therefore depend partly on banks’ individual positions andhence their interest in quoting a price.Example 26What are the theoretical GBP/USD 3-year outright and forwardswap, based on the following?GBP/USD spot:GBP 3-year interest rate:USD 3-year interest rate:
1.41235.15%4.35%
Forward outrights and swaps
141
Forward outright = 1.4123 ×Forward swap = 1.4123 ×
1.04351.05151.04351.0515
3 = 1.3803
3−1
= −0.0320 = −320 points
Synthetic agreements forforward exchange (SAFEs)SAFES are used very little now, but we have included them here forcompleteness. A SAFE is an off-balance sheet forward-forward foreignexchange swap. There are two versions of a SAFE – an FXA and anERA.An FXA ( forward exchange agreement) exactly replicates theeconomic effect of a forward-forward in the cash market which isreversed at the ﬁrst settlement date of the forward-forward in orderto take a proﬁt or loss. A price for an FXA is quoted in the sameway as a forward-forward price, and is dealt in the same way. Aforward-forward swap results in two cash settlements, each for thewhole amount of the deal. An FXA, however, is settled in a manneranalogous to the way an FRA is settled. On the nearer of the twoforward dates, a settlement amount is paid from one party to theother to reﬂect the movement in rates between dealing and settlement,using an agreed settlement rate.The settlement formula ensures that the result is economically thesame as the proﬁt or loss would be with a cash forward-forward. Todo so, it takes account of the movement in the spot rate from dealingto settlement, as well as the movement in the forward swap points.This is because, although a forward dealer takes a position on thebasis of his expectations of swap movements, his proﬁt or loss is alsoaffected to some extent by spot rate movements. The reason for thisis discussed in Chapter 10. As with an FRA, the settlement formulainvolves an element of discounting, because the settlement is madeat the beginning of the forward-forward period.An FXA can have equal or unequal notional base currency amountsat each end of the swap.An ERA (exchange rate agreement) price is exactly the same as anFXA price, and allows for a discounted settlement to be made at thebeginning of the forward-forward period in the same way as an FXA.
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The ERA settlement, however, deliberately takes no account of themovement in the spot rate, and the settlement formula is correspondingly simpler. The settlement amount is simply the notional amountof the contract multiplied by the change in the swap rate. With anERA, only one notional base currency amount is involved.The two instruments can therefore be compared as follows:An FXA replicates exactly the economic effect of a cash forwardforward. In a trading strategy that requires a forward-forward,an FXA is an alternative.An ERA may be used to trade movements in forward swap priceswhen the trader speciﬁcally wishes the result to be unaffectedby movements in the spot rate. This does not exactly replicate aforward-forward.
Advantages of SAFEsThe advantages of a SAFE lie in the problems which arise on creditlines and balance sheet utilization. In the absence of an appropriatenetting agreement, when a bank deals forward-forward, its creditlines to and from the counterparty are generally utilized to the extentof twice the notional credit amount applied to the deal – once foreach leg of the forward-forward. Between dealing date and the ﬁrstsettlement date, however, the real risk might be far less than this,because the two legs of the deal largely offset each other. The creditexposure allocated to a SAFE, as a contract for differences, willbe far less. The capital utilization requirements (see Chapter 12) aresimilarly reduced. Rather than having two deals on the balance sheet,there are none.A further advantage of an ERA arises if a forward trader wishes totrade the forward swap points without needing to hedge the effect ofpotential spot rate movements (although this does not avoid the effectthat a signiﬁcant spot rate movement has on the swap price itself).The FXA settlement amount(as an amount of the variable currency)Settlement amount = ﬁrst amount⎞⎛(outrightexchange rate − settlement spot rate)⎟⎜+ swap price dealt − settlement swap price⎟×⎜⎝days in swap period ⎠1 + variable currency LIBOR ×variable year− second amount × (outright exchange rate− spot price used for settlement)
Forward outrights and swaps
143
The ERA settlement amount(as an amount of the variable currency):Settlement amount = base currency amountswap price dealt − settlement swap price×days in swap period1 + variable currency LIBOR ×variable yearThe settlement amount is paid by the seller of the FXA orERA to the buyer (or vice versa if it is a negative amount),where the buyer is the party which ‘buys and sells’ the basecurrency.
In the above settlement formulas:• ‘First amount’ is the base currency amount transacted at thebeginning of the swap.• ‘Second amount’ is the base currency amount transacted at theend of the swap.(These amounts can be the same but do not need to be.)• ‘Outright exchange rate’ is the outright, to the near date of theforward-forward period, when the FXA is transacted.• ‘Settlement spot rate’ is the reference spot agreed 2 working daysbefore the swap period.• ‘Settlement swap price’ is the reference swap price agreed 2working days before the swap period.• ‘LIBOR’ is for the swap period, agreed 2 working days before theswap period.Example 27At the moment, dollar interest rates are lower than sterling rates.You expect this difference to narrow and therefore decide to sella 1v3 SAFE for GBP 5 million. The 1v3 month period is 61 days.Rates are quoted to you as follows:GBP/USD 1-month outright:1v3 swap:
1.467586/80.
You sell the SAFE at −80 points. Two business days before the1-month settlement date, rates are as follows:
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Foreign exchange and money markets
GBP/USD spot:2-month swap:USD 2-month LIBOR:
1.4915−76.4.23%.
If you have used an FXA, the settlement amount will be a proﬁtof USD 1131.79 (the settlement formula gives a negative amountso it is payable by the buyer to the seller):⎞⎛(1.4675 − 1.4915)⎜ + (−0.0080 − −0.0076) ⎟ ⎟5,000,000 × ⎜⎠⎝611 + 0.0423 ×360− 5,000,000 × (1.4675 − 1.4915) = −1,131.79If you have used an ERA, the settlement amount will be a proﬁtof USD 1,985.77:(−0.0080 − −0.0076) = −1,985.775,000,000 × 611 + 0.0423 ×360
Summary of uses of forwardFX instrumentsHedgingA company which expects to pay or receive foreign currency at afuture date can lock in the exchange rate for doing this with aforward outright. If the currency requirement is earlier than spotthen, depending on the currency and provided the deal is done earlyenough, the company can deal for outright value today or tomorrow.If a company has already transacted a forward deal but wishes todelay settlement because the commercial requirement has not arisenas early as originally anticipated, it can roll the maturing deal forwardwith a swap. If the requirement is earlier than expected, it can rollit nearer with a swap the other way round. If the need to adjustthe date in this way is seen ahead of time, the company can use aforward-forward in the same way.Time options, while generally rather cost-inefﬁcient, provide ﬂexibility to a hedger. NDFs provide a mechanism for hedging currencieswhich are not fully convertible.A bank dealer can use forwards to hedge his existing positions. Atrading bank which needs to provide an outright for a customer will
Forward outrights and swaps
145
construct it from a spot and a swap. However, a dealer in a smallbank covering a customer position might himself ask another bank,more active in foreign exchange, for a forward outright price.
SpeculationA dealer wishing to take a strategic (i.e. medium-term) speculativeposition in a currency, will use a forward outright, rather than a spotdeal which would continually require rolling over with swaps.Forward swaps are essentially interest rate instruments. A dealerwishing to speculate on the interest rate differential between twocurrencies will ‘buy and sell’ or ‘sell and buy’. Frequently, a dealer willestablish forward-forward positions, either directly for this purpose,or as a result of two or more swap deals he has transacted withcustomers in different maturities.
ArbitrageThe relationship between interest rates and swap prices allows forthe possibility of arbitrage. This is considered in Chapter 9.
Exercises1
Which of the following are true?(a)(b)
(c)
(d)
(e)
(f)
If the 6-month USD/CHF forward swap points change from125/120 to 135/130, USD interest rates might have fallen.If the 3-month forward swap points are greater on the leftthan the right, then the variable currency has a higherinterest rate than the base currency.The 2-month GBP/USD swap points are 67/72. If dollarinterest rates then rise but nothing else changes, the swappoints will get bigger.If the 1-month forward points for AUD/CAD are 123/118,the Canadian dollar is at a forward discount against theAustralian dollar.If the 3-month EUR/GBP swap is par and the 3-month GBPinterest rate is 5.0%, then the 3-month euro interest rate isalso 5.0%.An FX spot trader who went home last night leaving an openposition will adjust his position at the start of today usingO/N and T/N swaps.
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Foreign exchange and money markets
2
What should the mid-rate theoretically be for the USD/CHF 3month outright, given the following? The 3-month period is92 days.USD/CHF spot:USD 3-month interest rate:CHF 3-month interest rate:
3
1.7120/26,5.10/5.20%2.70/2.80%
What is the two-way 3-month swap price for USD/CHF, based onthe following borrowing and lending rates? The 3-month periodis 91 days.USD/CHF spot:USD 3-month interest rate:CHF 3-month interest rate:
1.7120/26,5.10/5.20%2.70/2.80%
4 You wish to take a particular speculative position and ask abank for a 3-month USD/CHF swap price. It is quoted to youas 127/122 and you deal at 127. What is your expectation formarket movements?5
EUR/USD forward swaps are as follows. What can you say aboutthe euro and dollar yield curves?6 months:12 months:
10/55/10
6 You are a dealer and quote a customer 56/61 for aEUR/GBP 6-month swap (182 days). The customer buys andsells GBP 10 million and you base the spot on 0.6215.You immediately ask another bank for a 6-month price becauseyou wish to cover this position. You deal on the price quoted toyou of 58/62 and you base the spot on 0.6205.What is your resulting proﬁt or loss? Euro interest rates are4% and sterling interest rates are 6%.7
Given the following prices:USD/CADUSD/SEK(a)
(b)
spot:spot:
1.5671/7710.3458/68
6-month swap 30/336-month swap 70/67
What is the two-way 6-month forward outright price forCAD/SEK and at what price can a customer sell Canadiandollars?What is the two-way 6-month swap price for CAD/SEK, andat what price can a customer sell and buy Canadian dollars?
Forward outrights and swaps
147
8 You are a dealer and quote a 6-month GBP/JPY swapto a customer as 435/425. The customer buys and sellsGBP 1,000,000, based on a spot of 178.10. You cover thisposition using two 6-month swaps quoted to you as follows:73/69 for GBP/USD (the deal is for GBP 1,000,000 and the spotis set at 1.4260)240/235 for USD/JPY (the deal is for USD 1,426,000 and thespot is set at 124.85).What are your net cashﬂows spot and forward?9 You are quoted all the following rates. What is the best rateat which you can sell sterling against yen 6 months forwardoutright, and how do you achieve it?GBP/JPYGBP/USDUSD/JPY10
spot:spot:spot:
178.05/151.4255/65124.80/90
6-month swap:6-month swap:6-month swap:
435/42573/69240/235
Given the following rates for GBP/USD:Spot:O/N:T/N:S/N:3 months:
1.4253/581.80/1.302.10/1.602.20/1.70183/178
(a)
At what rate can a customer buy sterling for outright valuethe day after spot?(b) At what rate can a customer sell dollars for outright valuetomorrow?(c) At what rate can a customer sell sterling for outright valuetoday?(d) What is a two-way forward-forward swap from the day afterspot until 3 months after spot?(e) What is a two-way swap from today until 3 months afterspot?11 Today is Monday 27 October 2003. What are the spot and1 month value dates?12 Today is Wednesday 25 February 2004. What are the spot and1-month value dates?13 You need to sell and buy dollars against sterling forward-forward2v5, given the following:
148
Foreign exchange and money markets
GBP/USD spot:2-month swap:3-month swap:5-month swap:
1.4235/4515/118/312/18
(a)
What two-way forward-forward swap price do you expect tobe quoted to you?(b) At what price do you deal?(c) What settlement rates might be set for the two legs of thedeal?14
What is the two-way time option outright price for deliverybetween 3 and 5 months, given the following prices?GBP/USD spot:3-month swap:5-month swap:
15
1.4235/458/312/18
You transact an NDF to buy HUF 1,000 million against USD at301.55, for value 17 August. On 15 August, the spot rate forsettlement of the NDF is 295.71. What is your proﬁt or loss inUS dollars?
9
Hedging swapswith deposits,FRAsand futures,covered interestarbitrageand creatingsynthetic FRAsThe link between interest rates and forward swaps explained in theprevious chapter allows dealers and end-users of the market to takeadvantage of opportunities in different markets, in two ways. Firstly,it enables a dealer with a forward swap position to hedge this positionby using money market borrowings and deposits, if it turns out to becheaper or easier to do so.Secondly, it enables a borrower or investor to borrow or invest in adifferent currency from that in which he originally intended to deal,and then to convert this transaction to the intended currency byusing a swap. Again, he would do so if the result were a better all-inrate, or if it were easier to arrange.
150
Foreign exchange and money markets
These two strategies are in fact essentially the same idea, viewedfrom different angles; the second strategy is known as covered interestarbitrage. Both depend on the fact that an FX swap is broadly equivalent to a borrowing plus a deposit.Both these ideas can be extended from forwards to forwardforwards. This means that a forward-forward swap position can behedged by using FRAs and futures, and an FRA in one currency canbe created from, or arbitraged against, an FRA in another currencyby using forward-forward swaps.
Hedging FX forwards usingborrowings and depositsHedging a forward swapWhen a dealer buys and sells one currency against another, he istaking a position economically very similar to borrowing the ﬁrstcurrency and lending the second. Therefore, he can hedge the swapposition by doing the opposite – i.e. lending the ﬁrst currency andborrowing the second.Example 1A dealer buys and sells USD 10 million against yen, spot against3 months (91 days) at 118.50 and 117.25.He hedges the position by lending USD 10 million for 3 monthsat 4.8% and borrowing JPY 1,185,000,000 for three months at0.5%. The total proceeds due back from the lending, and therepayment amount on the borrowing, are as follows:Interest = USD 10,000,000 × 0.048 ×
91= USD 121,333360
Principal + interest = USD 10,000,000 + USD 121,333= USD 10,121,333Interest = JPY 1,185,000,000 × 0.005 ×
91= JPY 1,497,708360
Principal + interest = JPY 1,185,000,000 + JPY 1,497,708= JPY 1,186,497,708
Hedging swaps
151
The cashﬂows from the deal and the cover are therefore asfollows:spot
3 months
original deal: + USD10,000,000 − USD10,000,000− JPY 1,185,000,000 + JPY 1,172,500,000lend dollars:borrow yen:
− USD10,000,000 + USD10,121,333+ JPY 1,185,000,000 − JPY 1,186,497,708
net cashﬂows:
+ USD− JPY
121,33313,997,708
If the dealer is dollar-based, for example, he could then removethe remaining small risk by buying JPY 13,997,708 3 monthsforward outright. If the rate for this forward outright is 117.25,this would give additional cashﬂows as follows:forward outright hedge:
− USD+ JPY
119,38313,997,708
net proﬁt:
+ USD
1,950
This gives the dealer a net proﬁt of USD 1,950 after 3 months.The dealer is now hedged, as the result measured in dollars isunaffected by any subsequent change in rates. The result is a smallproﬁt, rather than zero, because the rate of the original swap deal(−125 points) is not exactly the same as the rate implied by theborrowing and lending interest rates – see ‘Why bother?’ below.The small forward outright purchase of JPY 13,997,708 in theprevious example is intended to ‘tidy up’ the position by removingany residual currency risk. In practice, this amount might be leftunhedged. For completeness however, we will continue to assume inour examples here that the bank does want to hedge this completely.If this amount is to be hedged, using a forward outright as a hedgeis rather messy. An alternative would be to use a small spot hedgerather than a small forward outright hedge. In this case, however, inorder to hedge completely, the amounts of the borrowing and lendingwould need to be slightly different. It would be necessary to calculatethe amount of dollars it is necessary to lend at the beginning, inorder to achieve proceeds of exactly USD 10,000,000 after 3 months.Similarly, it would be necessary to calculate the amount of yen it is
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Foreign exchange and money markets
necessary to borrow at the beginning, in order to achieve a repaymentof exactly JPY 1,172,500,000 after 3 months. This is effectively thesame as calculating present values (see Chapter 2) and can be seenin the following example.Example 2With the same original deal as in the previous example, thedealer hedges by matching the 3-month FX cashﬂows exactlywith a borrowing and a deposit, and then doing a spot hedge forthe small unmatched amount of yen, which can be seen to beJPY 13,980,039.USD 10,000,000Amount of dollars to lend = 911 + 0.048 ×360= USD 9,880,121JPY 1,172,500,000Amount of yen to borrow = 911 + 0.005 ×360= JPY 1,171,019,961The cashﬂows from the deal and the cover are then as follows:spot
3 months
original deal: + USD10,000,000 − USD10,000,000− JPY 1,185,000,000 + JPY 1,172,500,000lend dollars: − USD9,880,121 + USD10,000,000borrow yen: + JPY 1,171,019,961 − JPY 1,172,500,000spot hedge:
− USD+ JPY
117,97513,980,039
net proﬁt:
+ USD
1,904
This second example gives the dealer a net proﬁt of USD 1,904,rather than the USD 1,950 in the ﬁrst example. The difference arisesin two ways. Firstly, the USD 1,904 proﬁt is value spot, whereasthe USD 1,950 proﬁt is in 3 months’ time. The present value of theUSD 1,950 (i.e. the worth of that cashﬂow now – see Chapter 2) is infact USD 1,927, as follows:
USD 1,950 = USD 1,927911 + 0.048 ×360
Hedging swaps
153
Secondly, the forward swap price and interest rates in the examplesare slightly out of line. That is, the dollar rate of 4.8% and the yen rateof 0.5% do not correspond exactly to the swap price of −125 points(the difference between 118.50 and 117.25). Indeed, this might bethe reason why the dealer is using the borrowing and deposit (ratherthan a swap) to hedge the position in the ﬁrst place. The sizes of theborrowing and deposit are slightly greater in the ﬁrst example thanin the second example, so that slightly greater advantage is taken ofthis discrepancy, leading to a slightly greater proﬁt.Why bother?The dealer could have hedged his original forward swap position byusing another swap. How did he know that he would beneﬁt by usinga borrowing and deposit instead? He could calculate the effectiveswap price achieved via the borrowing and deposit by using exactlythe same formula as in the previous chapter for deriving swap pointsfrom interest rates:Forward swap⎞ ⎛⎞⎞⎛⎛basevariable⎜⎜ currency days ⎟ ⎜ currency days ⎟⎟⎟ ⎜⎟⎟⎜⎜⎝⎝ interest × year ⎠ − ⎝ interest × year ⎠⎠raterate= spot × days1 + base currency interest rate ×yearThis gives:Forward swap effectively achieved 9191− 0.048 ×0.005 ×360360= 118.50 ×= −1.2726911 + 0.048 ×360The forward swap achieved synthetically is therefore −1.2726, whichis −127.26 points. Presumably, therefore, the dealer has chosen tohedge via the borrowing and deposit because the straightforwardswap price available for hedging is not as good as −127.26 points.In practice, a bank would need to take account also of the balancesheet and capital adequacy implications of hedging by using depositsin this way – see Chapter 12.The original deal was transacted at −125 points. If the borrowingand deposit hedge is used, the dealer expects a proﬁt after 3 months of2.26 points (the difference between −125 points and −127.26 points).
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Foreign exchange and money markets
This is JPY 226,000, which has a present value of JPY 225,715, whichis worth USD 1,904 as expected:10,000,000 × JPY 0.0226 = JPY 226,000JPY 226,000 = JPY 225,715911 + 0.005 ×360225,715= 1,904118.50A foreign exchange swap position to buy and sell one currencyagainst another can be hedged by lending the ﬁrst currencyand borrowing the second currency, plus small spot or outrighthedges to bring net foreign currency cashﬂows to zero.
Hedging a forward outrightA forward outright can be hedged in the same way. A forward outrightis constructed from – and normally hedged by – a spot deal and aswap deal. The swap hedge can be replaced by a borrowing and adeposit as above.Example 3A foreign exchange dealer sells USD 10 million 3 monthsoutright to a customer, against yen at 117.25. The US dollardeposit dealer in his own bank is short of dollars and is preparedto pay the foreign exchange dealer 4.8% to borrow dollars fromhim. The foreign exchange dealer therefore covers his forwardoutright position by buying dollars spot in the market at 118.50,lending dollars to his colleague, and borrowing yen from themarket at 0.5%. His cashﬂows are as follows:spot
− USD10,000,000+ JPY 1,172,500,000
original deal:spot hedge:
+ USD10,000,000− JPY 1,185,000,000
lend dollars:borrow yen:
− USD10,000,000+ JPY 1,185,000,000
net cashﬂows:
3 months
+ USD10,121,333− JPY 1,186,497,708+ USD− JPY
121,33313,997,708
Hedging swaps
155
Exactly as in Examples 1 and 2, the remaining USD/JPY riskcan be hedged by a spot or forward deal.
A forward outright position to sell one currency against anothercan be hedged by buying the ﬁrst currency spot, lending theﬁrst currency and borrowing the second currency, plus smallspot or outright hedges to bring net foreign currency cashﬂowsto zero.
Hedging FX forward-forwardswith FRAs or futuresIn running a forward book, a dealer will normally have forwardforward positions. Suppose, for example, that a dealer does only twodeals, each in response to a customer. In the ﬁrst deal, he buys andsells USD 10 million against yen, spot against 1 month. In the seconddeal, he sells and buys USD 10 million against yen, spot against4 months. The dealer now has a net forward-forward position inUSD 10 million, 1 month against 4 months. Alternatively, the dealermight have established the same forward-forward position withoutany customer-related business, purely as a speculative position.If the dealer wishes to hedge this position, he could do so simplyby buying and selling USD 10 million, 1 month against 4 months.Alternatively, he could hedge the position by borrowing and lending,as in the examples above. Because it is a forward-forward positionrather than a spot-to-forward position, however, the borrowing andlending must also be forward-forward, to match the cashﬂow timings.Another approach, which uses the balance sheet less, is to use FRAsor futures, because these are exactly off-balance sheet equivalents ofcash forward-forward borrowings. These instruments are covered inChapter 6.The following example is parallel to Example 2, with the sameexchange rates, but with the cashﬂows in the future rather thanbased on spot.Example 4A dealer buys and sells USD 10 million against yen, 1 monthagainst 4 months (91 days) at 118.50 and 117.25.
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Foreign exchange and money markets
He hedges the position by selling a 1v4 FRA for USD 9,880,121at 4.8% and buying a 1v4 FRA for JPY 1,171,019,961 at0.5%.As in Example 2, there is another small FX risk to be hedged.Consider what the cashﬂows would be if, instead of using a yenFRA, the dealer used a cash forward-forward yen borrowing.There would be a cash inﬂow of 1,171,019,961 after 1 monthand a cash outﬂow of JPY 1,172,5