Arbitrage involves taking advantage of the imbalance between two or more markets. People who take such advantages in business are known as the arbitragers. They make profit by observing the market situation and exploit the imbalance in the market to their advantage. Generally, an arbitrager profit is generated from the imbalance in the market price or the fluctuating foreign exchange. Triangular arbitrage is as a result of a discrepancy between the three foreign currencies, the arbitragers take advantage of this inconsistency to make profit. Triangular arbitrage happens on the current exchange markets where there is instant exchange rate, wasting time on exchange rate can result in discrepancy recovery; hence, no profit is generated by the arbitrager. This paper will analyzes how the triangular arbitrage method can be used to make a profit between Japan, the UK, and the USA.
There are several conditions for the triangular arbitrage method that are applied, one of which is three states with different currencies. Having two states will only bring a loss for the arbitrager, due to the transaction cost. Furthermore, the profit is not likely to be generated since it is a back and forth business when the exchange rate is similar. On the other hand, each state should have its currency, without different currency, there is no exchange rate; hence, the business cannot work. For example, in this case, the exchange rate involves the US dollar, European British pound, and the Japanese yen. This is the basic condition for the triangular arbitrage to work, for example, it cannot work on states like California, Texas, and a country like Hawaii since they use the same currency, which is the US dollar.
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The major conditions for the triangular arbitrage are the presence of discrepancy on the exchange market. The discrepancy is inconsistency on the currency similarity; it happens if the money is valued more than it is supposed to be valued in one state. If one US dollar is valued at 82 yen, when it is converted to British pounds the value of the British pound should be worth one US dollar. Discrepancy happens when this rule is not followed, for example, if one US dollar is converted to British pounds it will be valued at 0.625 British pounds; this is equal to 80 yens while the US dollar is valued at 82 yen. Therefore, the three countries have discrepancies, and an arbitrager can yield profit by exchanging the three states valuation for money. To avoid this, the US dollar should be valued at 80 yens as opposed to 82 yens. Generally, the value of a given currency should be the same in all countries. The 2yen value of the US dollar in japan can yield a big profit, especially when dealing with a large amount of money. Currently, triangle discrepancy is made through the online platforms that have the ability to instantly complete the whole exchange process. Most central banks will notice the case of discrepancy within seconds and equate the process hence if not done instantly; there are possibilities of losses ( Gradojevic, Gencay, & Erdemlioglu, 2017) .
The level of discrepancy should be higher than the transaction cost of the exchange rate in the three countries. Therefore, an arbitrager should be aware and calculate the cost of exchange rate for the three countries. If this exchange rate is higher than the level of discrepancy, then losses are made from the transaction. Generally, one should calculate the cost of the exchange rate before anything else.
The triangular arbitrage process involves the three exchange rates in the three countries. The Japanese yen is exchanged to British pounds, then the British pound is exchanged to US dollars, and the US dollar is exchanged to yen again. To make a profit from the triangle arbitrage the three exchange rates should be followed, the higher the amount of money exchanged the higher the profit created by the arbitrager.
British pound
Negative direction Positive direction
US dollar Yen
The triangular exchange of USA, Europe, and Japan.
Generating profit from a triangular Arbitrage method
To create profit from the process, one has to follow the positive direction of the triangle; the other direction will be a negative route and can result to losses. Therefore, from the triangle profit can only be generated when one converts yens, to British pound then British pound to US dollars and finally US dollars to yens. Therefore, to create a profit 100,000,000 the method should be as follows.
Yens to British pounds 100,000,000/128= 781,250
British pounds to US dollars 781250*1.6= 1,250,000
US dollars to yen =102, 500, 000
Therefore, from the triangle the profit of 2, 500,000 is created in the exchange rate among the three countries. If the market has not yet balanced, the arbitrager can choose to repeat the same process until the market recovers. If one uses the entire price during the second process, a larger profit is created since the additional profit in the first case used in the process. As long as the arbitrage uses the same process of converting money, there is no loss expected to be generated unless the value of one of the currencies changes on the way.
Loss from the triangle
Every business has both losses and profits, same case happen to the triangular arbitrage method. If the arbitrager uses the wrong direction of the triangle, then they are subjected to make losses. The loss happens when one follows the negative direction and converts yens to US dollars then to British pounds and finally to yens again. The process for 100,000,000 yen is as follows.
To convert yen to British pound = 100,000,000/82= 1,219,512.1951
Convert US dollars to British pound = 1,219,512.1951/1.6=762,195.123
Converting British pounds to yen = 762,195.123 * 128=97, 560,975.61
Therefore from the process, a loss of 2,439,024.39 yens is made because the arbitrager used the negative direction that results to losses. If the same process is repeated, more losses are made. However, this is a rare case since arbitragers know exactly what to do.
However, even though the triangular arbitrage is profitable, the case of price misplacing is rare and such opportunities happen to keen observers in the foreign exchange market. A case of mispricing among banks range between one to five seconds, and it is hard to take such an opportunity within a few seconds. Additionally, the triangle assumes the fact that every bank has a currency selling price that is relatively higher than the buying price. Therefore, even if there is an opportunity the profit might be too low for the risk.
In conclusion, the triangular arbitrage is the method by which people make profit from the mispricing of different currencies. People generate profit only when they follow the positive side of the triangle, but when one follows the negative side a loss is made. Apart from mispricing, one should know the transaction cost of the three countries involved. The triangular arbitrage activity is a speedy one since mispricing happens in less than five seconds. Generally, for one to make a profit, all conditions must be followed.
Reference
Gradojevic, N., Gencay, R., & Erdemlioglu, D. (2017). Robust Prediction of Triangular Currency Arbitrage with Liquidity and Realized Risk Measures: A New Wavelet-Based Ultra-High-Frequency Analysis . In 151 Trading Strategies by Zura Kakushadze and Juan Andrés Serur. Palgrave Macmillan
