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:

$\backslash$table$[[,$US Dollar,$\backslash$table$[[$British$],[$Pound$]],$Euro,Indian Rupee,$\backslash$table$[[$Japanese$],[$Yen$]],\backslash$table$[[$Brazilian$],[$Real$]]],[$US Dollar,$1\mathrm{.}00000,0\mathrm{.}59423,0\mathrm{.}72978,58\mathrm{.}46660,101\mathrm{.}39000,2\mathrm{.}20612],[\backslash$table$[[$British$],[$Pound$]],1\mathrm{.}68264,1\mathrm{.}00000,1\mathrm{.}22797,98\mathrm{.}3782,170\mathrm{.}60000,3\mathrm{.}71211],[$Euro$,1\mathrm{.}37017,0\mathrm{.}81421,1\mathrm{.}00000,80\mathrm{.}10920,138\mathrm{.}92000,3\mathrm{.}02276],[$Indian Rupee,$0\mathrm{.}01706,0\mathrm{.}01014,0\mathrm{.}01245,1\mathrm{.}00000,1\mathrm{.}73000,0\mathrm{.}03764],[$Japanese Yen,$0\mathrm{.}00986,0\mathrm{.}00586,0\mathrm{.}00720,0\mathrm{.}57661,1\mathrm{.}00000,0\mathrm{.}02176],[\backslash$table$[[$Brazillan$],[$Real$]],0\mathrm{.}45202,0\mathrm{.}26861,0\mathrm{.}32988,26\mathrm{.}42830,45\mathrm{.}83000,1\mathrm{.}00000]]$

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?