The aim of this article is to consider both foreign exchange futures and options using real market data. The basics, which have been well examined in the recent past, will be quickly revisited. The article will then consider areas which, in reality, are of significant importance but which, to date, have not been examined to any great extent.
Imagine it is 10 July. A UK company has a US$6.65m invoice to pay on 26 August. They are concerned that exchange rate fluctuations could increase the £ cost and, hence, seek to effectively fix the £ cost using exchange traded futures. The current spot rate is $1.71110/£1.
Research shows that £/$ futures, where the contract size is denominated in £, are available on the CME Europe exchange at the following prices:
September expiry – 1.71035
December expiry – 1.70865
The contract size is £100,000 and the futures are quoted in US$ per £1.
CME Europe is a London based derivatives exchange. It is a wholly owned subsidiary of CME Group, which is one of the world’s leading and most diverse derivatives marketplace, handling (on average) three billion contracts worth about $1 quadrillion annually!
The company will sell 39 September futures at $1.71035/£1.
Outcome on 26 August:
On 26 August the following was true:
Spot rate – $1.65770/£1
September futures price – $1.65750/£1
$6.65m/1.65770 = £4,011,582
Gain/loss on futures:
As the exchange rate has moved adversely for the UK company a gain should be expected on the futures hedge.
|Sell – on 10 July|
|Buy back – on 26 August|
This gain is in terms of $ per £ hedged. Hence, the total gain is:
0.05285 x 39 contracts x £100,000 = $206,115
Alternatively, the contract specification for the futures states that the tick size is 0.00001$ and that the tick value is $1. Hence, the total gain could be calculated in the following way:
0.05285/0.00001 = 5,285 ticks
5,285 ticks x $1 x 39 contracts = $206,115
This gain is converted at the spot rate to give a £ gain of:
$206,115/1.65770 = £124,338
£4,011,582 – £124,338 = £3,887,244
This total cost is the actual cost less the gain on the futures. It is close to the receipt of £3,886,389 that the company was originally expecting given the spot rate on 10 July when the hedge was set up. ($6.65m/1.71110). This shows how the hedge has protected the company against an adverse exchange rate move.
All of the above is essential basic knowledge. As the exam is set at a particular point in time you are unlikely to be given the futures price and spot rate on the future transaction date. Hence, an effective rate would need to be calculated using basis. Alternatively, the future spot rate can be assumed to equal the forward rate and then an estimate of the futures price on the transaction date can be calculated using basis. The calculations can then be completed as above.
The ability to do this would normally earn four marks in an exam. Equally, another one or two marks could be earned for reasonable advice such as the fact that a futures hedge effectively fixes the amount to be paid and that margins will be payable during the lifetime of the hedge. It is some of these areas that we will now explore further.
When a futures hedge is set up the market is concerned that the party opening a position by buying or selling futures will not be able to cover any losses that may arise. Hence, the market demands that a deposit is placed into a margin account with the broker being used – this deposit is called the ‘initial margin’.
These funds still belong to the party setting up the hedge but are controlled by the broker and can be used if a loss arises. Indeed, the party setting up the hedge will earn interest on the amount held in their account with their broker. The broker in turn keeps a margin account with the exchange so that the exchange is holding sufficient deposits for all the positions held by brokers’ clients.
In the scenario above the CME contract specification for the £/$ futures states that an initial margin of $1,375 per contract is required.
Hence, when setting up the hedge on 10 July the company would have to pay an initial margin of $1,375 x 39 contracts = $53,625 into their margin account. At the current spot rate the £ cost of this would be $53,625/1.71110 = £31,339.
In the scenario given above, the gain was worked out in total on the transaction date. In reality, the gain or loss is calculated on a daily basis and credited or debited to the margin account as appropriate. This process is called ‘marking to market’.
Hence, having set up the hedge on 10 July a gain or loss will be calculated based on the futures settlement price of $1.70925/£1 on 11 July. This can be calculated in the same way as the total gain was calculated:
Sell – on 10 July
Settlement price – 11 July
Gain in ticks – 0.00110/0.00001 = 110
Total gain – 110 ticks x $1 x 39 contracts = $4,290
This gain would be credited to the margin account taking the balance on this account to $53,625 + $4,290 = $57,915.
At the end of the next trading day (Monday 14 July), a similar calculation would be performed:
Settlement price – 11 July
Settlement price – 14 July
Gain in ticks – 0.00120/0.00001 = 120
Total gain – 120 ticks x $1 x 39 contracts = $4,680.
This gain would also be credited to the margin account taking the balance on this account to $57,915 + $4,680 = $62,595.
Similarly, at the end of the next trading day (15 July), the calculation would be performed again:
Settlement price – 14 July
Settlement price – 15 July
Loss in ticks – 0.00545/0.00001 = 545
Total loss – 545 ticks x $1 x 39 contracts = $21,255.
This loss would be debited to the margin account, reducing the balance on this account to $62,595 – $21,255 = $41,340.
This process would continue at the end of each trading day until the company chose to close out their position by buying back 39 September futures.
Having set up the hedge and paid the initial margin into their margin account with their broker, the company may be required to pay in extra amounts to maintain a suitably large deposit to protect the market from losses the company may incur. The balance on the margin account must not fall below what is called the ‘maintenance margin’. In our scenario, the CME contract specification for the £/$ futures states that a maintenance margin of $1,250 per contract is required. Given that the company is using 39 contracts, this means that the balance on the margin account must not fall below 39 x $1,250 = $48,750.
As you can see, this does not present a problem on 11 July or 14 July as gains have been made and the balance on the margin account has risen. However, on 15 July a significant loss is made and the balance on the margin account has been reduced to $41,340, which is below the required minimum level of $48,750.
Hence, the company must pay an extra $7,410 ($48,750 – $41,340) into their margin account in order to maintain the hedge. This would have to be paid for at the spot rate prevailing at the time of payment unless the company has sufficient $ available to fund it. When these extra funds are demanded it is called a ‘margin call’. The necessary payment is called a ‘variation margin’.
If the company fails to make this payment, then the company no longer has sufficient deposit to maintain the hedge and action will be taken to start closing down the hedge. In this scenario, if the company failed to pay the variation margin the balance on the margin account would remain at $41,340, and given the maintenance margin of $1,250 this is only sufficient to support a hedge of $41,340/$1,250 ≈ 33 contracts. As 39 futures contracts were initially sold, six contracts would be automatically bought back so that the markets exposure to the losses the company could make is reduced to just 33 contracts. Equally, the company will now only have a hedge based on 33 contracts and, given the underlying transaction’s need for 39 contracts, will now be underhedged.
Conversely, a company can draw funds from their margin account so long as the balance on the account remains at, or above, the maintenance margin level, which, in this case, is the $48,750 calculated.
Imagine that today is the 30 July. A UK company has a €4.4m receipt expected on 26 August. The current spot rate is £0.7915/€1. They are concerned that adverse exchange rate fluctuations could reduce the £ receipt but are keen to benefit if favourable exchange rate fluctuations were to increase the £ receipt. Hence, they have decided to use €/£ exchange traded options to hedge their position.
Research shows that €/£ options are available on the CME Europe exchange.
The contract size is €125,000 and the futures are quoted in £ per €1. The options are American options and, hence, can be exercised at any time up to their maturity date.
As the company is selling €, it wants the maximum net £ receipt for each € sold. The maximum net receipt is the exercise price minus the premium cost.
This is calculated below:
0.7900 – 0.00465 = 0.78535
0.79250 – 0.00585 = 0.78665
Hence, the company will choose the 0.79250 exercise price as it gives the maximum net receipt. Alternatively, the outcome for all available exercise prices could be calculated.
In the exam, either both rates could be fully evaluated to show which is the better outcome for the organisation or one exercise price could be evaluated, but with a justification for choosing that exercise price over the other.
4. How many? – 35
This is calculated in a similar way to the calculation of the number of futures. Hence, the number of options required is:
€4.4m/€0.125m ≈ 35
The company will buy 35 September put options with an exercise price of £0.79250 /€1
Premium to pay – £/€0.00585 x 35 contracts x €125,000 = £25,594
Outcome on 26 August:
On 26 August the following was true:
Spot rate – £ 0.79650/€1
As there has been a favourable exchange rate move, the option will be allowed to lapse, the funds will be converted at the spot rate and the company will benefit from the favourable exchange rate move.
Hence, €4.4m x 0.79650 = £3,504,600 will be received. The net receipt after deducting the premium paid of £25,594 will be £3,479,006.
Strictly a finance charge should be added to the premium cost as it is paid when the hedge is set up. However, the amount is rarely significant and, hence, it will be ignored in this article.
If we assume an adverse exchange rate move had occurred and the spot rate had moved to £ 0.78000/€1, then the options could be exercised and the receipt arising would have been:
Pay – 35 x 125,000
Buy £ at spot (£0.78/€1)
Deduct premium cost
Net receipt – see Note 1
1. This net receipt is effectively the minimum receipt as if the spot rate on 26 August is anything less than the exercise price of £ 0.79250/€1, the options can be exercised and approximately £3,461,094 will be received. Small changes to this net receipt may occur as the €25,000 underhedged will be converted at the spot rate prevailing on the 26 August transaction date. Alternatively, the underhedged amount could be hedged on the forward market. This has not been considered here as the underhedged amount is relatively small.
2. For simplicity it has been assumed that the options have been exercised. However, as the transaction date is prior to the maturity date of the options the company would in reality sell the options back to the market and thereby benefit from both the intrinsic and time value of the option. By exercising they only benefit from the intrinsic value. Hence, the fact that American options can be exercised at any time up to their maturity date gives them no real benefit over European options, which can only be exercised on the maturity date, so long as the options are tradable in active markets. The exception perhaps is traded equity options where exercising prior to maturity may give the rights to upcoming dividends.
Much of the above is also essential basic knowledge. You are unlikely to be given the spot rate on the transaction date. However, the future spot rate can be assumed to equal the forward rate which is likely to be given in the exam. The ability to do this may earn up to six marks in the exam. Equally, another one or two marks could be earned for reasonable advice.
This article will now focus on other terminology associated with foreign exchange options and options and risk management generally. All too often students neglect these as they focus their efforts on learning the basic computations required. However, knowledge of them would help students understand the computations better and is essential knowledge if entering into a discussion regarding options.
A ‘long position’ is one held if you believe the value of the underlying asset will rise. For instance, if you own shares in a company you have a long position as you presumably believe the shares will rise in value in the future. You are said to be long in that company.
A ‘short position’ is one held if you believe the value of the underlying asset will fall. For instance, if you buy options to sell a company’s shares, you have a short position as you would gain if the value of the shares fell. You are said to be short in that company.
In our example above where a UK company was expecting a receipt in €, the company will gain if the € gains in value – hence the company is long in €. Equally the company would gain if the £ falls in value – hence, the company is short in £. This is their ‘underlying position’.
To create an effective hedge, the company must create the opposite position. This has been achieved as, within the hedge, put options were purchased. Each of these options gives the company the right to sell €125,000 at the exercise price and buying these options means that the company will gain if the € falls in value. Hence, they are short in €.
Therefore, the position taken in the hedge is opposite to the underlying position and, in this way, the risk associated with the underlying position is largely eliminated. However, the premium payable can make this strategy expensive.
It is easy to become confused with option terminology. For instance, you may have learnt that the buyer of an option is in a long position and the seller of an option is in a short position. This seems at variance with what has been stated above, where buying the put options makes the company short in €. However, an option buyer is said to be long because they believe that the value of the option itself will rise. The value of put options for € will rise if the € falls in value. Hence, by buying the €/£ put options the company is taking a short position in €, but is long the option.
The hedge ratio is the ratio between the change in an option’s theoretical value and the change in the price of the underlying asset. The hedge ratio equals N(d1), which is known as delta. Students should be familiar with N(d1) from their studies of the Black-Scholes option pricing model. What students may not be aware of is that a variant of the Black-Scholes model (the Grabbe variant – which is no longer examinable) can be used to value currency options and, hence, N(d1) or the hedge ratio can also be calculated for currency options.
Hence, if we were to assume that the hedge ratio or N(d1) for the €/£ exchange traded options used in the example was 0.95 this would mean that any change in the relative values of the underlying currencies would only cause a change in the option value equivalent to 95% of the change in the value of the underlying currencies. Hence, a €0.01 per £ change in the spot market would only cause a €0.0095 per £1 change in the option value.
This information can be used to provide a better estimate of the number of options the company should use to hedge their position, such that any loss in the spot market is more exactly matched by the gain on the options:
Number of options required = amount to hedge/(contract size x hedge ratio)
In our example above, the result would be:
€4.4m/(€0.125m x 0.95) ≈ 37 options
This article has revisited some of the basic calculations required for foreign exchange futures and options questions using real market data, and has additionally considered some other key issues and terminology in order to further build knowledge and confidence in this area.
William Parrott, freelance tutor and senior FM tutor, MAT Uganda