چکیده:
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.
خلاصه ماشینی:
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.
Approach If we consider all the seven major currencies (USD, EUR, JPY, GBP, CHF, CAD, and AUD) we will have 35 baskets of triangles of three currency pairs: C37= 35 These baskets are listed in table 1.
Table 3 (Basket 1, profit / loss derived from 8 different approaches) SSB SBS BSS BBS BSB SBB SSS BBB Month -$23,277 $577 -$27,757 $85,347 $56,861 $49,156 $22,700 -$72,894 -$37,144 $139,837 .
Apr-90 Mar-90 Feb-90 Jan-90 $287,121 $219,984 $1,099,772 -$287,121 -$219,984 -$1,099,772 $1,606,877 -$1,606,877 SUM Monthly averages of profit / loss are calculated.
Columns ‘Positive %’ and ‘Negative %’ represent the present of months with profit / loss from all 258 months: Vol. 1 / No. 2 / Spring 2011 Table 4 (Monthly average of returns, Risks, Percent of months with profit / loss) Negative % Positive % Negative # Positive# STDEV MPornotfhitly Profit Approach Basket 50.
Vol. 1 / No. 2 / Spring 2011 Diagram 3 (profits and risks of various approaches in all baskets) Efficient Frontier N 8,000 M L 7,000 K 6,000 J H I 5,000 FG 4,000 3,000 2,000 E CD 1,000 B A 0 0 20,000 40,000 60,000 80,000 100,000 -1,00 -2,000 -3,000 -4,000 -5,000 -6,000 -7,000 -8,000 Standard Deviation Table 8 (dots on the efficient frontier curve) Details BSS Currencies JPY-CHF-CAD Positive60.
9% STDEV2,800 Profit 178 Approach 7 Basket 29 A SBS USD-EUR-CHF 47.