# An introduction to the foreign exchange market Moorad Choudhry September 2002

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2 against the variable currency. For example a quote of for GP/USD means that the bank is prepared to buy sterling for \$1.6245, and to sell sterling for \$ The convention in the FX market is uniform across countries, unlike the money markets. Although the money market convention for bid-offer quotes is for example, 5½% - 5¼%, meaning that the bid for paper - the rate at which the bank will lend funds, say in the CD market - is the higher rate and always on the left, this convention is reversed in certain countries. In the FX markets the convention is always the same one just described. The difference between the two side in a quote is the bank s dealing spread. Rates are quoted to 1/100 th of a cent, known as a pip. In the quote above, the spread is 10 pips, however this amount is a function of the size of the quote number, so that the rate for USD/JPY at say, , indicates a spread of 0.10 yen. Generally only the pips in the two rates are quoted, so that for example the quote above would be simply The big figure is not quoted. Example 1 Exchange cross-rates Consider the following two spot rates: EUR/USD AUD/USD The EUR/USD dealer buys euros and sells dollars at (the left side), while the AUD/USD dealer sells Australian dollars and buys US dollars at (the right side). To calculate the rate at which the bank buys euros and sells Australian dollars, we need: / = is the rate at which the bank buys euros and sells Australian dollars. In the same way the rate at which the bank sells euros and buys Australian dollars is given by / or Therefore the spot EUR/AUD rate is The derivation of cross-rates can be depicted in the following way. If we assume two exchange rates XXX/YYY and XXX/ZZZ, the cross-rates are: YYY/ZZZ = XXX/ZZZ XXX/YYY ZZZ/YYY = XXX/YYY XXX/ZZZ Given two exchange rates YYY/XXX and XXX/ZZZ, the cross-rates are: YYY/ZZZ = YYY/XXX XXX/ZZZ ZZZ/YYY = 1 (YYY/XXX XXX/ZZZ)

3 Forward exchange rates Forward outright The spot exchange rate is the rate for immediate delivery (notwithstanding that actual delivery is two forward). A forward contract or simply forward is an outright purchase or sale of one currency in exchange for another currency for settlement on a specified date at some point in the future. The exchange rate is quoted in the same way as the spot rate, with the bank buying the base currency on the bide side and selling it on the offered side. In some emerging markets no liquid forward market exists so forwards are settled in cash against the spot rate on the maturity date. These non-deliverable forwards are considered at the end of this section. Although some commentators have stated that the forward rate may be seen as the market s view of where the spot rate will be on the maturity date of the forward transaction, this is incorrect. A forward rate is calculated on the current interest rates of the two currencies involved, and the principle of no-arbitrage pricing ensures that there is no profit to be gained from simultaneous (and opposite) dealing in spot and forward. Consider the following strategy: borrow US dollars for six months starting from the spot value date; sell dollars and buy sterling for value spot; deposit the long sterling position for six months from the spot value date; sell forward today the sterling principal and interest which mature in six months time into dollars. The market will adjust the forward price so that the two initial transactions if carried out simultaneously will generate a zero profit / loss. The forward rates quoted in the trade will be calculated on the six months deposit rates for dollars and sterling; in general the calculation of a forward rate is given as (1). Fwd = Spot ( 1 + variablecurrency deposit rate ) ( 1 + base currency deposit rate ) (1)ril The year day-count base will be either 365 or depending on the convention for the currency in question.

4 Example 2 Forward rate 90-day GP deposit rate: 5.75% 90-day USD deposit rate: 6.15% Spot GP/USD rate: (mid-rate) The forward rate is given by: ( ) 90 ( ) = Therefore to deal forward the GP/USD mid-rate is , so in effect 1 buys \$ in three months time as opposed to \$ today. Under different circumstances sterling may be worth more in the future than at the spot date. Forward swaps The calculation given above illustrates how a forward rate is calculated and quoted in theory. In practice as spot rates change rapidly, often many times even in one minute, it would be tedious to keep re-calculating the forward rate so often. Therefore banks quote a forward spread over the spot rate, which can then be added or subtracted to the spot rate as it changes. This spread is known as the swap points. An approximate value for the number of swap points is given by below. Forward swap spot deposit rate differential (2) The approximation is not accurate enough for forwards maturing more than 30 from now, in which case another equation must be used. This is given as (2).It is also possible to calculate an approximate deposit rate differential from the swap points by re-arranging Forward swap = spot (3) ( variablecurrency depo rate base currency depo rate ) ( 1 + base currency depo rate )

6 borrowing to the first currency. It will do this if the all-in cost of borrowing is less than the cost of borrowing directly in the first currency. Forward cross-rates A forward cross-rate is calculated in the same way as spot cross-rates. The formulas given for spot cross-rates can be adapted to forward rates. Forward-forwards A forward-forward swap is a deal between two forward dates rather than from the spot date to a forward date; this is the same terminology and meaning as in the bond markets, where a forward or a forward-forward rate is the zero-coupon interest rate between two points both beginning in the future. In the foreign exchange market, an example would be a contract to sell sterling three months forward and buy it back in six months time. Here, the swap is for the three-month period between the three-month date and the six-month date. The reason a bank or corporate might do this is to hedge a forward exposure or because of a particular view it has on forward rates, in effect deposit rates. Example 4 Forward-forward contract GP/USD spot rate: month swap: month swap: If a bank wished to sell GP three month forward and buy them back six months forward, this is identical to undertaking one swap to buy GP spot and sell GP three months forward, and another to sell GP spot and buy it six months forward. Swaps are always quoted as the quoting bank buying the base currency forward on the bid side, and selling the base currency forward on the offered side; the counterparty bank van buy and sell GP spot against three months at a swap price of -45, with settlement rates of spot and (spot ). It can sell and buy GP spot against six months at the swap price of -125 with settlement rates of spot and (spot ). It can therefore do both simultaneously, which implies a difference between the two forward prices of (-125) - (- 45) = -90 points. Conversely the bank can buy and sell GP three months against six months at a swap price of (-135) - (-41) or -94 points. The two-way price is therefore (we ignore the negative signs).

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