When the New York quotation for sterling is $4.85 and the London quotation for francs 25.20, the New York parity quotation for francs is 5.1959; if the mar ket rate differs from this there is an opportunity for arbitrage. Conversely, given the two franc quota tions, the table shows the parity of the pound sterling in New York, or, given the sterling and franc rate in New York, the table shows the parity quotation of francs in London. Intermediate rates can be arrived at by interpolation. For instance, in the example given in Section 6, the sterling rate is 4.8560, the nearest quotation in the table is for 4.8550—a quarter cent making a difference of .0026 centime (5.1905 —5.1879) in the quotation. Therefore, — 25 X.0026 =.0010 centime deducted from 5.1905 = 5.1895. The table is calculated by divid ing the value of the sovereign in francs by its value in dollars, thus = 5.1895.
4. Parity in when applied to a stock, means the price which is its equivalent when quoted in a different market. For instance, the Lon don price of a stock exceeds the New York price of the same stock by about 21'' or 3 per cent, after the exchange rate and the London method of quot ing American stocks ($5 to the pound) are taken into consideration. With a cable rate of 4.87% the London parity of New York stock at 68 would be 69.75.
N. Y. parity parity rate of exch. 69.74 or 68. ==5 5 New York parity X 5 691 X 5 London parity = = 69.74.
Rate of exchange or 4871/4 In commodities, the prices at two different centers are at parity when the difference represents only the actual cost of transportation and interest.
5. Chain rule.—Most of the calculations in arbi trage transactions can be put in the form of simple equations, and require only correct reasoning for their solution. A quick tho mechanical method of calcu lation is called the chain rule. It consists of arrang ing the terms of the exchange of the various currencies under consideration, in such a manner that the re quired equivalent, or parity, is easily obtained. A study of the following example will make the method clear : The last term is always in the same currency as the unknown quantity, or first term. It will be noted that these equations are arranged in such a manner that the denominations are in sequence like the links of a chain; hence the name. The value of the unknown quantity (x) is then taken as equal to a fraction, the quantities on the right-hand side forming the numerator, and those on the left-hand side, the denominator. The product of the numerator divided by that of the de nominator will give the required answer. "Chain rule" is applicable to all kinds of exchange and mer cantile calculations.
How many dollars (x) = £1 If the weight of £1 = 123.274 grains standard gold If 12 grains of standard gold =11 grains of fine gold And if 232.2 grains of fine gold =$10 X 12.3.q.74 X 11X 10 - ---= X x 2.32.E" 6. Simple rate of exchange be tween two or more places corresponds or tends to cor respond. In a preceding section it was shown how exchange rate between two places is almost auto matically adjusted.. Similar influences in the form of arbitrage are brought into operation to synchronize the exchange rates the world over. There is thus a
certain sympathy or relation between all foreign ex change quotations. The quotations in New York for exchange on Berlin or Paris are largely influenced by the price of sterling exchange. If the price of marks in New York should fall to a point where there would be a profit in an arbitrage transaction, the de mand for drafts on Berlin, by those who wish to make this profit, would almost immediately force the mark quotation up again. Similarly New York, while a debtor to England with consequent high sterling rates, may be the creditor of France or other countries in Europe, and drafts on these countries are remitted to London and thus tend to improve (i.e., lower) the rate of sterling exchange. When only three places are involved, the transaction is called simple arbi trage.
To 'give a concrete case of simple arbitrage: Sup pose a banker in New York has the following data before him: London check rate in New York $4,8560 per £ Paris check rate in New York Fcs. 5.16% per $ Paris check rate in London Fes. 25.20 per £ A brief calculation or a glance at his table of pari ties shows that there is an opportunity for a profit able arbitrage in francs between London and New York. He therefore sells a draft on Paris for Fcs. 252,000 at and with the proceeds buys a draft for £10,000 at 4.8560 per X, at the same time cabling his London correspondent to purchase a draft for Fes. 252,000 at 25.20 per X, or better, and send it to Paris to the credit of his account there. This pur chase costs £10,000 and is provided for by a draft for the same amount remitted from New York. The banker's position is now as follows: Sale of francs 252,000 at 5.1678 $48,754.56 Purchase of draft for 110,000 at 4.8560 to cover purchase of Fcs. 252,000 in London at 25.20 48,560.00 Profit $194.56 Without using any of his own capital and without any expense except the cost of a cable and a small commission to his London and Paris correspondents, the banker has made a profit of over $190. The re sult of this and similar transactions made at the same time by other New York bankers would be to lower the New York rate for francs by increasing the sup ply, and to raise the London rate for francs by ab sorbing the supply, thus tending to equalize rates all round.
7. Compound example of arbi trage just given is of the simplest form, but it is typi cal of such transactions. The banker might have found it more profitable to provide cover for his draft on Paris by remitting marks to Berlin and purchas ing his francs there, or he might have instructed his London correspondent to purchase and remit a draft to Berlin with instruction to the Berlin bankers to remit francs to Paris. In the first instance he sim ply substitutes Berlin for London in the trans action, but in the second instance he would operate both thru London and Berlin; four places are in volved, and the transaction is known as compound arbitrage.
The study of arbitrage operations is both interest ing and instructive. The following transaction will bring out some of the underlying principles more clearly: