The calculation of a 3o-,45-, or 9o-day bill would proceed in the same manner; interest would be calculated for 33, 48, or 93 days respectively and at the discount rates quoted for such usances; these rates are sufficiently higher to cover the greater risk.
The calculation would also be the same in case the bill were a prime commercial instead of a banker's bill; and also in case of commercial bills, not prime, except that the rates of discount and profit would be higher, to cover the greater risk.
2. Price that can be bid for a 6o-day sight documentary payment bill on prime London bank, covering a shipment of perishable goods. This bill will presumably be taken up on day of acceptance and interest will be re bated at I% less than the Bank of England rate.
Interest rebated on date of prepayment (the date of acceptance) at drawee's option, for 63 days at 3% on $4.85 $.402325o English stamp duty, 1/2o% of 4.85 .00243o Margin of profit to American bank, 1/4.0% of 4.85 .00r215 Total charges to be deducted from demand rate $.028895 4.875 — .029 = $4.846, which is the highest price the American can pay for the 6o-day bill and make the profit contemplated.
The calculation of the same bill, if drawn to cover a shipment of non-perishable goods, would proceed on the assumption that, since the goods are carried by slow steamers and are almost always warehoused upon arrival, the drafts will not be paid until maturity, but that, to be safe, the discount should be calculated at the retirement rate. Since banks do not have funds sufficient to carry many such payment bills, a method of handling these non-discountable bills is used whereby the bills are accepted as collateral by the London banker against the Americanbank's long bills drawn for discount in the New York or London market.
Many banks are opposed to offering their own long bills for sale; in such case, of course, this method cannot be used.
Arbitrage Calculations As previously explained, arbitrage is the contemporaneous purchase of exchange in one market at one price and the sale in another at a higher price; or, at least, the transfer of funds in directly from one market to another, whether or not price con siderations are the chief factors. Formerly a wider margin of profit was made at arbitrage, but as the world is more closely knit together and as the number of arbitrageurs increase, the prices of exchange in the different markets more closely approximate one another. This tendency was disrupted temporarily by the war. The narrowing of profits because of the agreement of prices on the world's markets at any instant has fostered arbi trage transactions on the basis of the prices that are likely to prevail on markets tomorrow or a week hence; that is, it has introduced into arbitrage as between places a speculative time element.
The variations in arbitrage transactions are, of course, legion, and only a few illustrative calculations can be given here: i. Covering the Sale of a Cable on Switzerland.
Suppose a cable has been sold by the bank on Switzerland, but the bank has no balances in Switzerland and must provide cover at once for this sale. This can be done with sterling, francs, or marks. The problem is to know which is cheapest.
the three exchanges are practically on a parity, and the bank could remit cover in francs, marks, or sterling at about the same cost. But if the bank could sell mark cable in Switzerland at, say, 1.23 instead of 1.2296, this exchange would work out more favorably than the other two (123 ÷ .2384375 = 5.1585 francs), and would afford a profit (5.1585 — 5.1,57).
If the rates of marks and francs in New York had been quoted in cents per mark and franc, respectively, the cost of covering would have been calculated as follows: Rate of franc cables in New York, 19.4175 cents (that is, the equivalent of 5.15 francs per dollar).
Rate of mark cables in New York, 23.84375 cents (that is, the equiva lent of .95375 Per 4 marks).
Gold Shipments and the Calculations of Their Profits Very intimately connected with the arbitrage and other trad ing operations are the importation and exportation of gold, the time and direction of which are determined upon by the traders. As explained in Chapter LIV, the gold export and import points depend primarily upon the expense of shipping specie. In the case of exportation of gold to London from New York, the ele ments of calculation of profit include the initial outlay for the gold coin or bullion, the incidental expenses for packing, cartage, freight, insurance, and interest, and the proceeds of the coin or bullion. when sold to the Bank of England, and the pre vailing price of exchange which is sold against the ship ment. The following problems will illustrate the calculation of profits: Therefore, the total cost of procuring £2o5,2or credit abroad is $ ,002, 58o (or 1,000,000 + 2,58o). This is equivalent to $4.8858 per pound sterling. If, by hypothesis, the bank can sell sight exchange at 4.8925 on day of gold shipment, its profits will be $o.0067 (or 4.8925 — 4.8858) per pound sterling. Under normal circumstances banks are unwilling to undertake the exportation of gold for less profit than $.0015 per pound, which. is 1/32%. The above calculation assumes that the bank loses 3 days' interest ; the loss ranges from to 3 days in actual practice, depend ing upon the day and hour when the steamer sails and whether the sight exchange is paid in currency or by draft on a clearing house bank.