An Analysis of ‘Triangle Ordering’ in Foreign Exchange Market (Forex): Simultaneous Ordering of Three Major Currency Pairs

With considering a ‘triangle of three major currency pairs’, there is a tiny difference between multiplication of exchange rate for the first two currency pairs and the third. To discover whether this little difference can lead to a neutral arbitrage or not, I took portfolios of 35 baskets of three major currency pairs(combinations of all 7 major currencies). There are eight approaches (different cases of short and long positions) in each basket; for example buying 1st currency pairs and selling two others, etc. Historical monthly FX rates were gathered from January 1990 until July 2011. Profit or loss derived from eight approaches in all baskets has been calculated. Number of months with a profit has been compared with the months with a loss. Covariance’s of all approaches of FX rates between growth rates were calculated. I found that this ‘triangle ordering’ of three currency pairs will not always eventuate to a profit. In the other meaning, this is not a neutral strategy. The results showed that in 94% of 280 cases, the probability of gaining profit is almost equal to gaining loss. Also it was found that the most profitable approach is not the best in probability of profit. Standard deviations of results (as indicators of risk of the approaches) were diagramed with the amount of profits. This figured ‘efficient frontier’ of approaches, the best combinations of risks and profits. Covariance were often positive (in 70% of 280 cases), showing probability of simultaneous effectiveness of external factors on all currencies.