Question

You specialize in cross-rate arbitrage. You notice the following quotes: Singapore dollar/U.S. dollar (S$/S) spot rate = S$1.60/$ Canadian dollar/U.S. dollar (CD/$) spot rate = CD1.33/$ Singapore dollar/Canadian dollar (S$/CD) spot rate = S$1.15/CD Ignoring transaction costs:

A) Do you have an arbitrage opportunity based on these quotes? B) If an arbitrage opportunity exists, what transactions would you undertake to secure the arbitrage profit? C) How much would your profit be if you have $1,000,000 available for this purpose?

Answer 1

A)This is a triangular arbitrage

Here we can make arbitrage profit when there is difference in the synthetic and actual rates

Given quotations -

SGD/USD = 1.6

CAD/USD = 1.33

SGD/CAD = 1.15

Here transaction costs are ignored .

Let us calculate synthetic SGD/CAD rate =SGD/USD * USD/CAD = 1.6 * (1/1.33)

Hence the synthetic rate is 1.203008

This is different from the actual given rate hence we can make arbitrage profits.

B) The following transactions can be undertaken

Step -1)First sell USD in the quote SGD/USD and get SGD

Step-2)Then use this SGD to buy CAD in SGD/CAD quote

Step-3)Not sell the CAD to Brought for USD in CAD /USD

C) Let us make the above transaction using the $1,000,000

Covert USD to SGD = 1,000,000 * 1.6 = 16,00,000

Convert the SGD to CAD = 16,00,000 * 1.15 = 1840000

Convert the CAD to USD = 1840000 /1.33 = 13,83,458.65

Hence we can see that we started with 1,000,000 we ended up with 13,83,458.65

Arbitrage profit is 3,83,458,65

Note - SGD is the singapore dollar

CAD - Canadian Dollar

AUD - Australian Dollar