Question

1. Given the following three currency quotes given by a Tokyo bank and a London bank:

¥112.14/$

¥141.92/₤

₤0.7862/$

Please answer parts (a) and (b) in the order they are given.

1. Show whether there is an arbitrage opportunity implied in these three quotes.
2. Starting with a nominal $32 million, show how much arbitrage profit (if any) you can make by trading the currencies at the given rates.

Answer 1

Fair rate Pound/Dollar = (Pound/Yen)*(Yen/Dollar)

= (1/141.92)*112.14

= Pound 0.7902/Dollar

Since actual rate is different, arbitrage opportunity exists

b.Convert Dollar into Yen = 32,000,000*112.14 = Yen 3,588,480,000

Convert into Pound = 3,588,480,000/141.92 = Pound 25,285,231.12

Convert back into Dollars = 25,285,231.12/0.7862

= $32,161,321.69

Hence, arbitrage profit = $161,321.69