Why Use a Forward Hedge?
A business that knows it will buy an asset in the future may be exposed to a rising market price. A business that knows it will sell an asset may be exposed to a falling price. A forward contract can reduce that price uncertainty by fixing a delivery price today for an exchange at a specified future date.
The key is to take the forward position that offsets the planned transaction. A future buyer takes a long forward; a future seller takes a short forward. When the asset, quantity, and delivery date match, the spot-market price at maturity affects the spot transaction and the forward settlement in opposite directions.
For a newly entered, standard forward, \(K\) is commonly set equal to the forward price for delivery at \(T\), denoted \(F_0(T)\). Once the contract has been entered, its delivery price \(K\) is fixed. The hedge calculations below assume the forward is entered with no initial payment, the contract settles at the same date as the planned transaction, and its quantity and asset match that transaction. There are no transaction costs, default, or delivery-quality differences.
Combining the Forward with the Planned Transaction
For a cash-settled hedge, the hedger separately transacts in the asset at its maturity spot price and receives or pays the forward payoff. A physical-delivery forward instead exchanges the asset for the contract price. These are alternative settlement descriptions: do not count a physical delivery and a separate spot purchase or sale as two transactions.
The buyer’s spot outlay is reduced by a positive long-forward payoff, or increased by a negative one. The seller’s spot revenue is increased by a positive short-forward payoff, or reduced by a negative one. In either case, the final result is independent of \(S_T\), as long as the matching assumptions hold.
Why the Hedge Locks in the Delivery Price
The result follows directly from the definition of the forward payoff. At maturity, a buyer paying \(S_T\) per unit in the spot market has cost \(S_T\). The buyer’s long forward pays \(S_T-K\) per unit. Since a payoff received offsets cost, the combined cost per unit is \(S_T-(S_T-K)=K\). For a seller, spot revenue is \(S_T\), and the short forward adds \(K-S_T\). Combined proceeds per unit are \(S_T+(K-S_T)=K\).
Multiplying by the matched quantity \(Q\) gives the total amount \(QK\). The forward does not make the spot price stay still; it creates an offsetting cash flow. This is why the calculation uses the maturity spot price and forward payoff together, rather than treating either one as the hedged result by itself.
Worked Example: Hedging a Planned Purchase
A packaging company expects to buy 750 units of a resin at the end of six months. It enters a long forward for 750 units at \(K=\$64.20\) per unit. At maturity, the spot price is \(S_T=\$71.80\) per unit. Find the forward payoff, the spot-market cost, and the effective cost of the purchase.
Method and assumptions. Treat the asset, quantity, and maturity as exactly matched. The contract is cash-settled, so the company buys the resin at the spot price and combines that outlay with the long-forward payoff.
Step 1: Calculate the long-forward payoff. The payoff per unit is \(S_T-K=\$71.80-\$64.20=\$7.60\). For 750 units, the company receives \(750(\$7.60)=\$5,700.00\).
Step 2: Calculate the spot purchase cost. The spot outlay is \(750(\$71.80)=\$53,850.00\).
Step 3: Net the payoff against the purchase cost. The company receives the positive forward payoff, so its net cost is \(\$53,850.00-\$5,700.00=\$48,150.00\). Directly, \(750(\$64.20)=\$48,150.00\), which checks the result.
If the contract instead required physical delivery, the company would receive 750 units and pay \(750(\$64.20)=\$48,150.00\) under the contract. It would not also count a separate spot purchase. The common mistake is to add the positive long payoff to the spot cost; that reverses the effect of a payoff received.
Worked Example: Hedging a Planned Sale
A grower expects to sell 3,200 kilograms of a crop in three months. The grower takes a short forward for 3,200 kilograms at \(K=\$24.50\) per kilogram. At maturity, the spot price is \(S_T=\$21.80\) per kilogram. Calculate the short-forward settlement, total sale proceeds after hedging, and the proceeds per kilogram.
Method and assumptions. The grower sells all 3,200 kilograms in the spot market and combines that revenue with the cash settlement on the matching short forward. Ignore transaction costs.
Step 1: Calculate the short-forward payoff. Per kilogram, \(K-S_T=\$24.50-\$21.80=\$2.70\). The grower receives \(3,200(\$2.70)=\$8,640.00\) on the forward.
Step 2: Calculate spot-sale revenue. The spot sale produces \(3,200(\$21.80)=\$69,760.00\).
Step 3: Combine the cash flows. Total proceeds are \(\$69,760.00+\$8,640.00=\$78,400.00\). Per kilogram, \(\$78,400.00/3,200=\$24.50\). The check is \(3,200K=3,200(\$24.50)=\$78,400.00\).
Because the short-forward payoff is positive when the spot price falls below \(K\), it offsets the lower spot revenue. The grower should not subtract this positive payoff from the sale proceeds.
Check the Quotation Units
A matched hedge requires more than choosing the correct direction. The contract’s price quotation and quantity must use consistent units. If a price is quoted per 100 units, convert the total exposure into 100-unit blocks before multiplying by the per-block payoff. A contract on a different quantity or asset does not automatically lock in the price of the full planned transaction.
Worked Example: A Price Quoted per 100 Liters
A manufacturer plans to buy 18,000 liters of a liquid at the end of the quarter. It enters a long forward that quotes the delivery price per 100 liters, with \(K=\$129\) per 100 liters. At maturity, the spot price is \(S_T=\$144\) per 100 liters. Find the number of quotation units, the forward payoff, the spot cost, and the hedged cost.
Method and assumptions. The exposure is 18,000 liters and the forward covers the same amount. Use 100-liter blocks so the quantity and both prices share the contract’s quotation unit.
Step 1: Convert the exposure. The number of 100-liter blocks is \(18,000/100=180\).
Step 2: Calculate the long-forward payoff. The payoff per block is \(\$144-\$129=\$15\). Across 180 blocks, the manufacturer receives \(180(\$15)=\$2,700.00\).
Step 3: Calculate the spot purchase cost. The spot outlay is \(180(\$144)=\$25,920.00\).
Step 4: Calculate the hedged cost and check it. Net cost is \(\$25,920.00-\$2,700.00=\$23,220.00\). Directly, \(180(\$129)=\$23,220.00\). The manufacturer has locked in an effective price of \(\$129\) per 100 liters, or \(\$1.29\) per liter.
Using 18,000 as the multiplier with prices quoted per 100 liters would overstate the cash flows by a factor of 100. Converting the quantity before calculating avoids this unit error.
Common Sign and Interpretation Traps
The payoff belongs to the forward position, not to the physical transaction. Keep the position’s payoff sign separate from the direction of the asset purchase or sale, and then combine the cash flows according to whether the forward amount is received or paid.
- Wrong sign for a buyer. In the first example, a common incorrect calculation is \(\$53,850+\$5,700=\$59,550\). The forward payoff is received, so the correct net cost is \(\$53,850-\$5,700=\$48,150\).
- Wrong sign for a seller. In the second example, the positive short-forward payoff is added to spot-sale revenue. It is not a cost to subtract.
- Confusing proceeds with profit. Hedged sale proceeds equal \(QK\); profit also depends on the seller’s production or acquisition costs. The forward calculation alone does not determine profit.
- Assuming every exposure is fully hedged. The fixed result \(QK\) depends on a match in asset, quantity, and date. Differences between the actual transaction and contract can leave price exposure.
Check Your Understanding
For each question, identify the appropriate forward position and combine its maturity payoff with the planned transaction.
- A laboratory will buy 500 filters at maturity. It has a long forward at \(K=\$37.20\) per filter, and the maturity spot price is \(\$40.10\). What is the forward payoff and the effective total purchase cost? (Answer: Long-forward payoff received = $1,450.00; effective cost = $18,600.00.)
- A seller will deliver 1,250 units and has a short forward at \(K=\$8.60\) per unit. The maturity spot price is \(\$9.10\). What are the forward settlement and total sale proceeds after hedging? (Answer: Short-forward payment = $625.00; total proceeds = $10,750.00.)
- A buyer needs 7,200 kilograms of material. The forward price is \(\$46\) per 100 kilograms, and the maturity spot price is \(\$42.50\) per 100 kilograms. What is the buyer’s long-forward settlement and effective purchase cost? (Answer: Long-forward payment = $252.00; effective cost = $3,312.00.)
- A producer will sell 2,400 units and has a short forward at \(\$13.75\) per unit. At maturity the spot price is \(\$11.25\). Find the spot revenue, forward payoff, and total hedged proceeds. (Answer: Spot revenue = $27,000.00; short-forward payoff received = $6,000.00; total proceeds = $33,000.00.)
- A buyer plans to purchase 1,500 units and enters a long forward at \(\$5.84\) per unit. At maturity, the spot price is \(\$6.02\). Calculate the spot outlay, long-forward payoff, and effective cost. (Answer: Spot outlay = $9,030.00; long-forward payoff received = $270.00; effective cost = $8,760.00.)