Can someone please explain how to calculate arbitrage opportunity? I know how to determine whether there is arbitrage opportunity. The problem is understanding how to calculate the profits you can earn from taking advantage of the arbitrage opportunity. I usually get the correct answers, but I’m not very confident I understand it clearly. Here are two examples. Choose the correct answer and please explain them both and show your calculation. 1) Suppose the AUD trades for USD0.735802 in New York and JPY79.3048 in Tokyo. The USD trades for JPY109.2343 in Tokyo. Is there an arbitrage opportunity available for a currency trader? A) No, there is no arbitrage opportunity. B) Yes, the trader can make USD0.0872 per USD invested. C) Yes, the trader can make USD0.0135 per USD invested. Answer - If the U.S. trader converts USD1 for JPY109.2343, the JPY109.2343 can be converted to AUD1.3774 (109.2343/79.3048). The AUD1.3774 can then be converted to USD1.0135 (1.3774 × 0.735802). Therefore, the profit per USD invested is 0.0135. 2) Suppose the GBP trades for CHF2.20279 in Zurich and USD1.62699 in London. The USD trades for CHF1.2755 in Zurich. Is there an arbitrage opportunity available for a currency trader? A) Yes, the trader can make USD0.06147 per USD invested. B) No, there is no arbitrage opportunity. C) Yes, the trader can make USD0.0930 per USD invested. Answer - If the U.S. trader buys 1 GBP for $1.62699, that GBP can be converted to CHF 2.20279. The CHF 2.20279 can then be converted to 2.20279 × 1/1.2755 = USD 1.72700. The total profit is 1.727000 − 1.62699 = USD.10001. The profit per USD invested is 0.10001/1.62699 = 0.06147.
Since you already know how to calculate the existence of a triangular arbitrage opportunity, just complete the triangle and convert to the original currency you started with. In this case, it would be the USD. I tend to start off with a base of 1000 to make my calculation a bit easier going through the triangle. I cheated by using a spreadsheet, but this is the method I used: Question 1: 1) 1000 USD 2) 1000 USD *109.2343 JPY/USD = 109234.3 JPY 3) 109234.3 JPY / (79.3048 JPY/AUM) = 1377.98 AUM 4) 1377.98 AUM * .735802 = 1013.492 USD Profit per USD = (1013.492-1000) / 1000 = .013492 Question 2: 1) 1000 USD 2) 1000 USD * 1.2755 CHF/USD = 1275.5 CHF 3) 1275.5 CHF / (2.20279 CHF/GBP) = 579.0384 GBP 4) 579.0384 GBP *1.62699 USD/GBP = 942.0897 USD No profit here, so let’s go the other way: 1) 1000 USD 2) 1000 USD / (1.62699 USD/GBP) = 614.6319 GBP 3) 614.6319 GBP * 2.20279 CHF/GBP = 1353.905 CHF 4) 1353.905 CHF / (1.2755 CHF/USD) = 1061.47 USD Profit per USD = (1061.47-1000) / 1000 = .06147
I freakin’ got it! Thanks, dude. Now I can do it in my sleep! Movin’ on…
The way I solve first of these two problems is as follows: 1. Implied cross rate is USD:JPY = 107.7800. Calculated as: AUD:USD = 0.735802 AUD:JPY = 79.3048 So, USD:JPY = 107.7800 Therefore, if bank quote is USD:JPY = 109.2343, there is an arbitrage opportunity. I can sell dollars and get 109.2343 JPY as opposed to 107.7800 JPY that is implied by the spot rates. The arbitrage profit is as follows: Sell dollars for Yen at bank quote: 1 USD = 109.2343 JPY Sell Yen for AUD: 109.2343 JPY = 1.3774 AUD Sell AUD for USD: 1.3774 AUD = 1.01349 Hence, profit is 0.1349 per USD invested
The way I solve the second of these two problems is as follows: 1. Implied cross rate is USD:CHF = 1.3539. Calculated as: GBP:CHF = 2.20279 GBP:USD = 1.62699 So, USD:CHF = 1.3539 Therefore, if bank quote is USD:CHF = 1.2755, there is an arbitrage opportunity. The arbitrage profit is as follows: Buy GBP for dollars at spot: 1 USD = 0.6146 GBP Sell GBP for Swiss Francs: 0.6146 GBP = 1.3539 CHF Sell Swiss Francs for USD at bank quote: 1.3539 CHF = 1.06147 USD Hence, profit is 0.06147 per USD invested