Level III Core · Currency Management: An Introduction

Hedging Currency Risk with Forwards and Options

Q: Why does selling a foreign currency forward sometimes earn a positive carry?

It happens when the foreign interest rate is lower than the home rate. Covered interest rate parity then puts the foreign currency at a forward premium. You sell it forward above spot and earn the difference.

Q: What is the main risk of a rolling forward hedge?

It is cash-flow risk. If the foreign currency rises, the short forward loses and must be settled in cash at each roll. The offsetting gain on the asset is unrealised. The investor needs liquidity to cover this.

Q: When is an option better than a forward for currency hedging?

An option suits a client who wants protection from a fall but wants to keep gains from a rise. The cost is the premium. A forward is cheaper and fixes the rate but gives up the upside.

Q: How do collars and put spreads reduce hedging cost?

A put spread sells a lower-strike put to fund part of the premium, so protection stops below that strike. A collar sells a call to fund the put, so upside is capped. Both cut cost by giving something up.

Updated 8 October 2026 · Fact-checked

A currency hedge fixes or limits the home-currency value of foreign assets. A forward locks the rate and removes both gain and loss. A put option sets a floor and keeps the upside, for a premium. Hedging cost comes from the interest rate gap, and rolling forwards create cash-flow risk.

Understand Hedging Tools: Forwards, Options and Cost of Hedging

Start with the problem. You hold a foreign asset. Its home-currency return depends on the asset return and the currency return. If the foreign currency falls, you lose in home terms even when the asset rises in local terms.

A forward contract fixes an exchange rate for a future date. If you own foreign assets, you sell the foreign currency forward. The hedge removes currency risk on the amount hedged. It also removes any gain if the foreign currency rises. Forwards are over-the-counter, so you also carry some counterparty credit risk.

Forward points are not a forecast. They come from covered interest rate parity. The forward price of the foreign currency is higher than spot if the foreign interest rate is lower than the home rate. It is lower than spot if the foreign rate is higher. So when you sell the foreign currency forward, you earn the forward premium if foreign rates are lower than home rates. You pay a discount if foreign rates are higher. This is the cost (or carry) of hedging. State it plainly: hedging earns a positive carry when the home rate is above the foreign rate (i_home > i_foreign), and it costs carry when the home rate is below the foreign rate (i_home < i_foreign). To a first approximation, the hedged foreign return is the foreign asset return plus the home rate minus the foreign rate, ignoring the currency move.

The forward hedge is usually rolled. A short-dated forward expires before the asset is sold. You settle it and enter a new one. This is a rolling hedge. If the foreign currency rises, the forward loses money, and you must pay cash on settlement before you sell the asset. If the foreign currency falls, you receive cash. The loss on the forward is offset by a gain in the home-currency value of the foreign asset, but that gain is unrealised until the asset is sold. This is cash-flow (liquidity) risk. Plan for it with cash reserves or credit lines. A longer forward reduces roll frequency but is less flexible and may be less liquid.

Options give asymmetric protection. A put on the foreign currency (right to sell it at the strike) sets a floor and keeps the upside. You pay a premium up front. Alternatives include a put spread, which lowers premium but caps the protection, a collar, which sells a call to fund the put and gives up some upside, and seagulls or similar structures. Options need no cash-flow settlement for losses, but they cost more and the premium depends on volatility.

Key rules to remember

Covered interest rate parity (forward rate): F = S × (1 + i_price) ÷ (1 + i_base), with S and F quoted as price currency per 1 unit of base currency; The base currency is the foreign currency you are hedging. i_price is the interest rate of the price (home) currency. Use the rate for the forward period, not an annual rate unless the term is one year.
Forward premium or discount: (F − S) ÷ S ≈ i_price − i_base; Quote is price per base. If the foreign currency is the base and its rate is below the home rate, it trades at a forward premium.
Hedged return (approximation): R_hedged ≈ R_foreign asset (local) + (i_home − i_foreign); Valid when the hedge ratio is 100% and the hedge is sized to the asset value. It ignores the small cross term.
Domestic-currency return: R_DC = (1 + R_FC) × (1 + R_FX) − 1; R_FX is the % change in the home-currency value of the foreign currency.
Forward contract value before expiry (long base): V = PV of (F_t − F_0) × notional, discounted at the price-currency rate over the remaining term; Use the current forward for the remaining term. Short position value is the negative.
Put payoff for a foreign-currency holder: Payoff = max(K − S_T, 0) per unit of foreign currency; net = payoff − premium; Floor on the home value of the asset is about K minus the premium, ignoring financing of the premium.

How to solve Hedging Tools: Forwards, Options and Cost of Hedging questions

Use the same sequence for most hedging questions. Tie the answer to the client's goal and constraints.

1Identify the exposure: foreign currency, amount, and time until the cash is needed.
2Fix the quote convention. Mark which currency is the base (foreign) and which is the price (home) currency.
3Decide the direction: if you own foreign assets, sell foreign currency forward or buy a put on it. If you owe foreign currency, buy it forward or buy a call.
4Compute the forward rate or forward points using interest rate parity. State which rate goes in the numerator.
5Work out the hedge cost or carry: premium or discount, or the option premium. Include the result in the return.
6Check the cash-flow and liquidity effects: forward settlement at roll, margin or collateral, and option premium paid up front.
7Compare tools against the client's view: forwards for certainty and low cost, options for upside and downside protection, spreads and collars to cut premium.
8Write the answer with the number, the direction and a one-line reason.

Quickest way: Direction, carry and cash

When to use it: Use it in item sets when you need to pick the right hedge and the sign of its cost fast.

Own foreign: sell forward. Owe foreign: buy forward.
Compare rates: if home rate is above foreign rate, selling foreign forward earns carry. If lower, it costs carry.
Hedged return is roughly local return plus home rate minus foreign rate.
If the foreign currency rises, a short forward loses cash at settlement. If it falls, it gains cash.
Pick options when the client wants upside and can pay a premium. Pick forwards when cost and certainty matter most.

Common mistakes in Hedging Tools: Forwards, Options and Cost of Hedging

Putting the interest rates the wrong way round in the forward formula.
Quote conventions are confused, so students do not know which currency is the base.
Fix: Write the quote as price per base first. The price-currency rate goes on top and the base-currency rate goes on the bottom.
Thinking a forward discount or premium predicts where spot will go.
The forward rate looks like a market forecast.
Fix: Remember it is set by no-arbitrage from interest rates. It is the carry on the hedge, not a prediction.
Ignoring the cash-flow effect of a rolling hedge.
The hedge looks perfect on the economic balance sheet.
Fix: State that a loss on the forward is paid in cash while the offsetting asset gain is unrealised. Mention cash buffers or credit lines.
Saying a protective put gives a fixed rate like a forward.
Both are called hedges.
Fix: A put sets a worst-case rate, net of premium, and keeps upside. A forward sets the rate and gives up upside.
Ignoring the premium when comparing option and forward outcomes.
Students look only at the payoff.
Fix: Net the premium against the payoff before comparing. Include premium financing if the question gives a rate.
Assuming a hedge ratio of 100% is always right.
Textbook examples use full hedges.
Fix: Link the hedge ratio to the client's risk tolerance, costs and views. Partial hedges are valid.

Worked examples

Example 1

A euro-based investor holds US$10,000,000 of US equities and sells US dollars one year forward. Spot is EUR 0.9200 per USD. The one-year euro rate is 3.00% and the one-year USD rate is 5.00%. Calculate the forward rate and state whether hedging earns or costs carry.

Show the solution

Quote is price (EUR) per base (USD). F = S × (1 + i_EUR) ÷ (1 + i_USD).
F = 0.9200 × 1.03 ÷ 1.05.
0.9200 × 1.03 = 0.9476. 0.9476 ÷ 1.05 = 0.90248 (rounded).
F is below spot, so the USD trades at a forward discount.
The investor sells USD forward at a lower rate than spot, so the hedge costs about (0.92 − 0.90248) ÷ 0.92 = 1.90%, close to the 2.00% rate gap, as the approximation suggests.

Answer: Forward rate ≈ EUR 0.9025 per USD. Hedging costs the euro investor about 1.9% a year because USD rates are higher than euro rates.

Example 2

A UK-based manager holds one unit of a foreign currency (or an asset worth one unit of it). Spot is GBP 0.8000 per unit of foreign currency. The manager hedges with a one-year put on the foreign currency, strike GBP 0.8000 per unit, premium GBP 0.0150 per unit. Consider two spot outcomes at expiry: GBP 0.7400 and GBP 0.8400 per unit of foreign currency. Per unit, what is the net value of the put position in each case, and how does the hedged outcome compare with an unhedged position?

Show the solution

At spot 0.7400: put payoff = max(0.8000 − 0.7400, 0) = 0.0600.
Net of premium = 0.0600 − 0.0150 = 0.0450 per unit.
Unhedged value of the unit at 0.7400 is GBP 0.7400. Hedged value = spot + net put = 0.7400 + 0.0450 = 0.7850. The put adds 0.0450 compared with unhedged.
At spot 0.8400: the put expires worthless, payoff 0. Net = −0.0150.
Unhedged value at 0.8400 is GBP 0.8400. Hedged value = 0.8400 − 0.0150 = 0.8250. The hedge costs the 0.0150 premium compared with unhedged.
Floor on value is K − premium = 0.8000 − 0.0150 = 0.7850, matching the first case. Upside is kept less the premium.

Answer: At 0.7400 the put nets GBP 0.0450 per unit. Hedged value is GBP 0.7850 (the floor) against GBP 0.7400 unhedged, so the put adds 0.0450. At 0.8400 the put expires worthless and nets −0.0150. Hedged value is GBP 0.8250 against GBP 0.8400 unhedged, so the hedge costs the 0.0150 premium.

Exam tips

Write the quote convention before any calculation. It prevents most rate-direction errors.
When asked to justify a choice between forward and option, name the client's objective and constraint in the answer: certainty, cost, upside, or liquidity.
For calculation prompts, type the number on its own and state the units or currency. A correct number alone earns full credit.
Answer only the number of points asked for. Extra responses are ignored.
In rolling hedge questions, always mention cash-flow risk and liquidity planning when the currency moves against the forward.

Hedging Tools: Forwards, Options and Cost of Hedging in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Hedging Tools: Forwards, Options and Cost of Hedging: frequently asked questions

Why does selling a foreign currency forward sometimes earn a positive carry?

It happens when the foreign interest rate is lower than the home rate. Covered interest rate parity then puts the foreign currency at a forward premium. You sell it forward above spot and earn the difference.

What is the main risk of a rolling forward hedge?

It is cash-flow risk. If the foreign currency rises, the short forward loses and must be settled in cash at each roll. The offsetting gain on the asset is unrealised. The investor needs liquidity to cover this.

When is an option better than a forward for currency hedging?

An option suits a client who wants protection from a fall but wants to keep gains from a rise. The cost is the premium. A forward is cheaper and fixes the rate but gives up the upside.

How do collars and put spreads reduce hedging cost?

A put spread sells a lower-strike put to fund part of the premium, so protection stops below that strike. A collar sells a call to fund the put, so upside is capped. Both cut cost by giving something up.