Question

Assume the following exchange rates: $2 = £1 in New York ¥410 = £1 in London ¥200 = $1 in Tokyo Indicate how profitable triangular, or three-point, arbitrage can take place.

Answer 1

Lets estimate the rates:$\$ / \pounds = 2, \pounds / \yen = \frac{1}{420}, \yen /\$ =200$

Lets Multiply the rates: $2 \times \frac {1}{420} \times 200 = \frac {400}{420} \cancel {=} 1$ therefore there is an arbitrage possibility

1)Lets suppose we have 100 ¥ and we exchange it for $ then $100 \yen = \frac {100}{200} =0.5\$$

2) then exchange 0.5$ for pounds: $0.5\$ = 0.25 \pounds$

3) then exchange it for yen $0.25 \pounds = 0.25 \times 410 = 102,5 \yen$

that means that we earned 2.5 yen from 100 yen. In percentage we gained 2.5%