Examine the cross-spot rates shown in Exhibit 2. Are there any triangular arbitrage opportunities among these currencies (assume deviations from theoretical cross rates of 5 points or less are attributable to transaction costs)? How much profit could be made on a $5 million transaction? Show and explain.
Table 1 - Spot 3-Month Forward 3001425 7.7150/200 French Franc 3 Mo. Eurofranc Deposit Rate 3 Mo. Eurodollar Deposit Rate 11 5/8 - 11314% 7 7/8-8% The French franc is selling at a forward discount against the dollar. Using the midpoints of the quotes, the discount is 1.88% on an annualized basis. This is smaller in absolute terms than is theoretically justified on the basis of differences in interest rates: 3.68% = {[(1+11.6875/400)/(1+7.9375/400))-1}xdx100 Consequently, an arbitrageur could profit risklessly by taking the following steps: 1. Borrow 1,000,000 Eurodollars for 3 months at 8%. 2. Purchase FF7,715,000 at the spot bid rate. 3. Invest the francs for 3 months at the Eurofranc deposit rate of 11-5/8%, 4. Simultaneously sell francs (buy dollars) forward at the forward offer rate of 7.7625. The amount of the forward sale should equal the total amount of franc proceeds at the deposit's maturity, or FF7,939,217 [FF7,715,000 X ( + 11625/4). Exhibit 1 - Spot and forward exchange rates Currency Spot 1 Month 3 Months 6 Months 12 Months Sterling 1.4890/00 55/52 160/156 302/289 560/523 Deutsche mark 2.0310/20 22/18 64/54 128/105 277/228 French Franc 6.6575/625 73/86 263/296 505/590 1194/1351 Yen 154.20/30 8/6 33/27 75/62 164/137 SDR 1.2141/43 5/3 12/8 18/11 24/12 DM U.S. dollars per unit of currency Exhibit 2 - Cross-Spot Exchange rates - DM FF Yen 3050/51 1.3169/71 3.2779/88 4.3365/84 Yen 75.9232/350 23.1595/618 Quotes should be interpreted as units of the currency represented in the left hand column per unit of currency shown in the top row. Quotes for the DM yen and FF yen are expressed in units per 100 yen. Exhibit 3- Eurocurrency interest Rates FF Currency US Dollar 1 Month 5.6875-5.8126 3 Months 5.5000-6.6250 6 Months 5.5000-8.6250 12 Months 65.6250-57500 100525-10.1875 Sterling Deutscher French France 0.8750-00375 43125-44375 7.1875-7.3125 4437544.5625 7. 1250-7,2500 9.6875-0.7500 4.3125-44375 7.1875-7.3125 9.6250-97500 4.3125-44375 7.2500.7.3750 Yon 5.1250-51675 4.7500-4.8125 4.6250-4.6875 4.6250-46875 SOR 6.9375-60625 5.8125-6.9375 6.7500-3.8750 5.8125-5.9375 Table 1 - Spot 3-Month Forward 3001425 7.7150/200 French Franc 3 Mo. Eurofranc Deposit Rate 3 Mo. Eurodollar Deposit Rate 11 5/8 - 11314% 7 7/8-8% The French franc is selling at a forward discount against the dollar. Using the midpoints of the quotes, the discount is 1.88% on an annualized basis. This is smaller in absolute terms than is theoretically justified on the basis of differences in interest rates: 3.68% = {[(1+11.6875/400)/(1+7.9375/400))-1}xdx100 Consequently, an arbitrageur could profit risklessly by taking the following steps: 1. Borrow 1,000,000 Eurodollars for 3 months at 8%. 2. Purchase FF7,715,000 at the spot bid rate. 3. Invest the francs for 3 months at the Eurofranc deposit rate of 11-5/8%, 4. Simultaneously sell francs (buy dollars) forward at the forward offer rate of 7.7625. The amount of the forward sale should equal the total amount of franc proceeds at the deposit's maturity, or FF7,939,217 [FF7,715,000 X ( + 11625/4). Exhibit 1 - Spot and forward exchange rates Currency Spot 1 Month 3 Months 6 Months 12 Months Sterling 1.4890/00 55/52 160/156 302/289 560/523 Deutsche mark 2.0310/20 22/18 64/54 128/105 277/228 French Franc 6.6575/625 73/86 263/296 505/590 1194/1351 Yen 154.20/30 8/6 33/27 75/62 164/137 SDR 1.2141/43 5/3 12/8 18/11 24/12 DM U.S. dollars per unit of currency Exhibit 2 - Cross-Spot Exchange rates - DM FF Yen 3050/51 1.3169/71 3.2779/88 4.3365/84 Yen 75.9232/350 23.1595/618 Quotes should be interpreted as units of the currency represented in the left hand column per unit of currency shown in the top row. Quotes for the DM yen and FF yen are expressed in units per 100 yen. Exhibit 3- Eurocurrency interest Rates FF Currency US Dollar 1 Month 5.6875-5.8126 3 Months 5.5000-6.6250 6 Months 5.5000-8.6250 12 Months 65.6250-57500 100525-10.1875 Sterling Deutscher French France 0.8750-00375 43125-44375 7.1875-7.3125 4437544.5625 7. 1250-7,2500 9.6875-0.7500 4.3125-44375 7.1875-7.3125 9.6250-97500 4.3125-44375 7.2500.7.3750 Yon 5.1250-51675 4.7500-4.8125 4.6250-4.6875 4.6250-46875 SOR 6.9375-60625 5.8125-6.9375 6.7500-3.8750 5.8125-5.9375
