market has historically quotedmostly against US dollars, so reducing the number of individual ratesthat needed to be quoted. The exchange rate between any two nonUS dollar currencies could then be calculated from the rate for eachcurrency against US dollars. Such a rate between any two currencies,neither of which is the dollar, is known as a cross-rate.Some of these cross-rates (for example, euro/sterling, euro/yen,euro/Swiss franc) have, however, increasingly been traded betweenbanks in addition to the dollar-based rates. This sometimes reﬂectsthe importance of the relationship between the pair of currencies.The economic relationship between the Swiss franc and the euro,for example, is closer than the relationship between the Swiss francand the dollar. It is therefore more true nowadays to say that the
96
Foreign exchange and money markets
dollar/franc exchange rate is a function of the euro/dollar rate andthe euro/franc rate, rather than that the euro/franc rate is a functionof the euro/dollar rate and the dollar/franc rate. The principle ofcalculating one rate from two others remains the same, however. Thecalculations are explained below.
Bid and offer ratesAs in other markets, a bank normally quotes a two-way price, wherebyit indicates both at what level it is prepared to buy the base currencyagainst the variable currency (the bid for the base currency – acheaper rate), and at what level it is prepared to sell the base currencyagainst the variable currency (the offer of the base currency – a moreexpensive rate). For example, if a bank is prepared to buy 1 US dollarfor 1.6375 Swiss francs, and sell 1 US dollar for 1.6385 Swiss francs,the USD/CHF rate would be quoted as ‘1.6375/1.6385’.In the spot market, the price is always quoted so that the quotingbank buys the base currency on the left. This is the quoting bank’sbid for the base currency, which is the lower number. Similarly,the quoting bank always sells the base currency – its offer for thebase currency, which is the higher number – on the right. If thebank quotes such a rate to a company or other counterparty,the counterparty would sell the base currency on the left, and buythe base currency on the right – the opposite of how the bank itselfsees the deal. The universal rule is that the party quoting the pricedeals on the side which is more advantageous to it, while the partyasking for the price – if it decides to deal – is obliged to deal on theside which is less advantageous to it.As the market moves very quickly, dealers need to deal with greatspeed and therefore abbreviate when dealing. For example, if onedealer wishes to buy USD 5 million from another who is quotinghim a USD/CHF price, he will say simply ‘‘5 mine’’; this means ‘‘Iwish to buy from you 5 million of the base currency and sell theother currency, at your offered price’’. Similarly, if he wishes to sellUSD 5 million, he will say simply ‘‘5 yours’’, meaning ‘‘I wish to sellyou 5 million of the base currency and buy the other currency, atyour bid price’’.Example 1Bank A asks Bank B and Bank C each for a price in EUR/USD.Bank B quotes 0.9349/54.Bank C quotes 0.9350/55.
Spot foreign exchange
97
Bank A wishes to buy EUR 5 million. The quoting bank willtherefore be selling EUR, the base currency. If Bank A choosesto deal on either of these prices, it will therefore deal on the rightside. Bank A is therefore looking for the most attractive rightside price, which in this case is Bank B’s price at 0.9354.Bank B therefore replies ‘‘Nothing thanks.’’ to Bank C andreplies ‘‘5 mine’’ to Bank B. He has then bought EUR 5 millionfrom Bank B at 0.9354.The difference between the two sides of the quotation is known asthe spread and represents the dealer’s proﬁt for being willing to takethe risk of quoting prices to other parties. Historically, a two-wayprice in a cross-rate would have a wider spread than a two-way pricein a dollar-based rate, because the cross-rate constructed from thedollar-based rates would combine both the spreads. Now, however,the spread in say a euro/Swiss franc price might be proportionally narrower than a dollar/franc spread, because it is more theeuro/franc price that is driving the market, as noted above, than thedollar/franc price.Dealers generally operate on the basis of small percentage proﬁtsbut large turnover. These rates will be good for large, round amounts.For very large amounts, or for smaller amounts, a bank wouldnormally quote a wider spread. The amount for which a quotation isgood (i.e. a valid quote on which the dealer will deal) will vary to someextent with the currency concerned and market conditions.Rates are often quoted to 1/100th of a cent etc. (known as a pointor a pip). For example, the US dollar/Swiss franc rate would usuallybe quoted to four decimal places – for example, ‘‘1.5375/1.5385’’.This depends on the size of the number, however, and in the case ofUSD/JPY, for example, which might be quoted say ‘‘105.05/105.15’’,‘‘15 points’’ means 0.15 yen. One point is thus one unit of the lastdecimal place quoted.Example 2You buy USD 1 million against CHF at 1.6920 and sellUSD 1 million against CHF at 1.6921. You have made 1 pointproﬁt, which is CHF 100:1,000,000 × 0.0001 = 100You also buy USD 1 million against JPY at 109.20 and sellUSD 1 million against JPY at 109.21. Again, you have made
98
Foreign exchange and money markets
1 point proﬁt, which is JPY 10,000:1,000,000 × 0.01 = 10,000As the ﬁrst three digits of the exchange rate (known as the bigﬁgure) do not change in the short term, dealers generally do notmention them when dealing in the interbank market. In the exampleabove (1.6375/1.6385) the quotation would therefore be given assimply ‘‘75/85’’. However, when dealers are quoting a rate to a corporate client they will often mention the big ﬁgure also. In this case, thequotation would be ‘‘1.6375/55’’.If the bid and offer prices are close to a round number, it cansometimes appear that the right side is smaller than the left side.For example, the price might be abbreviated as ‘‘1.6395/05’’. Thisin fact means ‘‘1.6395/1.6405’’ and might be expressed as ‘‘Ninetyﬁve/o ﬁve, around one sixty-four’’. Similarly, a price of ‘‘1.6390/00’’means ‘‘1.6390/1.6400’’ and might be expressed as ‘‘One sixty-three,ninety/the ﬁgure’’, where ‘‘the ﬁgure’’ means ‘‘00’’.
Some more terminologyA long position is a surplus of purchases over sales of a givencurrency – i.e., a position which beneﬁts from a strengthening ofthat currency. Similarly, a short position is a surplus of sales overpurchases of a given currency, which beneﬁts from a weakening ofthat currency. A square position is one which is neither long norshort – i.e. one in which the sales and purchases are equal.A yard of a currency is an American billion units of that currency(i.e. 1,000,000,000 units).Cable is a nickname for the sterling/US dollar exchange rate.If one party asks another for a two-way price and then chooses todeal on the bid side of the price, he is said to hit the bid. If he choosesto deal on the offer side of the price, he is said to lift the offer.Occasionally a dealer will narrow the bid/offer spread to zero – i.e.he will quote a single price and the party asking for the price canchoose whether he will buy or sell at that price. This is known as achoice price.If a dealer quoting puts his price under reference, it means that thecounterparty must ask again for a reconﬁrmation of the price beforedealing on it.If a party who has asked for a price says ‘‘My risk’’, he is acknowledging that the price may change before he has accepted it – generallybecause he knows that he may not be able to respond immediately
Spot foreign exchange
99
as to whether or not he will choose to deal on the price. If a dealersays ‘‘Off!’’, he means that the last price he quoted is no longervalid.
Position-keepingTo earn proﬁt from dealing, the bank’s objective is clearly to sell thebase currency at the highest rate it can against the variable currencyand buy the base currency at the lowest rate.
Example 3You are a dealer and are long of USD 4 million against CHF at1.6612. You want to close this position because you expect thedollar to weaken.You therefore ask another bank for a USD/CHF price and arequoted 1.6610/15. You decide that you will deal on this price.You need to sell US dollars, so that the quoting dealer is buyingdollars, the base currency. You therefore hit his bid at 1.6610.You have a net loss of CHF 800:CHF
USDOriginal position:Deal to close:Net result:
+4,000,000−4,000,000
at 1.6612:at 1.6610:
−6,644,800+6,644,000−800
Example 4You have the same original situation as in the previous example.This time, however, another bank calls you to ask for a price.The market is currently 1.6610/15. What price should you quotein order to encourage the other bank to buy dollars from you,so that your position will be squared up, which is what youwant?You hope that the other dealer will lift your offer and nothit your bid. You should therefore show him a two-way pricewith a more attractive offer than the market generally, but anunattractive bid. You might therefore quote, say, 1.6608/13 toencourage him to deal at 1.6613.
100
Foreign exchange and money markets
At any time, a dealer needs to know what is his position resultingfrom the net of all the deals he has undertaken during the day so far.He also needs to know what is the average exchange rate of this netposition, so that he can compare it with the current market rate tosee whether or not the position is proﬁtable. At the end of the day, hemight not close out the position, but will in that case need to markto market the position – i.e. calculate the unrealized proﬁt or loss onthe position so far. This is achieved by calculating what the proﬁt orloss would be if he did in fact close out the position out at the currentrate (i.e. the end-of-day closing market rate).
Example 5You undertake three spot deals in USD/CHF as follows.Sell USD 4 million at 1.6723Buy USD 1 million at 1.6732Buy USD 5 million at 1.6729The market closes at 1.6730.What is your position? What is the average rate of this position? What is your net proﬁt or loss?CHF
USD−4,000,000+1,000,000+5,000,000Position:
+2,000,000
+6,689,200−1,673,200−8,364,500−3,348,500
3,348,5002,000,000=1.67425
Average rate:−2,000,000Loss:
at 1.6723:at 1.6732:at 1.6729:
at 1.6730:
+3,346,000−2,500
The position is therefore long USD 2 million. The average rateis 1.67425. The loss is CHF 2,500. This loss could be expressedin US dollars by converting it into US dollars at the spot rate,or in any other currency by converting it at the appropriate spotrate.
Spot foreign exchange
101
Reciprocal ratesAny quotation with a particular currency as the base currency canbe converted into the equivalent quotation with that currency as thevariable currency by taking its reciprocal. Thus a USD/CHF quotationof 1.4375/1.4385 can be converted to a CHF/USD quotation of(1 ÷ 1.4375)/(1 ÷ 1.4385). However, this would still be quoted with asmaller number on the left, so that the two sides of the quotationare reversed: 0.6952/0.6957. In every case, the bank buys the basecurrency against the variable currency on the left, and sells the basecurrency against the variable currency on the right.Example 6The AUD/CAD rate is 0.7954/0.7959. What is the CAD/AUDrate?1 ÷ 0.7954 = 1.25721 ÷ 0.7959 = 1.2564Therefore the CAD/AUD rate is 1.2564/1.2572
Cross-rate calculationsAs mentioned earlier, it is often necessary to calculate an exchangerate between two currencies from two other rates, because onlya small proportion of possible currency pairs are regularly tradedinterbank. Frequently, but not always, it is the dollar-based rateswhich serve as the starting point for these calculations.Example 7Given the following rates, what is the CAD/CHF rate?USD/CHFUSD/CAD
1.6348/531.5497/02
The left side (i.e. the bid side) of the resulting CAD/CHF rate iswhere the quoting bank buys CAD and sells CHF. The bank’sUSD/CAD dealer buys CAD (the same as selling USD) on theright side of his own price – i.e. 1.5502. The bank’s USD/CHFdealer sells CHF (the same as buying USD) on the left side of hisown price – i.e. 1.6348.
102
Foreign exchange and money markets
Each USD 1 is worth CAD 1.5502 and is also worthCHF 1.6348. Therefore the rate between CAD and CHF is theratio between these two numbers:1.6348 ÷ 1.5502 = 1.054571.0546 is therefore the left side of the resulting CAD/CHF price.Similarly, the right side is derived from the right side of theUSD/CHF price and the left side of the USD/CAD price:1.6353 ÷ 1.5497 = 1.05524The CAD/CHF price is therefore 1.0546/52. Note that in practice a dealer would probably round down the left price(to 1.0545 in this example) and round up the right price(to 1.0553) to ensure that he does not make a loss. Forsimplicity however, we have used normal rounding rules inthis book.In summary, to calculate a spot rate from two other rates whichshare the same base currency (in our example this was USD), divideopposite sides of the exchange rates. Following the same logic showsthat to calculate a spot rate from two other rates which share thesame variable currency (in the following example this is also USD),we again need to divide opposite sides of the exchange rates:Example 8Given the following rates, what is the GBP/NZD rate?GBP/USDNZD/USD
1.4320/250.4460/65
The left side (i.e. the bid side) of the resulting GBP/NZD rate iswhere the quoting bank buys GBP and sells NZD. The bank’sGBP/USD dealer buys GBP on the left side of his own price – i.e.1.4320. The bank’s NZD/USD dealer sells NZD on the right sideof his own price – i.e. 0.4465.Each GBP 1 is worth USD 1.4320. Each NZD 1 is worthUSD 0.4465. Therefore the rate between GBP and NZD is theratio between these two numbers:1.4320 ÷ 0.4465 = 3.20723.2072 is therefore the left side of the resulting GBP/NZD price.Similarly, the right side is derived from the right side of the
Spot foreign exchange
103
GBP/USD price and the left side of the NZD/USD price:1.4325 ÷ 0.4460 = 3.2119The GBP/NZD price is therefore 3.2072/19
Finally, to calculate a cross-rate from two rates where the commoncurrency is the base currency in one quotation but the variablecurrency in the other, following the same logic through shows thatwe multiply the same sides of the exchange rates:
Example 9Given the following rates, what is the GBP/CHF rate?GBP/USDUSD/CHF
1.4320/251.6348/53
The left side (i.e. the bid side) of the resulting GBP/CHF rate iswhere the quoting bank buys GBP and sells CHF. The bank’sGBP/USD dealer buys GBP on the left side of his own price – i.e.1.4320. The bank’s USD/CHF dealer sells CHF (the same asbuying USD) on the left side of his own price – i.e. 1.6348.Each GBP 1 is worth USD 1.4320. Each of these USD is worthCHF 1.6348. Therefore the rate between GBP and CHF is theproduct of these two numbers:1.4320 × 1.6348 = 2.34102.3410 is therefore the left side of the resulting GBP/CHF price.Similarly, the right side is derived from the right side of theGBP/USD price and the right side of the USD/CHF price:1.4325 × 1.6353 = 2.3426The GBP/CHF price is therefore 2.3410/26To calculate an exchange rate by combining two othersFrom two rates with the same base currency or the same variablecurrency: divide opposite sides of the exchange rates. See thenext box for deciding which exchange rate to divide by whichFrom two rates where the base currency in one is the sameas the variable currency in the other: multiply the same sides ofthe exchange rates.
104
Foreign exchange and money markets
The construction of one exchange rate from two others in this waycan be seen algebraically:Given two exchange rates A/B and A/C, they can be combinedas follows:B/C = A/C ÷ A/BGiven two exchange rates B/A and C/A, they can be combinedas follows:B/C = B/A ÷ C/AGiven two exchange rates B/A and A/C, they can be combinedas follows:B/C = B/A × A/Cand
C/B = 1 ÷ (B/A × A/C)
When dividing, use opposite sides. When multiplying, use thesame sides.The examples above all construct exchange rates from two otherrates involving the US dollar (which is often the case). The sameapproach applies when constructing any rate from any other tworates. Considering the way in which each of the two separate dealerswill deal to create the combined rate, gives the construction:
Example 10Given the following rates, what are the USD/CHF and EUR/JPYrates?EUR/CHFEUR/USDEUR/GBPGBP/JPY
1.5348/530.9497/020.6378/83175.95/05
1.5348 ÷ 0.9502 = 1.61521.5353 ÷ 0.9497 = 1.6166Therefore the USD/CHF rate is 1.6152/660.6378 × 175.95 = 112.220.6383 × 176.05 = 112.37Therefore the EUR/JPY rate is 112.22/37
Spot foreign exchange
105
The market environmentIt is useful to have an idea of the size of the foreign exchange market.The total average daily volume of transactions worldwide is aroundUSD 1,200 billion. Of this total, only a tiny proportion representsdeals to convert the cashﬂows of international commercial trade; thevast majority represents position-taking and ﬁnancial ﬂows.Around 32% of the total is spot transactions and 68% is forwardswaps and outrights (covered in the next chapter). By far the largestturnover – around one third of the total world volume – takes placein the London market, followed by New York in second place andTokyo in third place. Around 57% of the total volume involves crossborder transactions – i.e. deals where the two banks are in differentcountries.As has been the case historically, around 90% of all transactionsinvolve the US dollar as one of the two currencies. Other importanttraded currencies, in decreasing order of volume, are the euro, theyen and sterling. The Swiss franc, Canadian dollar and Australiandollar are also traded in reasonable volume.
Exercises1
The SGD/NOK exchange rate is quoted as 2.9584. Does thisexchange rate express the number of Norwegian kroner equal to1 Singapore dollar, or the number of Singapore dollars equal toone Norwegian krone?2 You wish to sell US dollars against sterling and are given thefollowing quotes from two banks. At what price will you deal?• 1.4356/61• 1.4358/633 You are a dealer and a counterparty asks you for you price inEUR/USD. You quote ‘‘0.9503/08’’ and the counterparty replies‘‘5 yours’’. What have you sold or bought, how much, and atwhat rate?4 If the spot AUD/USD exchange rate is quoted as 0.5413, what isthe value of 1 ‘point’ on a deal of 1 million of the base currency?If the spot USD/JPY exchange rate is quoted as 107.13, whatis the value of 1 ‘point’ on a deal of 1 million of the basecurrency?5 You buy USD 10 million against Canadian dollars at 1.3785 andsell USD 10 million at 1.3779. What is your proﬁt or loss?
106
Foreign exchange and money markets
6
You are a dealer with a short position in US dollars against euros.A counterparty calls you for a price in EUR/USD. The marketis currently 0.9503/08. Which of the following prices might youquote if you now wish to reduce the size of your position?
7
8
910
• 0.9502/07• 0.9503/08• 0.9504/09You are a dealer. A customer asks you for a CHF/USD price. Youquote him 0.6330/38 and he buys CHF 5 million from you. Youwant to cover this position in the market and therefore deal ona price of USD/CHF 1.5783/88 quoted to you by another bank,for exactly the same amount of CHF 5 million. What proﬁt or lossin USD have you made?You sell EUR 5 million against USD at 0.9320, you buyEUR 2 million at 0.9325, you buy EUR 4 million at 0.9330 andyou sell EUR 3 million at 0.9327. The market closes at 0.9328and the closing rate for GBP/USD is 1.4730. At the end of theday, what is your EUR/USD position? What is the average rateof this position? What is your total net proﬁt or loss in GBP?The SEK/NOK exchange rate is 1.0523/28. What is the reciprocal rate?Current spot rates are as follows:USD/CHFUSD/SGDEUR/USDAUD/USD(a)
1.5384/892.3895/050.9678/830.5438/43
What is the two-way price for CHF/SGD? On which side ofthis price would the customer sell SGD?(b) What is the two-way price for EUR/AUD? On which side ofthis price would the customer buy EUR?(c) What is the two-way price for EUR/CHF? On which side ofthis price would the customer buy CHF?(d) What is the two-way price for CHF/AUD? On which side ofthis price would the customer sell CHF?
8
Forwardoutrights andswapsAt the end of this chapter, we have summarized the uses of thevarious instruments described in it. You might ﬁnd it useful to glancethrough this summary before reading the rest of the chapter.
Forward outrightsAlthough spot is settled 2 working days in the future, it is notconsidered in the foreign exchange market as ‘future’ or ‘forward’,but as the baseline from which all other dates (earlier or later) areconsidered.An outright is an outright purchase or sale of one currency inexchange for another currency for settlement on a ﬁxed date otherthan the spot value date. Rates are quoted in a similar way to thosein the spot market, with the quoting bank buying the base currencyon the left side and selling it on the right side. The term short date(see later in this chapter) is used for settlement on a date other thanspot but less than 1 month after spot, and the term forward outrightis therefore generally reserved for settlement later than that – i.e. atleast one month after spot – although short dates are really only aparticular range of forward outrights.Example 1The spot USD/CHF rate is 1.7166/1.7171, but the rate for value3 months after the spot value date is 1.7144/1.7151.
108
Foreign exchange and money markets
The spread (the difference between the bank’s buying priceand the bank’s selling price) is wider in the forward outrightquotation than in the spot quotation. Also, in this example, thedollar is worth less for delivery in the future than for deliveryon the spot date. USD 1 buys CHF 1.7144 in 3 months’ time, asopposed to CHF 1.7166 spot. In a different example, the dollarmight be worth more for delivery in the future than on the spotdate.
Where does the forward outright rate come from?The forward outright rate may be seen both as the market’s assessment of where the spot rate will be in the future and as a reﬂection ofcurrent interest rates in the two currencies concerned.Consider, for example, the following round-trip transactions, allundertaken simultaneously:(i) Borrow Swiss francs for 3 months starting from spot value date.(ii) Sell the Swiss francs and buy dollars for value spot.(iii) Deposit the purchased dollars for 3 months starting from spotvalue date.(iv) Sell forward now the dollar principal and interest which maturein 3 months’ time, into Swiss francs; use these Swiss francs torepay the borrowing in (i).In general, the market will adjust the forward price for (iv) so thatthese simultaneous transactions generate neither a proﬁt nor a loss.When the four rates involved are not in line (Swiss franc interest rate,USD/CHF spot rate, dollar interest rate and USD/CHF forward rate),there is in fact opportunity for making a proﬁt by round-tripping.That is, either the transactions as shown above will produce a proﬁt,or exactly the reverse transactions (borrow dollars, sell dollars spot,deposit Swiss francs and sell Swiss francs forward) will produce aproﬁt. The supply and demand effect of this arbitrage activity is suchas to move the rates back into line. If in fact this results in a forwardrate which is out of line with the market’s average view, supply anddemand pressure will tend to move the spot rate or the interest ratesuntil this is no longer the case.In more detail, the transactions might be as follows:(i) Borrow CHF 100 for 92 days at 3%The total repayment (principal plus interest) at maturity will be:92= CHF 1,007,667CHF 1,000,000 × 1 + 0.03 ×360
Forward outrights and swaps
109
(ii) Sell CHF 1 million for dollars at a spot rate of 1.7300 to give:1,000,000USD= USD 578,0351.7300(iii) Invest USD 578,035 at an interest rate of 4% per annum.The total repayment (principal plus interest) at maturity will be:92= USD 583,943USD 578,035 × 1 + 0.04 ×360(iv)
Sell USD 583,943 forward into Swiss francs to give:CHF 583,943 × forward outright exchange rate
Arbitrage activity will tend to make this last amount the same as thatin (i), so that:583,943 × forward outright exchange rate = 1,007,667Therefore, the forward outright exchange rate must be:1,007,667= 1.7256583,943This arbitrage idea gives the following formula for the theoreticalforward outright exchange rate:
Forward outrightdays1 + variable currency interest rate ×variable year= spot ×days1 + base currency interest rate ×base yearNotice that the length of the year may be 360 or 365, depending oneach currency (see Chapter 2).Applying the formula to the example above gives 1.7256 as expected:921 + 0.03 ×360 = 1.72561.7300 × 921 + 0.04 ×360Example 2What should the mid-rate theoretically be for the GBP/USD 3month outright, given the following? The 6-month period is183 days.
110
Foreign exchange and money markets
GBP/USD spot:
1.4120/26
GBP 6-month interest rate:
5.10/5.20%
USD 6-month interest rate:
4.30/4.40%
Note that sterling interest rates are on a 365-day year and dollarrates are on a 360-day year. Using middle rates both for spot,and for the interest rates, we have:1831 + 0.0435 ×360 = 1