A. This double-counts the rate differential and is not consistent with the FRA formula.
- B. This is the undiscounted payoff and omits the required present value adjustment.
- C. This understates the payoff by using an incorrect day-count or rate calculation.
FRA Payoff Discounting
An FRA settles at the beginning of the underlying loan period, so the interest rate differential payoff must be discounted back using the observed reference rate.
- Payoff (undiscounted) = (L - FRA rate) × (days/360) × Notional
- Discount factor = 1 + L × (days/360)
- Long FRA gains when reference rate rises above FRA rate
Memory trick: FRAs pay early, so discount the difference back to settlement day.