INDIRECT RATES. 245 agents in different places on whom they draw for the convenience of their customers. Rules and principles. 1o. Find the arbitrated rates of the indirect exchanges which seem likely to give better rates than the more advantageous of the direct rates (found as above) using the chain rule and adding in or subtracting the extra brokerages, commissions, bill stamps, and postage involved. Bills at short dates are seldom used for any but direct operations. Bills at long dates are specially suitable for arbitrations because there is time to wait for an improvement of the rate of exchange. No reductions are necessary for time as in the case of direct rates because all the operations are for present money. For instance, if I buy Hamburg bills at 3 mos.from the price would be deducted the interest for 3 mos. at the Hamburg rate-I should send them at once to Paris (say) to be sold and their interest for 3 mos. at the Hamburg rate would be deducted—thus what I gained in London I should lose in Paris, and the ultimate arbitrated rate would be unaffected by the time. Simple and compound arbitrated rates are equally unaffected by the time-both are determined by the chain rule. The charges involved in these indirect operations (brokerages, stamps, agents' commission, postage) seriously restrict the profit arising from them-in fact indirect exchanges even of the simple kind are only used to a large extent by banks or houses with branches in different places or for joint account. Compound and circuitous arbitrations especially require a large network of agents to make them possible or profitable. The usual charges are - p.c. for brokerage: op.c. for stamps: 1, or agreed. p.c. for commission as Whether these charges are to be added or subtracted will be clear on considering their effect in increasing the price or in diminishing the return. 2°. From a comparison of the direct short rates and the arbitrated rates (after observing whether the operation is in reality a remittance or a return and whether the rate is foreign or sterling)-decide whether any arbitrated rate is more advantageous than the more favourable direct-rate. The following rules will be a guide to the operator: (1) For remittances from A to B or drafts upon A by B. (a) If A has a foreign rate any greater arbitrated rate will be better than the direct rate. (b) If A has a sterling rate any less arbitrated rate will be better than the direct rate. (2) For returns to A from B, or drafts by A upon B. (a) If A has a foreign rate any less arbitrated rate will be better than the direct rate. (b) If A has a sterling rate any greater arbitrated rate will be better than the direct rate. The principle underlying these rules is that for remittances the highest foreign rate or lowest sterling rate requires least money from the payer, and for returns the least foreign rate or highest sterling rate will produce most money for the payee. With the best arbitrated rate, go through the routine necessary to obtain the value of any bill of exchange required with due regard to interest, broker ARBITRATIONS. 247 ages, commission, stamps, postage, etc.-employing tables or actual calculation for the various steps. Multiples may be constructed for frequently-occurring rates. The methods of approximation apply. Example. Find arbitrated rates between London and Paris from the formulæ. The rates for direct bills being at London 3 mos. 25-60, at Paris 3 mos. 25.12, and discount rate at both places being 4 p.c. Decide on the relative advantages of the direct rates and the arbitrated rates for remittances and returns. p.c. For direct remittances Paris should draw-difference about For direct returns London should draw-difference about p.c. For indirect remittances through Vienna-advantage over direct rate (Paris drawing)p.c. For indirect returns through rate (London drawing) 13 p.c. Direct remittance or return. 25.376 P. on L. 25.344 L. on P. 3.2 cents on 2500=p.c. Madrid-advantage over direct Indirect remittance. 25.415 Vienna. 4 4 cents on 2500p.c. or p.c. Indirect return. 25.344 London. 24.993 Madrid. 35 35 cents on 2500=1 p.c. (4) The routine of the work is shown thus for payments on account (indirect operations are almost always through agents). A. To pay a debt in Paris (Remittance). (1) By direct remittance. £1000 invested in buying Paris 3 mos. bills at 25.60 will purchase Disct. for 3 mos. at 4 p.c. 25600.00 Fr. 256.00 25344.00 Fr. French stamp (1⁄2 p.m.) 25.34 38.01 25305.99 Fr. Brokerage at 1 p.m. DIRECT AND INDIRECT RATES. 249 (2) By direct draft on London. £1000 draft offered in Paris at 25-12 3 mos. (3) By indirect remittance through Vienna. £1000 invested in Vienna bills at 12 will purchase 12000.00 Fl. Brokerage 1 p.m. 12.00 11988.00 Fl. 11988 Fl. sold in Paris at 212 will produce 25414.56 Fr. Brokerage 1 p.m. 25.41 Commission p.c. 31.77 (Vienna bill) French stamp ( p.m.) 6.35 63.53 25351-03 Fr. To receive a debt from Paris (Return). (1) By direct remittance. 25000 Fr. invested in 3 mos. London bills at 25.12 25000 Fr. draft offered in London at 25.60 3 mos. |