Question

3) Triangular arbitrage:

Price of a US dollar in Geneva is 1.0204-1030. Price of a US dollar in Japan is 99.8877-9876. Indirect Swiss franc for yen quote is 100.2468-3579. What is percentage return from triangular arbitrage?

Answer 1

SFr/$ = 1.0204-1.1030

Yen/$ = 99.8877-99.9876

From above,

Bid Yen/SFr = Bid Yen/$ * Bid $/SFr = 99.8877 * (1/Ask SFr/$) = 99.8877/1.1030 = 90.56

Ask Yen/SFr = Ask Yen/$ * Ask $/SFr = 99.9876 * (1/Bid SFr/$) = 99.9876/1.0204 = 97.9886

Cross Rate = Yen/SFr = 90.56-97.9886

2 approaches to arbitrage are as follows:

(i) Buy SFr via $ rate i.e. 97.9886(ask rate) and Sell SFr via cross rate i.e. 100.2468(bid rate)

(ii) Buy SFr via cross rate i.e. 100.3579(ask rate) and Sell SFr via $ rate i.e. 90.56(bid rate)

Only (i) approach will result in Profit. (ii) will generate loss

Therefore, % Return from triangular arbitrage = (Selling Price-Purchase Price)/Purchase Price = (100.2468-97.9886)/97.9886 = 0.023046 = 2.3046%