In general, arbitrage is the purchase or sale of any financial instrument and simultaneous taking of an equal and opposite position in a related market, in order to take advantage of small price differentials between markets. Essentially, arbitrage opportunities arise when currency prices go out of sync with each other. There are numerous forms of arbitrage involving multiple markets, future deliveries, options, and other complex derivatives. A less sophisticated example of a two-currency, two-location arbitrage transaction follows:
Bank ABC offers 170 Japanese yen for one U.S. dollar and Bank XYZ offers only 150 yen for one dollar. Go to Bank ABC and pur- chase 170 yen. Next go to Bank XYZ and sell the yen for $1.13. In a little more than the time it took to cross the street that separates the two banks, you earned a 13 percent return on your original invest- ment. If the anomaly between the two banks’ exchange rates persists, repeat the transactions. After exchanging currencies at both banks six times, you will have more than doubled your investment.
Within the FOREX market, triangular arbitrage is a specific trading strat- egy that involves three currencies, their correlation, and any discrepancy in their parity rates. Thus, there are no arbitrage opportunities when dealing with just two currencies in a single market. Their fluctuations are simply the trading range of their exchange rate.
In the subsequent examples, we refer to the following tables of currency pairs consisting of the five most frequently traded pairs (USD, EUR, JPY, GBP, and CHF) with recent bid/ask rates. See Table 15.1.
We omitted the other two majors, CAD and AUD, for the sake of simplicity and not because there is a lack of arbitrage opportunities in these two majors.
Example 1
Two USD pairs and one cross pair (multiply) First we must identify certain characteristics and distinguish the following categories:
• USD is the base currency (leftmost currency in the pair):
USD/CHF 1.2402/05 USD/JPY 105.61/64
• USD is the quote currency (rightmost currency in the pair):
EUR/USD 1.2638/40 GBP/USD 1.8275/78
A d v a n c e d To p i c s 147
• Cross rates (non-USD currency pairs):
CHF/JPY 85.14/19
EUR/CHF 1.5676/78 EUR/GBP 0.6915/17 EUR/JPY 133.51/54 GBP/CHF 2.2666/74 GBP/JPY 193.02/10
The fact that the USD is the base currency in two of the pairs (USD/CHF and USD/JPY) and is the quote currency in two other pairs (EUR/USD and GBP/USD) plays an important role in the arithmetic of arbitrage. We begin our investigation with just the bid prices (see Table 15.2).
TABLE 15.1 Combinations of the Five Most Frequently Traded Currencies
Currency Bid Ask Pip Spread
CHF/JPY 0.8514 0.8519 4
EUR/CHF 1.5676 1.5678 2
EUR/GBP 0.6915 0.6917 2
EUR/JPY 133.51 133.54 3
EUR/USD 1.2638 1.2640 2
GBP/CHF 2.2666 2.6674 8
GBP/JPY 193.02 193.10 8
GBP/USD 1.8275 1.8278 3
USD/CHF 1.2402 1.2405 3
USD/JPY 105.61 105.64 3
TABLE 15.2 Formulas for Cross Currencies
CHFJPY =USDJPY / USDCHF 85.14 =105.61 / 1.2402 85.1556 EURCHF =EURUSD ×USDCHF 1.5676 =1.2638 ×1.2402 1.567365 EURGBP =EURUSD / GBPUSD 0.6915 =1.2638 / 1.8275 0.691546 EURJPY =EURUSD ×USDJPY 133.51 =1.2638 ×105.61 133.4699 GBPCHF =GBPUSD ×USDCHF 2.2666 =1.8275 ×1.2402 2.266466 GBPJPY =GBPUSD ×USDJPY 193.02 =1.8275 ×105.61 193.0023
The criterion whether to multiply or divide the USD pairs in order to cal- culate the cross rate is simple:
• If the USD is the base currency in both pairs then divide the USD pairs.
• If the USD is the quote currency in both pairs then divide the USD pairs.
• Otherwise multiply the USD pairs.
To determine the deviation from parity for each cross pair, subtract the exchange rate from the calculated rate and convert the floating point decimals to pip values (see Table 15.3).
From the information in Table 15.3, we can see that the EUR/JPY is out of parity by four pips. To determine if an arbitrage opportunity is profitable, we must first calculate the total transaction cost by adding the three bid/ask spreads of the corresponding pairs:
EUR/USD 2
USD/JPY +3 EUR/JPY +3 8
An eight-pip transaction cost to earn a four-pip profit is counterproduc- tive—it amounts to a four-pip loss. If the parity deviation (the number of pips by which the three currency pairs are out of alignment) were greater—say, 30 pips—then a definite arbitrage opportunity exists.
The trading mechanism to take advantage of this anomaly requires some consideration. First, determine what market actions are necessary to correct this anomaly. Assume that the EUR/JPY rate is currently trading at 133.51 and the calculated rate using the current EUR/USD and USD/JPY pairs is 133.81 (a 30-pip deviation). Parity between the three currencies will be restored if the fol- lowing price action occurs:
TABLE 15.3 Calculations for Cross Currencies
Pair Rate Calculation Deviation Pip Values
CHFJPY 85.1556 −85.14 = +0.0156 +1.56 pips EURCHF 1.567365 −1.5676 = −0.000235 −2.35 pips EURGBP 0.691546 −0.6915 = +0.000046 +0.46 pips EURJPY 133.4699 −133.51 = −0.0401 −4.01 pips GBPCHF 2.266466 −2.2666 = +0.000134 +1.34 pips GBPJPY 193.0023 −193.02 = −0.0177 −1.77 pips
A d v a n c e d To p i c s
(A) The EUR/JPY pair rises to 133.81, or
(B) The product of the EUR/USD and USD/JPY pairs drops to 133.51.
Therefore the following trades are required to “lock in” the 30-pip profit:
• Buy one lot of the EUR/JPY pair.
• Sell one lot of the EUR/USD pair.
• Sell one lot of the USD/JPY pair.
• Liquidate all three trades simultaneously when parity is reestablished.
Note:Executing only one or two “legs” of the three trades required in an arbitrage package does not guarantee a profit and may be quite dangerous. All three trades must be executed simultaneously before the “locked-in” profit can be realized.
Example 2
Two USD pairs and one cross pair (divide) Example 1 used the product of the two USD currencies to calculate the cross rate. Now let’s take an example of the ratio of the two USD currencies. Assume the EUR/GBP cross pair is currently trading at 0.6992 and that the ratio between the EUR/USD and GBP/USD pairs is calculated as 0.6952, a 40-pip deviation. Parity will be restored when the following price actions occur:
(A) The EUR/GBP pair drops to 0.6952, or
(B) The ratio of the EUR/USD and GBP/USD pairs rises to 0.6992.
In order for the second action to rise, either the EUR/USD pair must also rise or the GBP/USD pair must decline (this differs from the previous example).
Therefore the following trades are required to realize a 40-pip profit:
• Sell one lot of the EUR/GBP pair.
• Buy one lot of the EUR/USD pair.
• Sell one lot of the GBP/USD pair.
• Liquidate all three trades the moment that parity is reestablished.
Example 3
Three non-USD cross pairs Technically the arbitrage strategy can be performed on three non-USD currency pairs. In this example, we examine a straddle between 149
the three European majors (EUR, GBP, CHF) while focusing on the EUR/CHF pair in respect to the two GBP currency pairs (GBP/CHF and EUR/GBP).
Assume the current rates of exchange are:
EUR/CHF=1.5676/78 EUR/GBP =0.6915/17 GBP/CHF =2.2604/12 and their relationship is:
EUR/CHF =EUR/GBP ×GBP/CHF
Thus the calculated value for the EUR/CHF rate is 0.6915 × 2.2604 or 1.5631. The deviation from parity is −.0045 (1.5631 −1.5676), or 45 CHF pips, since CHF is the pip currency in the EUR/CHF pair. The trading strategy is:
• Sell one lot of EUR/CHF.
• Buy one lot of EUR/GBP.
• Buy one lot of GBP/CHF.
• Liquidate all three when parity is reestablished.
If all three trades are executed successfully, a profit of 45 CHF pips is real- ized. Subtract the three bid/ask spreads for the transaction costs (2 +2 +8 =12) to see a net profit of 33 CHF pips. Now convert CHF pips to dollars (33 divided by the USD/CHF rate, 1.2402) to obtain 27 USD pips.