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The Break Forward
by Warren Edwardes
Break Forwards: A Synthetic Option Hedging Instrument, 1990 "The Handbook of Financial Engineering", Wiley, New York
This article forms the basis for a chapter in
"Key Financial Instruments: understanding innovation in the world of derivatives" 4 February 2000 Financial Times Prentice Hall ISBN 0273 63300 7 London link
Introduction and overview
The case studies in chapters 14 and 15 walk through the thinking process behind two of the financial products I developed in the 1980s. The first of the two case studies on the Break Forward relates to events in 1986 when currency and other options were only just being introduced into Europe. The term "Derivative" had not yet been coined. Legal documentation was very much done on a case by case basis. There was no ISDA and no British Bankers Association deal terms for derivatives. Legal documentation for swaps, for example, often took more than a year to process. In short, we were in the frontier stage for derivatives.
The Break Forward came about not as a result of a product looking for a client but very much the other way around. We had a problem in that these new fangled options were not selling despite their insurance-like benefits. Customers did not want to pay up-front options premiums. So we were selling deep out of the money options as a way of minimising option premiums. But such out of the money options were close in function to no hedge at all. Customers had, by then, got used to forward exchange contracts and the standard procedure was to fully cover everything in the forward market. But to produce an option that was close to a forward contract would have meant a very high option premium. We are back to the problem of nobody wanting to write out a cheque for option premiums. So we had to construct a package of a forward contract plus an option to unwind the forward contract. And the premium? The option to unwind would probably be out of the money so it would be small. Nevertheless, we could bundle it into the price of the forward contract. Hey presto the premium disappears and what we have is just a contract that looked like and largely behaved like a boring old-fashioned Forward Contract but with a twist.
And there was also a problem with the taxation treatment of these options. It took a good few years for the Inland Revenue to understand these new instruments and produce a fair and neutral tax treatment. Option premiums were not always tax deductible, I discovered at my regular lunch with my colleague in the taxation department. He suggested that I find a way to bundle the option premium into the price of the contract. "Ive just done that, Brian" I said with a cheesy grin. Not only would the Break Forward be more appetising to the Treasurer but also to his Tax accountant.
At that time there were a number of option strategies going by names such as Collar and Cylinder. What was the essential property of the contract? It was a hedge with holes. One evening, draining away freshly cooked pasta, I thought "Aha! Ill call this product a Colander". A hedge with the ability for the hedge to be released.! But no, I did not name the product a Colander. It was not meant to be flashy new turbo-charged product. I designed the Break Forward to be a boring and slightly but significantly different variation on an old favourite that the clients board of directors had become familiar with. It was a Forward Contract with a Break. I therefore named it the Break Forward.
Definition of a Break Forward
A Break Forward contract is a forward contract at a Forward rate that permits the holder to break or unwind the contract with an opposite transaction at another rate, the Break rate.
There is no option premium payable and the costs of the embedded option are included in the fixing of the Forward rate and the Break rate.
Background to its invention
I created the Break Forward at Midland Bank with the help of Edmond Levy, to solve two problems firstly, the reluctance by finance directors of corporate clients to pay premiums and secondly an unsatisfactory tax treatment.
In October 1986 currency options had only recently been introduced to the UK. Companies were still very reluctant to pay option premiums in advance. Under standard forward exchange contracts, no premiums were payable. The client simply entered into a contract with a bank for the exchange of, say, US Dollars for GB Pounds for delivery in six months time. At maturity, the two currencies were exchanged at the pre-agreed exchange rate and for the amounts specified. And by 1986 the exchange commission that had been commonplace a decade earlier had all but disappeared. So companies were not asked to make any payment up-front when they entered into forward contracts and they were going to take a lot of persuading to write a cheque in payment for a currency option. Some treasurers did persuade their boards to allow them to enter into options. However, many found that if the options, which were after all a form of insurance against adverse currency movements, were not exercised at maturity they were criticised with the benefit of hindsight by their boards. "We neednt have bought those new-fangled options" they were told. "Lets stick with forward contracts". So a structure was required with option characteristics but with no explicit premium for the customer to pay.
At that time, I happened to have lunch with my colleague, Midlands taxation manager Brian Atkinson. Apparently, in addition to the corporate treasurers reluctance to pay premiums, there was a significant tax problem. If the option was not exercised, the premium paid would not be tax deductible and turn out to be a wasting asset. There would be no tax loss generated to offset against profits. The treatment was therefore asymetric and therefore highly unsatisfactory. However, the UK inland revenue was comfortable with forward contracts and if we could structure an option to look like a forward contract then all would be well.
As it happens, I was also puzzled as to why when options were sold they were persuaded to buy out of the money options, rather than in-the-money or at-the-money options. A deeply out of the money option has the properties of no contract at all, whilst a deeply in the money contract, was almost certainly going to be exercised. Corporates traditionally covered everything in the forward market, so for me the first step into the options market should be something that behaved more or less like a forward contract and not like something that was no hedge at all. So my first brainwave was to sell Deep In-the-money European type options new slimline DIET options! Of course they did not get off the ground for hedging purposes because deep-in-the-money options cost a lot more than out-of-the-money options and corporates were reluctant to pay large upfront premiums. So I had to think of another structure. But before we consign DIET options to the derivatives graveyard, they turned out to have quite a useful property as an off-balance sheet deposit and loan structure. Because of the large premium payable, the pricing was simply based on the forward exchange rate and the interest rate. The moral here is never discard a solution just because it does not work. It may work splendidly for a completely differnet purpose. Disasters are indeed opportunities.
So the Break-Forward contract was constructed as a synthetic currency option. This chapter explains that the implied and embedded premium is the difference, in money terms, between the Fixed Rate, which coincides with the strike rate of the synthetic option, inclusive of the premium, and the Break Rate, which corresponds to this strike rate.
In managing foreign exchange exposure, the traditional hedges employed are forward exchange contracts or those arising from appropriate transactions in the spot exchange rate and related money markets. We might denote such hedging instruments as first generation products. The experience of high exchange rate volatility and the accepted rigidity of forward contracts created the need for more sophisticated and flexible exposure management instruments. Currency option contracts marked the beginning of the second generation. Such contracts were distinguished from conventional forward contracts in that the purchaser of a currency option is merely obliged to deliver an up-front premium to ensure protection against downside currency risk.
Break-Forwards were a new product developed by Midland Bank which combined the best features of both generations. Break-Forward contracts provide corporate treasurers with a hedging instrument which can mimic both fully forward hedged and unhedged strategies as well as the contintiunium of positions in between these extremes. Furthermore, the product was designed to overcome the corporate treasurer's aversion to up-front premiums and their associated taxation difficulties. There were circumstances where option premiums paid did not secure tax relief; given that Break-Forwards do not involve the payment of a premium this difficulty did not arise. This chapter identifies and clarifies the bridge that Break-Forwards provided; in addition it carries out a comparitive cost analysis of Break-Forwards relative to other hedging instruments.
The gap in first generation products
The example I focus attention on is that of a UK corporate treasurer seeking to manage the exposure generated by a US dollar principal sum which he anticipates having to pay in three months time. Of course the principles and analysis applied here are not specific to this case and can be extended to other situations in a similar manner.
I shall be working with a particular representation of such cases and so it is best if, by way of introduction, the familiar scenarios are considered first.
A treasurer of a UK importer of US goods expecting to pay Dollars in three months time may by using first generation products choose to either leave his position exposed to fluctuations in exchange rates or he may elect to hedge his position by buying today in the forward market at (say) 1.5000 $/£. For Completeness assume a current spot exchange rate of l.5130 $/£ with volatility at 14.60%. These parameters are not crucial to the discussion other than providing a possible indicator of the future spot rate in relation to the forward exchange rate. The outcome from these two decisions is presented in Figure 1.
Figure 1. Effective exchange rate at expiration
The horizontal axis denotes the spot rate on maturitv of the forward contract whilst the vertical axis denotes the exchange rate at which the treasurer effctively exchanges currencies under the alternative strategies.
The forward deal ensures that the treasurer receives $1 for every £0.6667 irrespective of the spot rate outcome on maturity; hence the forward position can be represented by the line HH'. On the other hand the unhedged position, represented by UU', enables him to take full advantage of favourable spot movements; but he leaves himself exposed to unlimited downside risk.
Currency exposure relates to the effects currency movements have on the cash flows and financial structure of the firm. A major concern for the treasurer is to adopt hedging strategies that minimise the danger of incurring a serious risk of loss should exchange rates mov against him. Few people would disagree that the decisions taken by treasurers in the management of exposure need to be monitored and continually assessed, but there is some doubt surrounding the criterion by which such decisions are judged. Generally exposure management performance is measured relative to some exchange rate yardstick. This yardstick is, however, often chosen retrospectively as the optimum exchange rate available over the exposure period; that is, the most favourable amongst the various forward rates that become available from the time the exposure is identified and the subsequent spot rate that arises on the maturity date of the transaction. In such cases the treasurer's efforts will inevitably attract criticism as the evaluation would always be made with the benefit of hindsight.
Ideally the treasurer would like a hedging instrument which ensures that he has the best of both positions; that is, one that enables him to exchange currencies at the ruling spot rate should it be greater than I .5000 and at 1 .5000 $/£ should spot fall below 1.5000 -- effectively he would like to ensure the line HEU'. The case ilustrated here relates to the exposure management of a UK importer. The ideal effective rate for a UK exporter would be that represented by ht ekinked line UEH. This would constitute a hedged position with rates above 1.5000 and an unhedged state below that rate (ignoring bid-offer spreads). This requires the ability to make dealing decisions with hindsight knowledge of the spot exchange rate outcome. Such a product is, of course, unobtainable in the market place but through Break-Forwards the treasurer can come close to it.
Break Forward versus First-generation products
Behind a Break-Forward contract is the explicit acceptance by the treasurer of a Fixed Rate, at which he is obliged to purchase Dollars, set worse than the ruling forward rate. The selling bank values this disadvantage and provides the treasurer with an option to unwind the 'fixed' position at a predetermined strike price the 'Break Rate'. The break-facility under a Break-Forward contract is the following right: Having bought Dollars at the Fixed Rate, the treasurer can sell back the Dollars at the Break Rate. He is then free to buy his Dollars again in the market but at the ruling spot rate. Clearly this can only be to his advantage if, on maturity, Dollars can be purchased at a more favourable rate than the Break Rate i.e., when spot is above the Break Rate. (Of course he is also free to take advantage of favourable forward rates should they occur at any time throughout the life of the contract, knowing that the fixed obligation can be unwound at no worse a rate than the Break Rate). Figure 2 presents three such Break-Forward contracts.
Figure 2. Effective exchange rate for various contracts at expiration
The first Break-Forward contract, S, assumes a relatively small loading ( l.00%) on the forward rate yielding a Fixed Rate of 1.4850. Under our market assumptions, this enables the treasurer to break at 1.5825. With the forward rate at 1.5000 this three-month European option to break the fixed obligation is out-of-the-money. As one might expect, the higher this loading the "better" will be the Break Rate in that, for a given movement in spot, it is more likely that the break-facility will be activated. Thus we might choose to define a medium loading as one where the Break Rate is at-the-money (in relation to the forward rate) and a large loading as one which ensures an in-the-money break-facility. With our assumed market conditions, an at-the-money Break Rate will be obtained with a loading of 2.90% (i.e. a Fixed Rate of 1.4565). The third contract in the diagram above assumes a relatively large loading of 4.80% (Fixed Rate of 1.4280) yielding a Break Rate of 1.4505. The effective exchange rates at which currencies are exchanged under each of these contracts is represented by the lines S, M and L. The kink in these lines represent the point beyond which the treasurer is able to take advantage of favourable spot rates by activating the break-facility. Note that in Figure 2 is also applicable to a particular forward rate vailable at any time during the life of the contract for the same value date.
At one extreme we can regard a conventional forward exchange contract as a Break-Forward with a zero loading; one providing no option to unwind. Likewise, the unhedged position can now be given the representation of a Break-Forward contract with an infinite loading; one where the fixed position is certain to be unwound to take advantage of favourable spot rates (thus the Fixed Rate would be equal to the Break Rate). Hence it only remains for our treasurer to specify a loading which best reflects his views on how much downside risk he is willing to accept.
This choice of loading should depend on three factors:
his capacity and willingness to accept risk;
his views, if any, on the likely direction or trend in spot movements and the degree of certainty with which such beliefs are held; and
his accounting treatment and performance measurement, i.e. is he judged against
the forward rate at the time the exposure is identified or
the spot rate on maturity of the foreign currency exposure.
For any chosen loading the Break-Forward provides a back-stop should the outcome of spot on maturity be widely at variant with the treasurer's expectations.
We will show that if the choice of hedging instrument is restricted to either a forward exchange contract or dealing spot for the same value date, the opportunity loss, that is performance measured relative to the optimum, can be unlimited should the wrong instrument be used. However with a Break-Forward contract this loss is always limited.
Exposure Management Evaluation
Consider first the case where the treasurer is judged relative to a forward contract. Here a highly risk-averse treasurer would aim at a minimal loading so as to eliminate all downside risk and effectively lock into the forward rate irrespective of his views on spot movements. Such a treasurer is blind to opportunity loss in that he is willing to forego all potential benefits to be earned should spot move favourably relative to the forward rate. Break-Forward contracts are aimed at those who are aware of such an opportunity and wish to insure against its loss. A loading on the forward rate is precisely the premium due for insurance against this opportunity loss. As in the case with general insurance policies these premiums can be reduced but only if the insured is willing to forego some of the compensation he would be entitled to (e.g. accepting a £100 excess on a motor car policy). The larger is this excess (i.e. the distance between the Break Rate and the traditional forward rate) the smaller the loading.
Figure 3 is constructed by measuring Break-Forward contracts relative to the fully forward covered position. That is, S1, M1, and L1 are the vertical distances in Sterling terms between HH' and S, M and L, respectively, in Figure 2. It is apparent that, for a given loading, Break-Forward contracts offer considerable advantages over the forward contract whilst still retaining downside protection against exchange rate risk. Note how, under these contracts, the benefits are obtained earlier the larger the loading on the forward exchange rate highlighting the premium/excess trade-off.
Figure 3. Break-Forwards measured relative to forwards
When performance is measured relative to the subsequent spot rate (e.g. when establishing accounting profits or losses) the highly risk-averse treasurer would adopt a fully unhedged position irrespective of his views on spot rate movements. Note that the analysis here applies equally well to performance measured relative to a forward rate that becomes available for the same value date. Here, the prime concern becomes the opportunity loss relative to the forward exchange contract should the spot rate move unfavourably. If such movements occurred then the unhedged strategy could lead to a harmful economic exposure on the business. For example the firm's competitors could have covered themselves in the forward market and guaranteed a price in Sterling terms. Our treasurer, however, would be forced to either charge his UK customers an exchange surcharge and incur adverse market sentinient or else suffer losses. Again, Break-Forward contracts can be viewed as providing insurance against such losses. In this instance, however, the "premium" is the money value of the difference between the Fixed and Break Rates with the "excess" being the loading on the forward rate.
Figure 4 is constructed in a similar manner to that of Figure 3, but now Break-Forward contracts are measured relative to the fully exposed position. The lines S2, M2 and L2 are the vertical distances, in Sterling, between S, M, and L and UU' of Figure 2.
Figure 4. Break-Forwards measured relative to spot
Choice of Break-Forward Loading
The treasurer's choice of Break-Forward loading is not only dependent on his view on Spot rate movements and on how firmly such beliefs are held, but also on his willingness or authority to bear risk. These factors should combine to produce an optimal Break-Forward loading which could in theory be any figure between zero and infinity. The extremes are, as we have already seen, the conventional forward hedge or a fully exposed position. Such positions are rarely the best strategies for the majority of situations.
I have argued that for highly risk-averse treasurers there is no desire to do any better than the criteria by which they are measured. That is, deal forward if performance is measured relative to the forward rate or leave the position exposed and deal at whatever spot rate occurs on the value date if performance is measured relative to that exchange rate. At the other extreme we have the risk lover with a view, however flimsy, that spot (or a subsequent forward rate) will be one side or other of the ruling forward rate. Such a treasurer will put all his eggs in one basket and either leave his funds exposed or will fully forward cover his funds.
Both such types of treasurers could suffer under one or other performance criterion should they be applied subsequent to the outcome of the spot rate on the value date (as depicted in Figure 1). Consider however one who takes out a Break-Forward contract. Recall that for our example the ideal position is represented in Figure 2 by the kinked line HEU'. The line M, representing the medium loading Break-Forward, remains roughly equidistant from HEU'. That is, whatever the spot rate is on the value date (or any subsequent forward rate for the same value date) the treasurer does no worse than exchanging at about 2.90% the wrong side of the optimum rate.
Treasurers typically do not hold identical views on spot movements nor do they perceive risk in a like manner. Thus a medium loading Break-Forward will not be suitable to all situations. Those whose performances are measured relative to the forward rate and perceive risk according to that measurement will be tempted towards a smaller loading Break-Forward contract, such as that depicted by S or in extreme circumstances a forward contract. Likewise, those whose performances are measured relative to the spot rate on the value date and perceive risk according to that criterion might well prefer a larger loading Break-Forward contract such as that represented by L.
An equally important factor is the treasurers view of how spot will move through the period of the contract. This could either strengthen his demands for a small or large loading or could act as an opposing force. For instance a moderately risk-averse treasurer (I will term him a risk manager), who perceives risk as the loss relative to forward cover, may think it quite likely that spot will move favourably relative to the forward rate. In such instances he would prefer a contract which offers flexibility so that should the outcome of spot coincide with his beliefs he is able to exchange at the more favourable rate. Thus, although a forward contract or low loading Break-Forward contract might initially be desirable, his views would lead him to accepting a medium Break-Forward loading. The extent of this increment being largely determined by how firmly such beliefs are held and how much risk he is willing to bear.
The number of such examples one could invent are too many to consider here in any detail. It useful, howver, to summarize suitable loadings under various scenarios in the form of Chart A and Chart B dependent on the choice of performance criterion. These can be used as a ready-reckoner in choosing a Break-Forward loading. The axes measure the probability, in the treasurer's view, that the spot rate will move favourably relative to the ruling forward rate and his degree of risk-bearing capacity. These together with his chosen performance criterion will indicate the appropriate Break-Forward loading. Whilst such constructions are largely subjective containing many "grey areas" sensible fine tuning will be applied by the user as necessary.
Break-forward versus second-generation products
The evaluation of Break-Forward contracts measured relative to spot, in Figure 4 and Chart B, brings out an important interpretation of such contracts as currency options.
One of the basic results from option-pricing theory is that the combination of a Dollar put / Sterling call option with a forward purchase of Dollars versus Sterling is simply an option to call Dollars / put Sterling. The break-facility component of our Break-Forward contracts could be viewed as the free provision of European Dollar put options. As with all options, their value, if any, will depend in part on the intrinsic value of the option - in this case the difference between the strike price and the ruling forward rate. It should not be surprising therefore, to find that Break-Forward contracts are equivalent to pure option contracts since the former entail a forward commitment coupled with a reversing option.
Suppose that, rather than take out Break-Forward contracts, our treasurer were to purchase dollar call options with strike rates at 1.5825, 1.5000 and 1.4505. The premiums for these options, compounded over three months, are the maximum loss relative to spot under their respective call option. Under a corresponding Break-Forward (when the Break Rate is set at the call option strike rate) the maximum loss relative to spot is equal to the difference between the Fixed Rate and the Break Rate in money terms. At the extremes we can see that an infinitely large difference between the Fixed and Break Rates (resulting from a zero loading or a forward contract) would be equivalent to an option with an infinite premium (i.e., a deep in-the-money option). On the other hand, a Break-Forward with the Fixed Rate equal to the Break Rate, (resulting from an infinitely large loading) would be such that the corporate would suffer no loss versus spot and must therefore be equivalent to an option with a nil premium (i.e., a deep out-of-the-money option, or a fully exposed position).
In general, then, the following rule applies: Small, medium and large loading Break-Forwards for the purchase (sale) of Dollars are equivalent to purchases of, respectively, in-the-money, at-the-money and out-of-the-money European dollar call (put) options. In every instance the Fixed Rate in a Break-Forward contract (representing the worst rate the treasurer receives) is precisely the strike rate under the corresponding option but with the premium (suitably compounded) incorporated into that rate.
This recognition of Break-Forwards as synthetic options can be seen diagramatically. Suppose a do-it-yourself small loading Break-Forward contract is constructed by combining an out-of-the-money put option (represented by P1 below in Figure 5) with a forward purchase. The overall position is given by the sum of the vertical distances of the lines P and HH' measured from the zero axis at each spot rate. This results in the line S2.
As can be seen the premium paid for the put option has been converted via the forward contract into a call option. However, whereas the put option is out-of-the-money, the call option is in-the-money and hence its associated premium is larger.
It is important to notice that this synthetic call option entails the payment of a premium as required by the put option. Break-Forward contracts however do not require any such payment. The insight by which such contracts can be offered is made immediately obvious once it is seen that S2 can be constructed in an infinite number of different ways. One in particular is to move P1 upwards until the horizontal segment coincides with the zero axis (thus eliminating the premium) and then to compensate this movement by shifting HH' across to the left accordingly. These two movements give rise to P2 and FF'. The line P2 represents a free put option with a strike rate at 1.5825. This option is paid for indirectly through the commitment of a forward purchase of Dollars at a Fixed Rate set worse than the forward rate i.e., at 1.4850.
It can be seen that the Break-Forward contract can be used whenever options are thought desirable by choosing the Break Rate to be equal to the desired strike price. In the UK in the mid-1980s customers liable to capital gains tax treatment on currency forward and option contracts recognised that the Break-Forward contract had a major advantage over over-the-counter options. Unlike a currency option, the Break-Forward contract did not entail payment of an initial premium which, in the case of an option, could have become a wasting asset affording no tax relief. Break-Forwards thus economically dominated currency options in that they were tax efficient instruments.
Option contracts are flexible instruments for coping with natural option-type exposures. Setting aside any view the treasurer may have on spot rate movements, recall the basic rules for deciding when to use option contracts rather than forward contracts.
"Whenever a quantity of foreign currency receivable (payable) is uncertain, buy a put (call) option on the currency. If such sums are known then a forward contract is appropriate".
These rules apply equally well to Break-Forwards, i.e., such receivables (payables) can be hedged by selling (buying) the currency forward using a Break-Forward contract.
Break-Forward contracts were uniquely valuable tools for managing foreign exchange exposure and with their potential fiscally efficient properties marked the beginning of third generation treasury instruments. We have seen that the structure of such contracts is flexible enough to imitate both traditional forward and option contracts as well as the unhedged position.
Perhaps a fairer and more suitable measurement of a treasurer's performance is obtainable with the introduction of second and third generation foreign exchange products. Currency options limit downside risk whilst providing scope for taking advantage of favourable rates of exchange over the period of the exposure. It is often remarked that performance should be measured relative to some yardstick which is adjusted in some way to reflect the degree of volatility the market experiences. Break-Forward contracts can provide an adjusted forward rate (the Fixed Rate) which reflects the market's valuation of a treasurer's views and risk characteristic. Until a better yardstick is found the success of a treasurer's exposure management efforts is best measured relative to this optimal Break-Forward contract. These contracts combine discipline with motivation and a good defence against critics.
The pricing and quotation of Break-Forward contracts can be carried out to suit the customer's preferred position. Midland Bank quoted such contracts given either the Break Rate or the preferred loading on the forward exchange rate.
Just two weeks after Midland Bank launched the Break Forward, Hambros Bank announced the Fox A Forward Contract with an optional Exit. Nevertheless, this was no me-too copy cat product. It had taken us several months to develop the Break Forward including pricing systems, legal documentation, back office processing and risk management and I am sure that it would have taken Hambros just as long. Moreover, they could just as well have launched two weeks before us. It just goes to show that however wonderful your product is somebody else can launch it just before.
What happened next? Well pretty soon, I applied the Break Forward concept to Forward Rate Agreements and Interest Rate Swaps. I reconstructed Interest Rate Guarantees or Options on FRAs creating Break FRAs also known as Limit FRAs. The immediate next step was to repackage Interest Rate Caps into Break Swaps also known as Limit Swaps.
About six months after the launch of the Break Forward, Salomon Brothers launched the Participating Forward. This could have been called a Part Break Forward. Instead of the right to unwind the entire forward contract, the customer could unwind only a portion of the contract. However, for this benefit on only a part of the forward contract, the customer could start benefiting at the forward contract rate itself instead of at the break rate. He could "participate in the upside benefits".
Economically, a generalised Participating Forward could have been created simply through any desired customer-chosen combination of a normal Forward exchange contract and a Break Forward.