Estimated study time: 45 minutes
Content:
Currency derivatives — forwards, futures, options, and swaps — are used to manage foreign exchange risk in international portfolios. The choice among instruments depends on the investor's need for customization, desire for optionality (asymmetric payoffs), cost constraints, and counterparty risk tolerance.
Currency forwards are the dominant hedging instrument for institutional investors. A forward contract locks in an exchange rate for a future date. The forward rate is determined by covered interest rate parity (CIP): F = S × (1 + r_domestic) / (1 + r_foreign), where S is the spot rate, r_domestic is the domestic risk-free rate, and r_foreign is the foreign risk-free rate. If the foreign rate is higher, the foreign currency is at a forward discount — its forward price in domestic terms is below the spot rate. Hedging in this case "costs" the interest rate differential (the investor forgoes the higher foreign rate).
Currency futures are exchange-traded, standardized contracts. They offer superior liquidity and lower counterparty risk (centrally cleared) compared to forwards, but less customization. Currency options give the holder the right to exchange currencies at a specified rate — the strike price — paying a premium. Call options give the right to buy the foreign currency; put options give the right to sell the foreign currency. Options are used when the investor wants downside protection without giving up upside — for example, buying USD call/foreign currency put options to protect against foreign currency depreciation while retaining the ability to benefit if the foreign currency appreciates.
Dynamic currency option strategies: A risk reversal buys an out-of-the-money put and sells an out-of-the-money call on the foreign currency, creating a collar at potentially zero cost (if the two premiums are equal). This caps downside from currency depreciation while capping upside from currency appreciation. A seagull strategy extends the collar by selling a deeper out-of-the-money put to finance the hedge — this reduces premium cost but introduces downside risk below the short put strike.
Non-deliverable forwards (NDFs) are used for currencies with capital controls or limited convertibility — common in emerging markets. NDFs are settled in a major currency (USD) based on the difference between the contracted forward rate and the prevailing spot rate at expiration. No physical delivery of the restricted currency occurs. NDFs carry counterparty risk (OTC instrument) and basis risk (the NDF rate may diverge from the onshore spot rate if capital controls tighten).
Hedging cross-currency exposures: When direct hedging of a currency pair is unavailable or expensive, managers use proxy hedges — a currency whose movements are highly correlated with the target currency. The efficiency of a proxy hedge depends on the correlation and the hedge ratio. A proxy hedge using currency A to hedge currency B exposure: the hedge ratio = (correlation A,B × σ_B) / σ_A, analogous to a minimum variance hedge ratio. Proxy hedges carry the risk that the correlation breaks down, particularly in market stress periods.
Key Terms:
Quiz Questions:
Q1. A US investor holds EUR-denominated assets. The spot EUR/USD rate is 1.10 (1 EUR = 1.10 USD). The 1-year US interest rate is 4% and the 1-year EUR interest rate is 2%. The approximate 1-year EUR/USD forward rate is:
A) 1.10 B) 1.122 C) 1.078 D) 1.10 × (1.02/1.04) ≈ 1.079
Answer: D — F = S × (1 + r_USD) / (1 + r_EUR) — wait, using CIP from the perspective of quoting EUR/USD (domestic = USD, foreign = EUR): F = S × (1 + r_domestic) / (1 + r_foreign) = 1.10 × (1.04/1.02) ≈ 1.10 × 1.0196 ≈ 1.122. Actually since USD rate > EUR rate, USD is at a discount, EUR at a premium. The EUR should be worth MORE in USD forward. Let's check: F = 1.10 × (1.04/1.02) ≈ 1.1216. However if the question frames it as the cost to a USD investor hedging EUR: they sell EUR forward. If EUR rates are lower than USD rates, EUR is at a forward premium (costs more to sell EUR forward). Answer: approximately 1.122 (B).
Answer: B — CIP: Forward EUR/USD = 1.10 × (1 + 4%) / (1 + 2%) = 1.10 × 1.0196 ≈ 1.122. Since US rates exceed EUR rates, the EUR is at a forward premium — the forward rate is higher than spot in USD terms.
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Q2. A US investor hedging a EUR portfolio by selling EUR forward is paying the hedging cost equal to:
A) The difference between the spot rate and the forward rate — which equals approximately the interest rate differential B) The full EUR interest rate as a penalty C) Zero, because forwards are zero-cost instruments D) The bid-ask spread on the forward contract only
Answer: A — The cost of hedging = spot − forward (or forward − spot, depending on the direction) ≈ interest rate differential. If EUR rates are 2% and USD rates are 4%, hedging EUR costs approximately 4% − 2% = 2% per year (the investor gives up the 4% USD rate they could have earned by not hedging and holding dollars, while only earning the 2% EUR rate).
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Q3. A portfolio manager buys a EUR put option (right to sell EUR at strike $1.10/EUR) and simultaneously sells a EUR call option (right to buy EUR at strike $1.20/EUR) with equal premiums. This strategy is a:
A) Covered call on EUR B) Risk reversal / zero-cost collar — providing downside protection below $1.10 while capping upside above $1.20 C) Straddle — profiting from large moves in either direction D) Non-deliverable forward
Answer: B — Long put (floor at $1.10) + short call (cap at $1.20) with equal premiums = zero-cost collar (risk reversal). The investor is protected if EUR falls below $1.10 but forgoes gains if EUR rises above $1.20. This is the standard "risk reversal" structure used in FX options.
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Q4. A manager wants to hedge currency exposure to the Brazilian real (BRL), which has no liquid forward market. She observes that BRL movements are highly correlated (ρ = 0.85) with the Mexican peso (MXN), which has liquid futures. The minimum variance hedge ratio for the proxy hedge is:
A) 0.85 B) σ_BRL / σ_MXN × 0.85 C) σ_MXN / σ_BRL × 0.85 D) Cannot be determined without knowing the actual standard deviations
Answer: B — The minimum variance hedge ratio for a proxy hedge = ρ × (σ_S / σ_F), where σ_S is the volatility of the asset being hedged (BRL) and σ_F is the volatility of the hedging instrument (MXN). Without actual standard deviation values, the formula cannot be fully computed — but the structure of the answer is ρ × (σ_BRL / σ_MXN) × 0.85 simplifies to option B when the ratio is included.
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Q5. A non-deliverable forward (NDF) on the Chinese renminbi (CNY) settles in USD. At settlement, the contracted forward rate was 7.00 CNY/USD, and the prevailing spot rate is 7.20 CNY/USD. The USD has strengthened relative to the forward rate. An investor who sold CNY forward (hedging CNY assets by agreeing to receive USD at 7.00) will:
A) Receive a gain because CNY depreciated (fewer CNY per USD at the contracted rate) B) Pay a loss because CNY appreciated C) Receive a gain because the spot is now 7.20, meaning CNY is weaker than expected, and the hedger's short CNY position benefits D) Receive no payment because NDF contracts are rolled rather than settled
Answer: C — The hedger sold CNY forward (short CNY, long USD) at 7.00 CNY/USD. At settlement, CNY is weaker at 7.20 CNY/USD. The short CNY position benefits from CNY depreciation. Settlement payment = notional × (spot − forward) / spot = cash gain to the short CNY party. CNY depreciated as expected, so the hedge worked.
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