Question

Interest Rate Arbitrage

Bank A is offering 82 Yen per dollar.

Bank B is offering $1.60 per British Pound

Bank C is offering 128 Yen per British Pound.

           

If you have 100,000,000 Yen, can you make a triangular profit? The quoted cross rate is the Yen per British Pound?

Identify the paths you would take to make a profit and the path that would yield a loss instead of a profit?

Which banks would you do your sell and buy transactions with?

Answer 1

We can make triangular profit.

here is two paths availble

1) bank A -bank B - bank C

2) bank C -bank B - bank A

1) bank A -bank B - bank C ( Analysis)

sell Yen 100,000,000 in bank A against dollar for YEN/ $ = 82

so. $ inflow = 100,000,000 / 82 = $12,19,512.19

sell  $ 12,19,512 in bank B against pound for $ / pound = 1.60

so. pound inflow = $12,19,512 / 1.6 = 7,62,195.11

sell pound 7,62,195 in bank C  against Yen for YEN/ pound  = 128 yen

so. Yen inflow = 7,62,195.11 * 128 = Yen 9,75,60,974.08

loss = 100,000,000 - 9,75,60,974.08 = Yen 24,39,025.92

2) bank C -bank B - bank A ( Analysis)

sell Yen 100,000,000 in bank C against dollar for YEN/ pound = 128

so. pound inflow = 100,000,000 / 128 = 7,81,250 pound

sell  7,81,250 pound in bank B against $ for $ / pound = 1.60

so. $ inflow = 7,81,250 / 1.6 = $12,50,000

sell $12,50,000 in bank A against Yen for YEN/ $ = 82

so. Yen inflow = $12,50,000 * 82 = Yen 102,500,000

Profit = 102,500,000- 100,000,000 = Yen 25,00,000