How do you price a currency forward using covered interest rate parity?
CFA Level II Derivatives requires pricing currency forwards using interest rate differentials. I know the formula involves domestic and foreign interest rates, but I keep getting confused about which rate goes in the numerator vs. denominator. Can someone break it down step by step?
Currency forward pricing trips up many CFA Level II candidates because of the convention confusion. Let's nail it down.
Covered Interest Rate Parity (CIP)
The forward exchange rate is determined by the spot rate and the interest rate differential between two currencies. The no-arbitrage relationship is:
F = S₀ × [(1 + r_d) / (1 + r_f)]
Where:
- F = Forward exchange rate (domestic per foreign)
- S₀ = Spot exchange rate (domestic per foreign)
- r_d = Domestic interest rate
- r_f = Foreign interest rate
The Key Convention:
Always think in terms of 'domestic per foreign' (DC/FC). If you're a US investor and the quote is USD/EUR = 1.08, that means $1.08 per euro.
Worked Example:
Elmwood Asset Management (US-based) needs to hedge a EUR 10M receivable due in 6 months.
- Spot rate: USD/EUR = 1.0850
- US 6-month rate (annualized): 5.20%
- Eurozone 6-month rate (annualized): 3.80%
Step 1: Convert to semi-annual rates
- r_d = 5.20% / 2 = 2.60%
- r_f = 3.80% / 2 = 1.90%
Step 2: Calculate the forward rate
- F = 1.0850 × (1.0260 / 1.0190)
- F = 1.0850 × 1.00687
- F = USD/EUR 1.0925
The euro trades at a forward premium (F > S₀) because US rates are higher than eurozone rates. The higher-yielding currency (USD) depreciates in the forward market.
Intuition: Why Does the Higher-Rate Currency Depreciate?
If USD rates are higher, a US deposit earns more interest than a euro deposit. To prevent arbitrage, the forward rate must offset this advantage by making the dollar cheaper (weaker) in the future. Otherwise, you could borrow euros cheaply, convert to USD, earn higher interest, and lock in a guaranteed profit.
Hedging Application:
Elmwood sells EUR 10M forward at 1.0925, locking in:
- Guaranteed receipt = EUR 10M × 1.0925 = $10,925,000
Without the hedge, they'd face exchange rate risk — the spot in 6 months could be 1.05 or 1.12.
CFA Exam Trap: If the question uses the convention FC/DC (e.g., EUR/USD), the formula inverts: F = S₀ × [(1 + r_f) / (1 + r_d)]. Always check the quote convention before plugging in numbers.
Practice more currency derivatives in our CFA Level II community.
Master Level II with our CFA Course
107 lessons · 200+ hours· Expert instruction
Related Questions
What exactly is the Capital Market Expectations (CME) framework and why does it matter for asset allocation?
How do business cycle phases affect asset class return expectations?
Can someone explain the Grinold–Kroner model step by step with numbers?
How do you forecast fixed-income returns using the building-blocks approach?
PPP vs Interest Rate Parity for forecasting exchange rates — when do I use which?
Join the Discussion
Ask questions and get expert answers.