# Understanding Triangular Arbitrage

Understanding triangular arbitrage requires some knowledge of how currencies are converted through the available exchange rates in the market. Arbitrage is when you find a price disparity among two different markets and then take the opportunity to make a profit on that disparity. There is no change in the definition when it comes to triangular arbitrage except for the fact that we are now looking at three markets, or currencies to be exact, which you might have guessed based on the fact that it is triangular arbitrage. Triangular arbitrage is when you find a disparity between three different currencies that makes it possible to start with one currency, convert to the second currency, then the third, and then back to the original currency along with a profit.

#### Why Three Currencies?

We could not possibly arbitrage successfully with only two currencies and make an instant profit by simply converting dollars to yen, and then immediately converting yen back to dollars. In fact, you would lose some money due to the exchanger making their dime on the bid-ask spread. Since two currencies would only get you back to where you were (minus the spread), there needs to be a third currency for arbitrage to work successfully.

#### When is Arbitrage Possible?

Arbitrage is possible when three currencies are mispriced in relation to each other. A mispricing that allows for a quick profit, by simply converting an amount of cash three times, is a rare opportunity that arbitrageurs are always looking for. A mispricing might only last for 1 or 2 seconds, so traders have to be extremely quick to execute the transaction. Research has also shown that opportunities exist more during the part of the business day when markets are more liquid. An example of a time like this is when both foreign exchange traders from Europe and Asia are very active.

#### Example

You are given \$1 million to trade with and you notice the following exchange rates in the market:

• EUR/USD = .8631
• EUR/GBP = 1.4600
• USD/GBP = 1.6939

You realize that there is a mispricing among these currencies that will yield a profit through triangular arbitrage. So, if you sell your one million dollars for euros, then trade euros for pounds, and then sell those pounds for dollars, you will end up with a profit of \$1,373. To see how this works out, take your calculator and multiply the \$1 million you started with by .8631, then divide it by 1.46, and then finally multiply by 1.6939. You may then subtract your initial investment of \$1 million to see just your profit. It is important to understand that this example is simplified with no other costs like taxes. In a real arbitrage example you will be looking at bid-ask spreads as well, and so the computation gets slightly more in depth as you have to know when to use the bid or the ask price in the next part of the conversion computation.

#### Is Triangular Arbitrage feasible?

It has recently been claimed that triangular arbitrage is not really feasible because of how fast you would need to convert your money through currencies.