.40721.4123 × 1831 + 0.0515 ×365Forward outright prices can be quoted as two-way prices in thesame way as other prices. One could use the bank’s bid ratefor the spot, its offered rate for sterling (5.20%) and its bid ratefor dollars (4.30%) in the above example, to calculate the pricewhere the bank buys sterling from the customer against dollarsfor delivery in 6 months’ time, and use the bank’s offered ratefor spot, its bid rate for sterling (5.10%) and its offered rate fordollars (4.40%) to determine the other side of the price, as in thefollowing example.Example 3What two-sided price can be constructed for the GBP/USD 3month outright, given the following? The 6-month period is183 days.GBP/USD spot:
1.4120/26
GBP 6-month interest rate:
5.10/5.20%
USD 6-month interest rate:
4.30/4.40%
For the bid side:1831 + 0.0430 ×360 = 1.40621.4120 × 1831 + 0.0520 ×365
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For the offer side:1831 + 0.0440 ×360 = 1.40821.4126 × 1831 + 0.0510 ×365The two-sided outright price is therefore 1.4062/1.4082In minor markets where the price does need to be constructed andhedged in this way, this calculation might be necessary. In a wellestablished market, however, this would generally produce a ratherlarger bid/offer spread than is realistic. In this case, it might bebetter to use middle prices throughout to calculate a middle price,as in Example 2, and then to spread the two-way price around thismiddle price. In practice, a dealer does not recalculate forward pricescontinually in any case, but takes them from the market just as thespot dealer takes spot prices.
Forward swapsForward outrights are an important instrument because they enablea bank’s customer to lock in an exchange rate for the future. However,trading banks generally do not deal between themselves in forwardoutrights, but rather in forward swaps, where a forward swap is thedifference between the spot and the forward outright. The reason fornot dealing in outrights will become clear later. The forward outrightrate can therefore be seen as a combination of the current spot rateand the forward swap rate added together.
Forward outright = spot + forward swap
It is important to note that the forward swap is sometimes positiveand sometimes negative. As we shall see, this depends on which ofthe two currencies involved has higher interest rates. As with spotprices and outright prices, swap prices are quoted as two-way prices.
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Example 4Spot USD/CHF:Forward swap:
1.7166/1.71710.0150/0.0155spot + swap = forward outright
In this case:
1.7166 + 0.0150 = 1.73161.7171 + 0.0155 = 1.7326
Therefore the two-sided outright price is 1.7316/1.7326As before, it is possible to give a formula for what the forward swaptheoretically should be:
Forward swap⎞⎛days⎜ variable currency interest rate × variable year ⎟⎜ ⎟⎠⎝days− base currency interest rate ×base year= spot × days1 + base currency interest rate ×base year
As before, the length of each year may be 360 or 365 days.Example 5What two-sided price can be constructed for the GBP/USD 3month forward swap, given the following? The 6-month period is183 days.GBP/USD spot:GBP 6-month interest rate:USD 6-month interest rate:
1.4120/265.10/5.20%4.30/4.40%
For the left side: 1831830.0430 ×− 0.0520 ×3603651.4123 ×= −0.00581831 + 0.0520 ×365
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113
For the right side: 1831830.0440 ×− 0.0510 ×3603651.4123 ×= −0.00441831 + 0.0510 ×365The swap price is therefore −0.0058/−0.0044Note that in Example 5, we used the same spot rate to calculateeach side, and that the spot rate we used was a middle rate. Usingeither the bid or offer spot rate would make only an extremely smalldifference.As expected, the swap calculated in Example 5, when combinedwith the spot rate, gives the same outright as Example 3:Spot:6-month swap:
1.4120/ 1.4126−0.0058/−0.0044
6-month outright:
1.4062/ 1.4082
If the year basis is the same for the two currencies and the numberof days is sufﬁciently small, the following is a good approximation:ApproximationForward swap ≈ spot × interest rate differential ×
daysyear
Example 6USD/CHF spot:92-day USD interest rate:92-day CHF interest rate:
1.71005%2%
Using the precise formula: 9292− 0.05 ×0.02 ×3603601.7100 ×= −0.0129921 + 0.05 ×360Using the approximate formula:1.7100 × (−0.03) ×
92= −0.0131360
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Foreign exchange and money markets
USD/CHF spot:365-day USD interest rate:365-day CHF interest rate:
1.71005%2%
Using the precise formula: 365365− 0.05 ×0.02 ×360360= −0.04951.7100 ×3651 + 0.05 ×360Using the approximate formula:1.7100 × (−0.03) ×
365= −0.0520360
Example 6 shows that the approximation is generally rather goodfor short periods but rather inaccurate for longer periods. It alsobecomes less accurate if the base currency interest rate is large.
Discounts and premiumsWhen the base currency interest rate is lower than the variable currencyrate, the forward outright exchange rate is always greater than the spotrate. That is, the base currency is worth more units of the variablecurrency for delivery forward than it is for delivery spot. This can beseen as compensating for the lower interest rate: if I deposit moneyin the variable currency rather than the base currency, I will receivemore interest. However, if I sell forward the maturing deposit amount,in an attempt to lock in this advantage, the forward exchange rate iscorrespondingly worse so I lose the advantage. In this case, the basecurrency is said to be at a premium to the variable currency, and theforward swap price must be positive. At the same time, the variablecurrency is said to be at a discount to the base currency.The reverse also follows. In general, given two currencies, thecurrency with the higher interest rate is at a discount (worth fewerunits of the other currency forward than spot) and the currency withthe lower interest rate is at a premium (worth more units of the othercurrency forward than spot). When the base currency is at a premiumto the variable currency (and the variable currency is at a discount tothe base currency), the forward swap price is positive; when the basecurrency is at a discount (and the variable currency is at a premium),the forward swap price is negative.
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115
When the swap price is positive, and the forward dealer appliesa bid/offer spread to make a two-way swap price, the left priceis smaller than the right price as usual. When the swap price isnegative, he must similarly quote a more negative number on the leftand a more positive number on the right in order to make a proﬁt.This can be seen in Example 5 above, where the swap price was−0.0058/−0.0044.However, the minus sign ‘−’ is generally not shown. The result isthat, when the swap price is negative, the larger number appears tobe on the left. As a result, whenever the swap price appears larger onthe left than the right, it is in fact negative, and must be subtractedfrom the swap rate rather than added.Swap prices are generally quoted as points, in such a way that thelast digit of the swap points coincides with the same decimal place asthe last digit of the spot price. For example, if the spot price is quotedto 4 decimal places – say 1.7166 – and the swap price is 120 points,this means a swap price of 0.0120. If the spot price is quoted to 2decimal places – say 171.66 – and the swap price is 120 points, thismeans a swap price of 1.20.The currency with the higher interest rate is at a discount andthe currency with the lower interest rate is at a premium.When the base currency is at a premium and the variablecurrency is at a discount, the forward swap points are positiveand the left price appears smaller than the right price. Whenthe base currency is at a discount and the variable currency isat a premium, the forward swap points are negative and the leftprice appears bigger than the right price.
Example 7euro interest rate:dollar interest rate:yen interest rate:
4%5%1%
The euro is at a premium to the dollarThe dollar is at a discount to the euroThe forward swap points for EUR/USD are positiveThe dollar is at a discount to the yenThe yen is at a premium to the dollarThe forward swap points for USD/JPY are negative
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Foreign exchange and money markets
Example 8EUR/USD spot is 0.8723/28 and the 3-month swap rate isquoted as 20/22.Spot EUR/USD:3-month swap:
0.8723/20/
2822
3-month outright
0.8743/0.8750
USD/JPY spot is 127.23/28 and the 3-month swap rate isquoted as 20/22.Spot USD/JPY:3-month swap:
127.23/20/
2822
3-month outright
127.43/127.50
USD/CHF spot is 1.7723/28 and the 3-month swap rate isquoted as 22/20.Spot USD/CHF:3-month swap:
1.7723/−22/−
2820
3-month outright
1.7701/1.7708
If a forward swap price includes the word par it means that thespot rate and the forward outright rate are the same: par in this caserepresents zero. A/P is around par, meaning that the left-hand sideof the swap must be subtracted from spot and the right-hand sideadded. This happens when the two interest rates are the same or verysimilar.Example 9USD/CAD spot is 1.4723/28 and the 3-month swap rate isquoted as 6/4 A/P.Spot USD/CAD:3-month swap:
1.4723/−6/+
284
3-month outright
1.4717/1.4732
The swap price in Example 9 would often be written as −6/+4,which means the same as 6/4 A/P but indicates the price moreclearly.
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117
It is important to be careful about the terminology regardingpremiums and discounts. The clearest terminology, for example,is to say that ‘‘the euro is at a premium to the dollar’’ or that ‘‘thedollar is at a discount to the euro’’; there is then no ambiguity.If, however, a London dealer says that ‘‘the EUR/USD is at adiscount’’, he generally means that the variable currency, thedollar, is at a discount and that the swap points are to be addedto the spot. Similarly, if he says that ‘‘the GBP/JPY is at apremium’’, he means that the variable currency, the yen, is ata premium and that the points are to be subtracted from thespot. If there is no qualiﬁcation, he is generally referring to thevariable currency, not the base currency. This is not the samein all countries, however, so beware! It is better to avoid thisterminology and always explain which of the two currencies ismeant when referring to premiums and discounts.
What is a forward swap deal?In order to see why a bank trades in forward swaps rather thanforward outrights, consider how the following swap and outrightrates change as the spot rate and interest rates move:spot rate
USDinterest rate
CHFinterest rate
92-day forwardoutright
92-day forwardswap
1.71001.72001.7200
5.0%5.0%4.5%
2.0%2.0%2.0%
1.69711.70701.7091
−0.0129−0.0130−0.0109
A movement of 100 points in the exchange rate from 1.7100 to 1.7200has affected the forward swap price only slightly (by 1 point). A changein the interest rate differential from 3.0% to 2.5%, however, haschanged it signiﬁcantly. Essentially, a forward swap is an interestrate instrument rather than a currency instrument: when a banktakes a forward swap position, it is taking an interest rate view ratherthan a currency view. If bank dealers traded outrights, they wouldbe combining two related but different markets in one deal, which isless satisfactory.So far, we have seen what the swap price is only as a number tobe added to or subtracted from the spot rate in order to achieve theoutright rate. However, the forward swap is also an instrument in itsown right. The swap deal itself is an exchange of one currency foranother currency on one date, to be reversed on a given future date.A swap deal is therefore always a deal to ‘sell and buy’ or ‘buy andsell’ a currency – i.e., to sell it for settlement spot and buy it back for
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Foreign exchange and money markets
settlement forward, or vice versa. The following example shows howthis ﬁts into the construction of a forward outright. Then we considerwhat the swap is on its own.Example 10A bank sells dollars 3 months forward outright to a counterparty,against Swiss francs. The bank can be seen as creating theoutright in the following way:Spot deal:
bank’s spot dealer sells dollars spot⎧⎪⎪⎨
Forward swap deal:Net effect:
⎪⎪⎩
bank’s forward dealer buys dollarsspot andbank’s forward dealer sells dollars3 monthsbank sells dollars 3 monthsforward outright
The customer in the example above thinks of the deal as a singledeal, with a single price, for a single settlement and receives only oneconﬁrmation, for the forward outright settlement. However, internally,the deal is split between the spot dealer’s trading book and the forwarddealer’s trading book.When a bank quotes a swap rate, it quotes in a similar manner to aspot rate: the bank’s forward dealer buys the base currency forwardon the left (at the same time as selling it spot), and sells the basecurrency forward on the right (at the same time as buying it spot).For example, on a USD/CHF 3-month forward swap quote of 22/20,the bank quoting the price does the following:−22sell dollars spotand buy dollars forward
/
−20buy dollars spotand sell dollars forward
The quoting bank always ‘sells and buys’ (in that order) the basecurrency on the left and ‘buys and sells’ the base currency onthe right.
A forward foreign exchange swap viewed on its own, rather than aspart of an outright, is therefore a temporary purchase or sale of one
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119
currency against another. An equivalent effect could be achieved byborrowing one currency for a given period, while lending the othercurrency for the same period. This is why the approximate formulashown earlier for the swap points reﬂects the interest rate differential(generally based on Eurocurrency interest rates rather than domesticinterest rates) between the two currencies, converted into foreignexchange terms.Suppose that a forward dealer has undertaken a similar deal tothe one above – bought and sold dollars (in that order) – but as aspeculative position, rather than in order to provide an outright toa customer. In this case, what interest rate view has he taken? Hehas effectively borrowed dollars and lent Swiss francs for the period.He probably expects US interest rates to rise (so that he can relendthem at a higher rate) and/or Swiss rates to fall (so that he canreborrow them at a lower rate). In fact the important point is that theinterest differential should move in the dollar’s favour. For example,even if US interest rates fall rather than rise, the dealer will stillmake a proﬁt as long as Swiss rates fall even more than dollarrates.Although only one single price is dealt (the swap price), the swaptransaction has two separate settlements:(i) A settlement on the spot value date(ii) A settlement on the forward value dateThere is no net outright position taken, and the spot dealer’s spreadwill therefore not be involved, but some benchmark spot rate willnevertheless be needed in order to arrive at the settlement rates. Asthe swap is a representation of the interest rate differential betweenthe two currencies quoted, as long as the near and far sides ofthe swap settlement preserve this differential, it does not generallymake a signiﬁcant difference which exact spot rate is used as a basefor adding or subtracting the swap points. The rate must, however,generally be a current rate. This is discussed further below – see thesection on ‘Historic rate rollovers’ and also Chapter 10.Example 11At the moment, 3-month dollar interest rates are higher than3-month sterling rates. You expect this difference to narrow.Rates are quoted to you as follows:GBP/USD spot:3-month swap:
1.4752/5880/86.
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Foreign exchange and money markets
You ‘buy and sell’ GBP 5 million (which is also selling and buyingdollars), spot against 3 months. This is equivalent to borrowingsterling and at the same time lending dollars. This will make youa proﬁt if rates move as you expect: for example, if sterling ratesrise, you could lend out the sterling at a higher rate, or if dollarrates fall, you could borrow the dollars at a lower rate.You therefore deal at 80 points because the bank quoting theprice ‘sells and buys’ the base currency on the left. You agree asettlement rate for spot as say 1.4755 (the mid-rate). Thereforethe two legs of the swap are settled at 1.4755 and 1.4835(=1.4755 + 0.0080):Value spot, you buy GBP 5 million against dollars at 1.4755andValue 3 months, you sell GBP 5 million against dollars at1.4835Later in the same day, the rates have moved as follows. Thedifferential has narrowed as you expected, and the spot rate hasalso moved:GBP/USD spot:3-month swap:
1.4910/2070/76.
You now close out your position to take your proﬁt, by sellingand buying GBP 5 million at 76 points. You agree settlementrates of 1.4915 and 1.4991 (=1.4915 + 0.0076):Value spot, you sell GBP 5 million against dollars at 1.4915andValue 3 months, you buy GBP 5 million against dollars at1.4991Your cashﬂows are therefore as follows:Spot
3 months
Original deal:Original deal:Close out:Close out:
+ GBP 5,000,000− USD 7,377,500− GBP 5,000,000+ USD 7,457,500
− GBP 5,000,000+ USD 7,417,500+ GBP 5,000,000− USD 7,495,500
Net cashﬂows:
+ USD
− USD
80,000
78,000
You could therefore be said to have a proﬁt of USD 2,000(= + USD 80,000 − USD 78,000).
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121
However, this does not take account of the time value of money(see Chapter 2). Assuming that there are 91 days in the 3-monthperiod and that the 3-month dollar interest rate is 5%, the NPVof the net cashﬂows is USD 2,973.53:USD 78,000 = +USD 2,973.53+ USD 80,000 − 911 + 0.05 ×360
A dealer expecting the interest rate differential to move in favourof the base currency (for example, base currency interest ratesto rise or variable currency interest rates to fall) will ‘buy andsell’ the base currency. This is equivalent to borrowing the basecurrency and depositing in the variable currency. And vice versa.
Valuation of a swap bookIn Example 11, we valued the result of two swaps, where the secondswap neatly offset the ﬁrst. In practice, a dealer will have many swapson his book, resulting in many cashﬂows in different currencies ondifferent dates. The entire book can be valued by calculating thepresent value of each cashﬂow separately and then adding up all thepresent values – some positive and some negative – including thoseof the cashﬂows in the dealer’s home currency, to calculate a netpresent value (NPV).
Historic rate rolloversWe have mentioned above that the settlement rates (spot and forward)for a forward swap deal must generally be based on a current marketspot rate. This is because many central banks require that banksunder their supervision use only current rates, except in occasionaland well-documented circumstances. The following example illustrates why a corporate customer might wish to use a historic raterather than a current rate, and the effect.Example 12In June, a US company sells USD 1 million forward outrightfor value 15 August against Swiss francs, at a forward outrightrate of 1.7250. This deal is done to cover the cost the companyexpects to pay for Swiss imports. On 13 August, the companyrealizes that it will not need to pay the Swiss francs to its supplier
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Foreign exchange and money markets
until a month later. It therefore rolls over the foreign exchangecover by using a forward swap – buying and selling dollars, spotagainst one month.On 13 August, the exchange rates are as follows:USD/CHF spot:31-day swap:
1.8166/7120/22
The company therefore buys and sells dollars at 1.8168 (spot)and 1.8168 + 0.0020 = 1.8188 (forward).The company’s cashﬂows will then be:15 August
15 September
sell USD 1,000,000buy CHF 1,725,000buy USD 1,000,000sell CHF 1,816.800
sell USD 1,000,000buy CHF 1,818,800
Net:sell CHF 91,800
sell USD 1,000,000buy CHF 1,818,800
The overall net result is that the company sells USD 1 millionagainst CHF 1,727,000 (=CHF 1,818,800 − CHF 91,800) – anall-in rate of 1.7270, which is effectively the original rate dealtof 1.7250 adjusted by the swap price of 20 points. The companymight, however, have a cashﬂow problem on 15 August, becausethere is a cash outﬂow then of CHF 91,800.The company might therefore prefer to request the bank tobase the swap on the historic rate of 1.7250 – dealing instead at1.7250 spot and 1.7270 forward. The cashﬂows would then be:15 August
15 September
sell USD 1,000,000buy CHF 1,725,000buy USD 1,000,000sell CHF 1,725,000
sell USD 1,000,000buy CHF 1,727,000
Net:
sell USD 1,000,000buy CHF 1,727,000
The overall net result is the same as before, but there is nocashﬂow problem.Underlying this arrangement, however, is an effective loanfrom the bank to the company of CHF 91,800 for 31 days. If thebank is, exceptionally, prepared to base the swap on a historic
Forward outrights and swaps
123
rate in this way, it needs to charge the company interest on thishidden loan. This interest would normally be incorporated intoa less favourable swap price.The reason many central banks discourage historic rate rollovers isthat they might help a bank’s customer to conceal foreign exchangelosses. If a customer has taken a speculative position which has madea loss, a historic rate rollover enables it to roll the loss over to a laterdate rather than realize it.As a result, if a bank does agree to a historic rate rollover, it mustgenerally insist that the reasons be agreed between senior management of the customer and the bank, with appropriate documentaryevidence of this.
Short datesFor convenience, we have repeated here a short part of the introductory chapter. Value dates earlier than 1 month are referred to asshort dates. There are certain regular dates usually quoted, and theterminology used is the same as in the deposit market, as follows:Overnight (O/N):Tom-next (T/N):Spot-next (S/N):Spot-a-week (S/W):
a deposit or foreign exchange swap from todayuntil tomorrowa deposit or foreign exchange swap fromtomorrow until the next day (spot)a deposit or foreign exchange swap from spotuntil the next daya deposit or foreign exchange swap from spotuntil a week later
‘Tomorrow’ means the next working day after today and ‘next’ meansthe next working day following (i.e. spot).Outright deals (as opposed to swaps) are referred to as ‘value today’,‘value tomorrow’, etc.Deals cannot always be done for value today. For example, whenLondon and European markets are open, Japanese banks have generally closed their books for today, so deals in yen can only be donefor value tomorrow. Similarly in London, most European currenciescan only be dealt early in the morning for value today, because of thetime difference and the mechanical difﬁculties of ensuring good value.For many currencies, even the market for value tomorrow generallycloses during the morning.
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Foreign exchange and money markets
In considering swaps and outrights for short dates later than thespot date, exactly the same rules apply as in calculating longer dates.However, confusion can arise in considering outrights for dates earlierthan spot – i.e., outright value today and outright value tomorrow.The rules are still the same in that the bank always ‘sells and buys’(in that order) the base currency on the left and ‘buys and sells’ thebase currency on the right – regardless of whether it is before or afterspot. The confusion can arise because the spot value date – effectivelythe baseline date for calculation of the outright rate – is the near datewhen calculating most forward prices. For value today and tomorrow,however, the spot date becomes the far date and the outright date isthe near date.Example 13A bank sells dollars for outright value tomorrow to a counterparty, against Swiss francs. The bank can be seen as creatingthe outright in the following way:tom-next deal:
bank’s forward dealer sells dollarstomorrow andbank’s forward dealer buys dollars spot
spot deal:
bank’s spot dealer sells dollars spot
net effect:
bank sells dollars outright tomorrow
It is useful to compare this with Example 10. Importantly, noticethat, because tomorrow is earlier than spot, the tom-next deal inExample 13 is ‘sell and buy’, whereas in Example 10 the swap dealwas ‘buy and sell’. In Example 10, the spot dealer and the forwarddealer both dealt on the right side of the quote. In Example 13,however, the spot dealer still deals on the right side of the price butthe forward dealer deals on the left side of the price. For example, ona USD/CHF tom-next quote of 2/1, the bank quoting the price doesthe following (this is the same way round as for all swaps):−2sells dollars tomorrowand buys dollars spot
/
−1buys dollars tomorrowand sells dollars spot
Swap prices for very short periods like O/N, T/N and S/N arevery small numbers. The forward points are therefore often lessthan 1 point and it is important to line them up correctly whenthey are being added to or subtracted from the spot. Sometimes
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125
they are quoted as fractions – for example, a price of ‘‘1 21 /1 14 ’’ means‘‘one and a half points/one and a quarter points’’ – and sometimesas decimals – for example, a price of ‘‘1.5/1.25’’ again means‘‘1.5 points/1.25 points’’. In this case, that part of the price which isimmediately before the decimal point should be lined up with the ﬁnaldigit of the spot price. If, for example, USD/JPY spot is 125.67/72and the S/N price is 1.5/1.25, they would be combined as follows:
Spot:S/N:Outright:
↓↓125.67 /125.720.015/ 0.0125125.665/125.7075↑↑
Example 14Spot USD/CHF:Overnight swap:Tom-next swap:1-week swap:
1.7505/101/ 341/ 1427/ 5
(i) Suppose a customer wishes to sell dollars for outright valueone week after spot. The bank spot dealer buys dollars for valuespot on the left at 1.7505. The bank forward dealer ‘sells andbuys’ dollars also on the left at