Futures contracts mature at the month’s end. Basis can be assumed to diminish to zero at contract maturity at a constant rate, based on monthly time intervals.
The number of contracts to be used should be rounded to the nearest whole number. If the amount cannot be hedged using an exact number of futures contracts the balance should be considered immaterial.
SOLUTION
Forward market hedging
$20m/1.2274 = €16,294,606
This method has the advantage of being tailored to the exact timing and amount of Norris Co's exposure. However there is counterparty risk and, once entered into, the contract is not flexible or liquid.
Futures
As the transaction occurs in November, sell December euro futures now to hedge against a weakening of the € relative to the dollar. Note – always follow the flow of the currency to set up the hedge. We need to buy $ and sell € to pay the invoice. The futures contract is on the €, so the hedge needs us to sell contracts. December contracts are used as the June and September contracts will have expired before the actual transaction date.
To work out the number of contracts for this transaction, the transaction value has to be divided by the size of the contract. Since the transaction is in $ it needs to be translated into the contract currency using the current futures price of 1.2300.
Number of contracts = ($20m/1.2300)/€125,000 = 130.1
Therefore round to 130 contracts
Lock-in rate method
The basis within a futures hedge is calculated as follows:
Basis = spot price – futures price
Therefore, on 1 May: basis = 1.2100 – 1.2300 = -0.0200
The basis on the expiry date of the futures contract is always zero. Since Norris Co is selling December contracts and futures contracts expire at the month’s end, the expiry date in this example is 31 December.
Assuming that basis reduces to zero at contract maturity in a linear fashion, unexpired basis on the transaction date (ie 30 November) can be calculated as follows:
Unexpired basis = ([1.2100 – 1.2300] × 1/8) = – 0.0025
'Lock in rate' = opening futures price + unexpired basis
'Lock in rate' = 1.2300 + -0.0025 = 1.2275
Expected € net cost = $20m/1.2275 = €16,293,279
This calculation is an approximation to the full hedging transaction as shown below. It ignores the rounding of contracts and basis risk, both of which will lead to the actual outcome being slightly different to the calculated outcome. However, the benefit is that it gives an idea of the likely outcome and does not need actual or assumed spot rates in November to complete the calculation.
Future spot rate method
It is possible to calculate the futures outcome by making an assumption about the spot price in 7 months’ time ie on 30 November, and then working through the implications for the spot market and futures market transactions. For example, if the spot price on 30 November is assumed to be 1.2265, the following calculations would apply:
Expected futures price (to close out by buying futures) using assumed spot price of 1.2265 is 1.2265 – -0.0025 = 1.2290$/€1
Note - since the spot price on 1 May (ie 1.2100) is lower than the opening futures price (ie 1.2300), the unexpired basis is subtracted from the assumed spot price on 30 November when calculating the expected futures price.
Because the opening trade was to sell futures, we have a gain because the futures price has dropped.
Gain on futures market = (1.2300 – 1.2290)$/€1 x 130 x €125,000 = $16,250
Convert gain into euros at assumed spot price of 1.2265 = $16,250 / 1.2265 = €13,249
Convert $20m payment on spot market at assumed spot price of 1.2265 = $20m / 1.2265 = €16,306,563
Therefore futures outcome = €16,306,563 – €13,249 = €16,293,314
This is effectively the same outcome as from using the lock-in rate method previously. Any assumed spot rate could be used to get to a similar futures outcome.
In either method, the futures outcome is marginally cheaper than the forward market outcome, so futures would be the recommended method of hedging for Norris Co on a financial basis. Additionally, the futures contracts have the benefit of flexibility (can close out hedge any time up to end of the contract’s life) and there is no counterparty risk through using the exchange. The transaction has not been hedged exactly, because the number of contracts was rounded down to 130, meaning that the hedge efficiency would be less than 100%.
EXAMPLE 2
This example will use the original exchange rate data as the previous example, but looks at how a Mengian customer would hedge a payment of €15m to Norris Co on the same date.
SOLUTION
Forward market hedging
€15m x 1.2308 = $18,462,000
Futures
Again, December contracts will be used but the Mengian company needs to buy € and sell $. The futures contract is on the €, so the hedge needs the company to buy contracts. The number of contracts will be
Number of contracts =€15,000,000/€125,000 = 120
Therefore buy 120 contracts
Lock-in rate method
The basis within a futures hedge is calculated as follows:
Basis = spot price – futures price
Therefore, on 1 May: basis = 1.2116 – 1.2300 = –0.0184
The basis on the expiry date of the futures contract is always zero. Since the Mengian company is buying December contracts and futures contracts expire at the month’s end, the expiry date in this example is 31 December.
Assuming that basis reduces to zero at contract maturity in a linear fashion, unexpired basis on the tranasaction date (ie 30 November) can be calculated as follows:
Unexpired basis = ([1.2116– 1.2300] × 1/8) = –0.0023
'Lock in rate' = opening futures price + unexpired basis
Therefore, the 'lock in rate' = 1.2300 - 0.0023 = 1.2277
Expected $ net cost = €15m x 1.2277$/€1 = $18,415,500
Future spot rate method
If the spot price on 30 November is assumed to be 1.2310, the following calculations would apply:
Expected futures price (to close out by selling futures) using assumed spot price of 1.2310 = 1.2310 – -0.0023 = 1.2333
Because the opening trade was to buy futures, we have a gain because the futures price has risen.
Gain on futures market = (1.2333 – 1.2300) x 120 x €125,000 = $49,500
Convert €15m payment on spot market at assumed spot price of 1.2310 = €15m x 1.2310 = $18,465,000
Therefore futures outcome = $18,465,000 - $49,500 = $18,415,500
Once again, the futures outcome is cheaper than the forward market outcome so, on a financial basis, futures would be the recommended method of hedging for the Mengian customer with the same non-financial benefits as before. In this example, the outcome from using the lock-in rate method and the future spot rate method are the same, because this transaction uses an exact number of contracts to match the transaction amount, meaning the hedge efficiency is 100% in this example.
If a different assumption is made about the spot price on 30 November, the outcome will be exactly the same. For example, assume the spot price on 30 November is 1.2200 instead of 1.2310 as follows:
Because the opening trade was to buy futures, we have a loss because the futures price has fallen.
Expected futures price (to sell futures) using assumed spot price of 1.2200 = 1.2200 – -0.0023 = 1.2223
Loss on futures market = (1.2223 – 1.2300) x 120 x €125,000 = $115,500
Convert €15m payment on spot market at assumed spot price of 1.2200 = €15m x 1.2200 = $18,300,000
Therefore futures outcome = $18,300,000 + $115,500 = $18,415,500
This is exactly the same outcome as before. It does not matter if the assumed spot price on 30 November is not provided in an exam question because any assumption about the spot price on 30 November will result in the same outcome. In this case, although the spot price is more favourable to the Mengian customer, resulting in a lower payment in dollars, any advantage is cancelled out by the loss on the futures market.
Conclusion
This article has looked at different approaches which can be taken in the AFM exam for foreign currency futures hedging transactions. As long as there is no basis risk, either method is eligible for full credit, so the examining team recommends that you use the method which will best suit you under exam conditions. This will enable you to maximise your marks on a question which looks at foreign currency futures hedging transactions. If you are given an expected spot rate or closing futures rate in the exam it may be easier to use the information provided to close out the hedge than to use the lock-in rate.
Written by a member of the AFM examining team
