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The actual trading mechanism requires executing three market entry trades simul- taneously the exact moment that the exchange rate anomaly appears, then liquidating all three trades simultaneously as soon as the previous exchange rate parity has been reestablished.
TRIANGULAR ARBITRAGE CHART
In Figure 5.1, we examine the EURUSD, the GBPUSD, and their corresponding cross rate the EURGBP for Tuesday, January 14, 2003, 12:00 A.M. to 11:59 P.M. using one-minute closing quote data.
FIGURE 5.1 EUR-GBP-USD Triangular Arbitrage Chart
Arbitrage 25
EQUILIBRIUM
The upper three charts in Figure 5.1 are simply line charts of the three underlying cur- rency pairs, while the bottom chart illustrates any arbitrage opportunities present. The formula to calculate the data in the bottom chart is based on the theoretical identity known as the equilibrium formula, shown in Figure 5.2, which means the value of a cross rate should equal the ratio of the two corresponding USD pairs. In turn, that can be used to plot the corresponding arbitrage oscillator. (See Figure 5.3.)
To determine if an arbitrage opportunity does exist and is in fact profitable, we must first consider the transaction cost. We will assume that most reputable currency dealers will charge three pips for the transaction cost of the major currency pairs and four pips for the transaction cost of a major cross rate. Therefore, the cost to execute one round- turn arbitrage trade in the EUR-GBP-USD triangle is 10 pips.
If we had executed such a trade at 1:45 A.M. when the arbitrage oscillator hit 18 pips and liquidated as soon as the arbitrage oscillator returned to zero or less, we would have earned an 8-pip profit with minimal risk.
The chart in Figure 5.1 illustrates an instance of where only one major anomaly oc- curred within a 24-hour time frame. Figure 5.4, whose time range is one week later (Tuesday, January 21, 2003, 12:00 A.M. to 11:59 P.M.), illustrates numerous arbitrage op- portunities.
There are more than a dozen instances within a 24-hour time frame where the arbi- trage oscillator exceeds the transaction cost requirement. Notice that the cross rate chart (EURGBP, third from top) begins relatively smoothly but after 2:30 P.M., it becomes very spiky (i.e., less smooth). It is during these periods that numerous arbitrage opportu- nities may present themselves in a single triangle. Also interesting to note is the fact that all of the anomalies after 2:30 P.M. occurred on the same side of the zero mean line.
Figure 5.5 is an example of the CHF-JPY-USD triangle for Thursday January 9, 2003,
12:00 A.M. to 11:59 P.M., where there are at least six arbitrage opportunities with the 24- hour time frame using one-minute closing quotes.
EURGBP = EURUSD GBPUSD
FIGURE 5.2 EURGBP Equilibrium Formula
Arbitrage Oscillator =
EURUSD
GBPUSD − EURGBP
FIGURE 5.3 Arbitrage Oscillator Formula
FIGURE 5.4 EUR-GBP-USD Triangular Arbitrage Chart
FIGURE 5.5 USD-CHF-JPY Triangular Arbitrage Chart
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Arbitrage 27
We selected this specific triangle because the equilibrium formula differs slightly from the previous triangle: EURGBP = EURUSD/GBPUSD. This formula is applicable only when the USD is the quote currency in both the USD currency pairs. However, in the CHF-JPY-USD triangle, the USD is the base currency in the two USD currency pairs. This difference determines which pair is in the numerator and which is in the denomi- nator. The equilibrium formula for the CHF-JPY-USD triangle is shown in Figure 5.6.
In the preceding examples, we noticed that when anomalies do occur, the arbitrage oscillator normally returns to or near the zero mean shortly thereafter. In the next chart (Figure 5.7), we see a not-too-common phenomenon where a 14-pip anomaly occurs only to be immediately followed by a 19-pip anomaly in the opposite direction. Techni- cally, both anomalies could have been trapped with a single arbitrage trade, which would have netted the trader a 33-pip profit before transaction costs.
CHFJPY =
FIGURE 5.6 CHFJPY Equilibrium Formula
USDJPY USDCHF
FIGURE 5.7 USD-CHF-JPY Triangular Arbitrage Chart
28 FOREX-SPECIFIC CHARTING TECHNIQUES
TABLE 5.1 Equilibrium Formulas for
Major Currencies
Currency Formula
EURGBP EURUSD/GBPUSD EURCHF EURUSD × USDCHF EURJPY EURUSD × USDJPY GBPCHF GBPUSD × USDJPY GBPJPY GBPUSD × USDJPY CHFJPY USDJPY / USDCHF
MAJOR CURRENCIES
In any currency pair, the currency listed on the left is called the base currency and the currency on the right is the quote currency. Central banks and currency dealers have more or less arbitrarily established a relationship condition that determines the base/quote positions for each pair. It is this relationship that dictates what the mathe- matical formula will be on the right side of the equation. (See Table 5.1.) Note the im- portance of the arithmetic operators / and x.
OBSERVATION
As mentioned earlier, we included this chapter in the belief that, in currency trading, any information on the inner working of the market can be illuminating or at least help- ful. However, the small-cap day trader should be aware that even though arbitrage op- portunities are always present, they are unfortunately very short-lived and correct themselves in less than a minute or so. Automated trading software is the only realistic method of trapping risk-free arbitrage profits.
CHAPTER 6
The Mundo
OVERVIEW
In Currency Trader’s Companion: A Visual Approach to Technical Analysis of Forex Markets (2004), we introduced the synthetic global currency, the Mundo, to which we gave an International Organization for Standardization (ISO) symbol of ICU for interna- tional currency unit. We arbitrarily defined the prevailing price of the Mundo as the arithmetic average price of the 10 most frequently traded major and minor USD cur- rency pairs: EURUSD, GBPUSD, USDJPY, USDCHF, USDCAD, AUDUSD, NZDUSD, USDSEK, USDNOK, and USDDKK.
All pairs are treated with equal weight, which means six of the pairs must be ad- justed so that the USD is the quote currency. The reciprocals (divide the exchange rate into 1) of the USDJPY, USDCHF, USDCAD, USDSEK, USDNOK, and USDDKK must be calculated to create the JPYUSD, CHFUSD, CADUSD, SEKUSD, NOKUSD, and DKKUSD pairs. This ensures that any price change in any of the 10 pairs is measured in pips of the same currency unit, the USD.
Summing the most recent values of these 10 pairs and dividing by 10 yields the cur- rent price of the Mundo.
FOREX BETA
We can now use an analogous coefficient to compare the volatility of a single currency pair to the volatility of the overall forex market as described in terms of the volatility of the Mundo.
Rather than using the ratio of the slope of a single currency pair and the slope of the ICUUSD pair, we will use the standard deviation of each. We can justify this change
29
30 FOREX-SPECIFIC CHARTING TECHNIQUES
because of a major difference in the trading philosophies of stocks and spot currencies. Nearly all stock traders use a buy-and-hold strategy in which they hope that their invest- ment will more than better the current inflation rate over a long period of time. Thus stock traders hold a long position in their trades and, in nonleveraged positions, they own the shares of stock outright.
Spot currency traders, by contrast, are not buying shares in a corporation or a mu- tual fund. They feel equally comfortable on either side of a currency trade, long or short. A forex trade is, in fact, the simultaneous buying of one currency while selling another currency. Spot currency traders (particularly scalpers) may initiate a long trade, follow a five-minute rally, liquidate the long position at its peak, and then initiate a short posi- tion in the same currency pair and follow that security’s decline to the next trough.
Therefore, spot currency traders are not particularly interested in the long-term slope of any currency pair. Instead they are more interested in the number of significant peaks and troughs that occur during their trading sessions. The standard deviation is therefore employed in our model for forex beta (though many may agree that this is a misnomer).
To calculate the forex beta of, say, the EURUSD pair see Figure 6.1.
A running calculation of this statistic using streaming data informs the forex day trader which currency pairs are showing the highest volatility relative to the whole spot market. This identifies the pairs with the highest risk/reward factor. The order of these pairs may change throughout the day as central banks around the world open and close.
Table 6.1 illustrates the standard deviation and beta coefficient for each of the 10
Beta(EURUSD) = StdDev(EURUSD) StdDev(ICUUSD)
FIGURE 6.1 Forex Beta Formula
TABLE 6.1 Forex Beta for Mundo Pairs
Standard
Currency Pair Deviation Beta
EURUSD 802.61 2.28
GBPUSD 745.48 2.11
CHFUSD 570.65 1.62
JPYUSD 570.19 1.62
NZDUSD 506.27 1.44
AUDUSD 437.44 1.24
ICUUSD 352.70 1.00
CADUSD 253.73 0.72
NOKUSD 124.65 0.35
DKKUSD 109.26 0.31
SEKUSD 94.43 0.27
The Mundo 31
pairs for the time range 1/1/2000 through 6/30/2003. During this period, the Mundo ex- hibited a standard deviation of 352.70 pips (or 3.53 U.S. cents).
Thus, when compared to the aggregate currency pair ICUUSD, the EURUSD showed the highest beta coefficient and therefore carries the greatest risk/reward fac- tor. In other words, for the time period examined, the EURUSD was 2.28 times more volatile than the average of all 10 currencies.
MUNDO LINE CHART
Figure 6.2 is the line chart for the Mundo during the same time frame.
The first aspect to note is that the Mundo has a lower parity rate than the USD, roughly 53 to 67 U..S cents. Second, slight changes in the same price direction in the 10 underlying currency pairs may cause an exaggerated price change in the Mundo. This phenomenon is also partially due to the use of reciprocals in six of the currency pairs.
This study is in no way definitive or authoritative. It is simply a novel approach to currency pair selection using aggregate standard deviations.
FIGURE 6.2 Unweighted Mundo Chart