Case Goal:

Determine if an arbitrage opportunity exists in foreign currency trading.

Case Overview

Trading volume in currencies can exceed $$1$B per day. One type of currency trade is known as a

spot currency transaction where an investor buys one currency using another currency $"$on the

spot".

To illustrate a spot transaction, consider a US company seeking to buy Japanese yen using US

dollars. If each dollar was worth $101\mathrm{.}39$ yen, then one hundred US dollars would buy $10139$ yen

at that moment in time.

Now consider the reverse transaction. If the exchange rate from yen back to US dollars was

$0\mathrm{.}00986,$ the $10139$ yen would buy $99\mathrm{.}87054$ US dollars. The difference between the original

$$100$ investment and the final $$99\mathrm{.}87$ is the transaction cost.

Every so often the spot prices of currency are such that free money can be made. In these cases,

a dollar can be invested in a set of currency transactions that returns more than a dollar at the

end. In such a case the prices will quickly adjust to address this idiosyncrasy. However, if such

an opportunity does arise, then it makes sense to move quickly to take advantage of it$.$

The left side of the table is the currency that is being traded from and the top of the table is the currency

being traded to$.$ So$,$ for example, in the first table $$1$ US dollar is worth $0\mathrm{.}59423$ British Pounds at this

point in time. $1$ Euro is worth $80\mathrm{.}1092$ Indian Rupees.

ACTUAL QUESTION:

Develop a linear program in Excel similar to the example provided below to determine if an arbitrage

opportunity exists for Table $1.$ Note that this may require an investment in several currencies, that is$,$ a

situation where one trades from A to B from B to C$,$ and finally from C back to A$.$ The model should

show the precise arbitrage opportunity if one exists. That is$,$ what currencies should be used to create the

opportunity?