20.6960.7020.7110.7200.7240.7250.7250.7290.7440.8230.8730.886
4.21.90.91.31.30.50.20.40.10.20.0−0.1−0.60.0−0.2−0.20.00.20.60.81.41.20.60.1−0.10.62.110.66.01.5
−0.394−0.406−0.418−0.418−0.422−0.426−0.427−0.432−0.433−0.432−0.431−0.429−0.429−0.428−0.427−0.423−0.422−0.423−0.422−0.425−0.440−0.454−0.462−0.461−0.460−0.455−0.437−0.432−0.450−0.444−0.544
3.12.80.01.01.00.31.00.4−0.2−0.4−0.40.1−0.2−0.4−0.9−0.30.2−0.10.63.63.21.7−0.2−0.1−1.2−3.9−1.14.1−1.422.6
two days sooner than the gold–XAU. Both correlations then declined until the 20thday. The similarity, however, ended there. The gold–XAU correlation kept risingwhen taking longer time differences whereas the gold–dollar correlation peaked at35 days.
8Intraday Correlations
Probable impossibilities are to be preferred to improbable possibilities.–Aristotle
8.1
RELATIONSHIPS BETWEEN DIFFERENT TIME FRAMES
The analysis of correlations of weekly yields is not really very useful to day tradersor short-term traders of stock index futures.But what about intraday relationships?In Table 8.1 you can see the correlation of percentage changes between the DAX,the Euro Stoxx 50 and the S&P 500 and the DOW e-mini futures for different timeintervals ranging from five to 1500 minutes (25 hours). One trading day for the DAXand Euro Stoxx futures is 14 hours so the correlation study, although calculated overa three-month time span, involves only up to two days of percentage changes.An empirical relationship between time (in minutes) and correlation, which is notso obvious from Table 8.1, unravels when the correlation is plotted vs. time in thegraph in Fig. 8.1. You can see that the correlation increases exponentially up to acertain time increment (about 75 minutes) when it suddenly loses steam and starts tolevel out.To assist traders I have derived the following empirical equations to convert correlations between different time frames.For the DAX–Euro Stoxx relationship:ri = 0.87∗ (Ti ).01
(8.1)
ri = r ∗j (T i/T j).01
(8.2)
and
Gold
109
Figure 7.12 Graph of the correlation between gold bullion, the XAU (bold black line) andthe dollar index (grey line) for variable time segment percent changes for the 10-year periodfrom 1 January 1997 to 1 January 2007. The number of trading days used to calculate thepercent changes is plotted in the X-axis and Pearson’s correlation in the Y-axis.
In choosing the best time frame to use in a trading system or indicator, one’stime horizon should also be taken into consideration. A time increment of nine days,when taking percentage differences, might be the best to use when designing short tomedium term intermarket trading systems.
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Table 8.1 A total of 10 870 5-minute bars were used to calculate intradaycorrelation of percentage yields (changes) between the S&P 500 e-mini futures,the Euro Stoxx, the DAX and DOW e-mini futures for the 3-month period from1 January 2007 to 31 March 2007. Significant correlations are depicted in bold.Minutes
ESTX
DAX
YM
5101520253035404550556065707580859095100125150200250375500750100012501500
0.7250.7500.7670.7790.7830.7880.7820.7760.7800.7830.7870.7850.7860.7880.7880.7880.7880.7870.7860.7850.7850.7860.7830.7800.7780.7860.8120.8300.8310.842
0.7240.7410.7540.7630.7680.7740.7800.7820.7870.7890.7930.7970.8020.8070.8100.8120.8130.8140.8150.8160.8230.8300.8360.8420.8500.8620.8840.8970.9000.910
0.6140.6550.6670.6790.6830.6900.6940.6960.7000.7030.7060.7070.7240.7370.7500.7610.7710.7790.7870.7940.8180.8300.8510.8680.8890.9020.9130.9210.9250.928
and for the ES – DAX relationship:ri = 0.677∗ T .04
(8.3)
ri = r ∗j (T i/T j).04
(8.4)
and
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113
Figure 8.1 Intraday correlation of intraday percentage yields (changes) between the S&P500 e-mini futures, the Euro Stoxx, the DAX and the DOW e-mini futures for the 3-monthperiod from 1 January 2007 to 31 March 2007.
where ri = Pearson’s intraday correlation for time interval i; rj = Pearson’s intradaycorrelation for time interval j; T = time in minutes.Equations 8.1–8.4 above are useful in calculating correlations and regression coefficients for all intraday time frames. For example we can use formula (8.3) to calculatean estimate of the 60-minute correlation between DAX and S&P e-mini futures:r = 0.677∗ 60.04 = 0.797Formula (8.4) can be used to convert correlations between intraday time frames. Forexample we know that the 15-minute correlation between the S&P e-mini and DAXfutures is r = 0.754 and we want to know the corresponding 60-minute correlationcoefficient. By substituting the 15-minute correlation in formula (8.4) we get:r = 0.754∗ (60/15).04 = 0.797
8.2
INTERMARKET REGRESSION
The correlation coefficient calculated above can be used to forecast the expectedchange of one equity index future in terms of the other using the regression equationderived in Chapter 3. So for example:• On 23 March 2007 and at 10:00 CET (02:00 US ET) the price of DAX futures was6894.5 and the ES (S&P e-mini) was 1444.8.• At 11:00 CET the DAX went up by 0.2 % to 6908 but the ES did not move at all.
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• Using the regression equation we can calculate the expected change of the ES interms of the DAX, based on historical data of 60-minute intervals as follows:In the case of highly correlated indices the regression line usually crosses throughthe origin so the constant can be ignored and the regression equation is reducedto:ES = r ∗ sd(ES)/sd(DAX)∗ DAXwhere: ES = S&P e-mini hourly % change; DAX = DAX futures hourly %change; sd = the standard deviation of hourly changes; r = Pearson’s hourlycorrelation between the ES and the DAX. And the expected ES change basedon historical correlations was:ES = .797∗ .185/.239∗ .2 = .12 %.There was therefore a divergence between e-mini and DAX futures, most probablydue to the lateness of the hour (for US traders) and the e-mini needed to catch up.During the next two hours the ES outperformed the DAX by more than 0.16 %, thusnullifying the divergence.
8.3
WHICH TIME FRAME?
In order to choose the best time span for calculating percentage yields in a tradingsystem or indicator, I have listed in Table 8.1 Pearson’s correlation for up to 1500minutes (25 hours) of percentage yields between the S&P e-mini, the Euro Stoxx50 (ESTX), DAX and Dow e-mini futures. These were also plotted graphically inFig. 8.1.After carefully examining both the table and the graph the following conclusionscan be drawn:• Surprisingly, the S&P e-mini correlated better with the European futures thanwith its compatriot, the DOW e-mini, but only for shorter time segments up to35 minutes of yields.• Correlations with European futures peaked between 30 and 35-minute yields andthis is probably the best value to use for short-term predictions based on EuroStoxx futures.• The S&P e-mini correlated better with the Euro Stoxx for very short yields (up to35 minutes), with the DAX for medium (40 to 150 minute) yields and with DOWfutures for longer term (over 150 minute or 2 12 hour) yields.• The correlation between the S&P e-mini futures (ES) and the Euro Stoxx, aftermaking a short-term top at the first 30-minute yield segment, went sideways forthe next 470 minutes (8 hours) but started rising again sharply.• On the other hand, after rising sharply for the first 35 minutes, the correlationbetween the S&P and the DAX continued rising at a more moderate rate.
Intraday Correlations
115
• Similarly, the correlation between the S&P and DOW e-mini futures (YM), aftermaking a short term plateau between the 35-minute and 60-minute increment, keptrising rather steeply until the end.• The correlation coefficient between the S&P and Euro Stoxx futures improvedby only 7 % for longer than 30-minute yields, whereas the correlation with theDOW improved by more than 30 %. It is therefore advantageous to use longer timeframes when designing short-to-medium term intermarket trading systems to tradethe S&P based on its correlation with the DOW.Finally you should keep in mind that the values of the correlations in Table 8.1,although calculated from a big enough sample of 10 870 cases, are not written instone but can vary considerably over time. For example, take a look at the chart ofthe S&P e-mini and Euro Stoxx 15-minute December 07 contracts. The correlationof 30-minute changes (in the top window) varies from a maximum of r = 0.86 on19 September to a minimum of r = 0.72 on 9 October 2007. The correspondingaverage correlation calculated in Table 8.1 from a different sample from 1 January2007 to 31 March 2007 was r = 0.788 (in bold) which is pretty close to the averagein the chart in Fig. 8.2. In addition to the short-term variations mentioned above,
Figure 8.2 Intraday (15 minute) composite chart of the S&P e-mini (ESZ7), plotted with athick bold line and the Euro Stoxx 50 (FESXZ7) December 2007 contracts from 18 September2007 to 18 October 2007. The 10-day moving average of the correlation of the 30-minutechanges is plotted in the top window.
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the correlation can also digress from the mean during long time periods, caused bytemporary decoupling of the underlying equity indices which is usually caused by acomponent stock specific problem not present in the other index.
8.4
LAGGING OR LEADING?
In practice, the main purpose of a predictive model is not to get the maximumexplanatory value from a contemporaneous correlation analysis but to find a predictivemarket that shows changes and disparities between forecasted and observed values,warning of dangers and opportunities well ahead of time. In this context, we wantthe observed values to diverge from the statistically predicted values at times. Thiscan only be accomplished by a leading/lagging correlation analysis which is simplya list of the correlations between values of a time series and other values of a relatedtime series displaced at specified time intervals (lags).Some problems arise in running a correlation analysis between US and Europeanindex futures, mainly because of the different time zones and trading hours. To dealwith the time zone problem I had to convert all time zones to Central European time(CET) and in order to avoid division by zero errors in the correlation calculation(when one of the contracts was not trading), I deleted all US futures data when theEuropean futures were closed (from 22:00 to 7:50 CET).Although European index futures trade long after the underlying equity marketshave closed, after 17:30 CET (when the European equity exchanges close) they moveonly on news from the other side of the Atlantic.To deal with this problem and examine the effect of the US equity markets onEuropean futures after the underlying main equity exchanges have closed or viceversa, I have divided the data into five separate groups according to the time of day.In the first group I have included only data until 14:30 CET (8:30 US EST). This isthe time when European stock action and news are prevailing before the release ofany important US economic news.The second time segment was until US market open (15:30 CET or 9:30 US EST).The third group included only data until 17:30 CET (10:30 US EST) which is theclosing time of most European stock exchanges. In the fourth group I have includedall available data from 8:00 to 22:00 CET and, lastly, in the fifth group I haveincluded only data after 15:30 CET (9:30 US EST). This is the time segment whenthe prevailing news that drives the markets originates mostly from the United States.In addition, in order to determine which one was leading or lagging, the S&Pe-mini was shifted both forward and backward in time.Table 8.2 presents the leading, lagging and synchronous (coincident) correlationsof 30-minute yields during the different time segments of the trading day between theS&P e-mini and Euro Stoxx futures, the DOW e-mini and the DAX, and in Table 8.3you can see the intraday variability of the correlation between DAX and Euro Stoxxfutures.
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117
Table 8.2 Intraday correlation of 30-minute intraday yields (percentage changes) betweenS&P 500 e-mini futures, the Euro Stoxx, the DAX and DOW e-mini futures for specific timeof day segments. Column 3 shows only data until 14:30 CET (Central European time) or 8:30US EST, Column 4 shows only data until US market open (9:30 US EST), Column 5 showsonly data until European close (17:30 CET) and Column 6 shows only data after US marketopen (9:30 US EST). The S&P data were shifted forward and back in time in order tocalculate lagging and leading correlations.TIME (CET)30 minyields
lead/lag
<14:30
<15:30US open
<17:30EUR close
08:00–22:00All day
>15:30
ESTXESTXESTXYMYMYMDAXDAXDAX
synchronouslaggingleadingsynchronouslaggingleadingsynchronouslaggingleading
0.8110.6630.6680.6060.5120.4850.8180.6760.668
0.7950.650.6550.5960.5030.4830.7970.6580.654
0.7810.6320.6340.6800.5690.5580.7760.6350.63
0.7880.6520.6490.6900.5830.5710.7740.6440.64
0.8150.6760.6650.7350.6150.6090.7980.6630.655
The following conclusions were drawn from the leading, lagging and synchronoustime segmented correlations in Tables 8.2 and 8.3:• The best synchronous correlation was between S&P e-mini and Euro Stoxx futures(r = 0.788 in bold in the Column-5 of Table 8.2 and r = 0.815 after 15:30 CET).The Euro stoxx was slightly leading the e-mini up to 15:30 CET but the leadTable 8.3 Intraday correlation of 30-minute intraday yields (percentage changes) betweenthe Euro Stoxx and DAX futures for specific time of day segments. In the first row only datauntil US market open (15:30 CET) were used, in the second row only data until Europeanmarket close (17:30 CET) were used, and in the fourth row only data after US market open(9:30 US EST) were used. In order to calculate lagging and leading correlation the EuroStoxx data were shifted forward and back in time.DAX
<15:30<17:3010:00–22:00>15:30
Time of day CET
synchronous
lagging
leading
Before US openBefore EUR closeAll dayAfter US open
0.8570.8830.8970.948
0.6960.7160.7400.789
0.6870.7070.7310.781
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Intermarket Trading Strategies
Figure 8.3 Intraday (5 minute) composite chart of the S&P e-mini (thick bold line) andEuro Stoxx 50 (thin line with the scale on the right Y-axis) contracts from 18–20 December2007. The 5 bar moving average of the correlation of the 30-minute changes between the S&Pe-mini and Euro Stoxx futures is also plotted in the top window. To illustrate the correlationvariability during the trading day, vertical lines are drawn at the EUREX open (8:00 CET),at 14:30 CET (US pre-open), 17:30 CET (European equity close) and 22:00 CET (EUREXfutures close). Euro Stoxx futures trade in the EUREX from 8:00 am CET to 22:00 CET. Toavoid division by zero errors in the correlation calculation when the Euro Stoxx doesn’t trade,non overlapping e-mini data (from 22:00 to 8:00 CET) were deleted.
reversed dramatically to a considerable lag (r lagging = 0.676 vs. r leading =0.665) after the US market open. It is therefore better to avoid intermarket tradingsignals before 15:30 CET when designing an intermarket system to trade the EuroStoxx based on its correlation with the S&P e-mini.• The DAX futures lagged both the Euro Stoxx futures (Table 8.3) and the S&Pe-mini (Table 8.2) for all time frames; a slight lag up to European close deteriorated significantly after 17:30 CET (European close). As the DAX correlatedsignificantly better with Euro Stoxx futures than with the e-mini, it is better touse this relationship in designing an intermarket system to trade DAX futures,at least until US market open. After 15:30 both European futures lagged the USfutures; therefore replacing the Euro Stoxx with the e-mini might have a lead timeadvantage, despite the lower correlation.
Intraday Correlations
119
• Surprisingly, the DOW e-mini, despite the underlying index sharing all of itscomponent stocks with the S&P 500, did not correlate with the S&P e-mini aswell as Euro Stoxx futures. In addition, the DOW lagged the S&P e-mini duringall time segments. It is therefore preferable to trade the DOW e-mini based on itscorrelation with the S&P e-mini and not the other way around.The variability of the correlation during the trading day, presented in Table 8.2 intabular form, can also be seen graphically in the chart in Fig. 8.3 where the correlationof 30-minute changes between the S&P e-mini and Euro Stoxx futures is plottedin the top window. For example, you can see that on 18 December 2007, the correlationrose to a maximum during the first time segment (before 14:30 CET) and then fell toan intraday low during the second and third time segments. It then rose again exactlyto the level of the morning high during the end of the last time segment (after about22:00 CET).In designing intermarket systems to trade stock index futures, it is therefore betterto use intermarket generated signals only when the underlying equity markets areclosed and the leadership switches to related markets that are still open.
9Intermarket Indicators
I’m a great believer in luck, and I find the harder I work, the more I have of it.–Thomas JeffersonClassic technical analysis indicators, such as moving averages, only indicate thepossible likelihood of the continuation of the current trend and they are certainly noguarantee of future direction, which can reverse on a dime.The indicators presented in this chapter, unlike moving averages, will help youjudge the direction of tomorrow’s price, and possible trend reversals using intermarketcorrelations.
9.1
RELATIVE STRENGTH
Relative strength (RS) is a popular indicator which compares one security withanother or with a benchmark index, for example a specific US stock with the S&P500.Relative strength in the stock market was popularized in the 1980s by WilliamO’Niel in his classic How to Make Money in Stocks. O’Niel is also the founder ofR100 stock list featuringInvestor’s Business Daily, where he publishes the IBDcompanies that show superior earnings and strong price performance relative to themarket average.The relative strength is calculated by dividing the price of one security by thebenchmark. The ratio is further smoothed by a moving average in order to eliminatethe effect of erratic price movements or “noise” from daily price fluctuations.When this ratio is rising, the numerator is outperforming the denominator and viceversa.In Fig. 9.1 I use the ratio between the Gold ETF (GLD) and the dollar index(DXY). To remove daily noise the ratio is smoothed by its 3-day exponential moving
Intermarket Indicators
123
sell signals triggered by the oscillator crossing its 4-day moving average from belowon oversold (less than 50) levels and crossing its moving average from above onoverbought (over 80) levels respectively.The relative strength between a stock and the appropriate index can also be used toevaluate one’s stock portfolio. If the relative strength drops below its moving averagewhile the price of the security is still rising, then it is time to consider heading for theexit while the stock is still strong.This tactic can be combined with a moving average strategy to help you get out ata better price than if you were using a moving average of the price alone.
9.2
BOLLINGER BAND DIVERGENCE
This indicator was first introduced in my article “Detecting Breakouts” in TechnicalAnalysis of STOCKS & COMMODITIES (see Bibliography) in order to calculatethe divergence between price and money flow. It can also be used to calculate thedivergence between a security and a related market. First the relative position ofboth securities in the Bollinger Bands is calculated and the divergence is derived bysubtracting the relative position of the intermarket security from the base security.Indicator values vary from −100 to +100, values less than zero indicate negativedivergence and over zero positive divergence. Buy signals are generated when theindicator reaches a peak above a certain level (usually 10 to 30) and subsequentlydeclines. Similarly, sell signals are triggered when the indicator reaches a bottombelow a certain level (usually −10 to −30) and rises.The formula for the relative position of a security in the Bollinger Bands is derivedas follows:SEC1BOL=(C-BollingerBBottom)/(BollingerBTop-BollingerBBottom)but BollingerBandBottom=MA−2SD
(9.1)(9.2)
and BollingerBandTop=MA+2SD.
(9.3)
Substituting from (9.2) and (9.3) in (9.1) we getSEC1BOL=(C-MA+2SD)/4SD.
(9.4)
The formula above will produce the relative position of a security in the BollingerBands. Values of 1 indicate that it has reached the top band and values of zero indicatethat it has reached the bottom band. To eliminate negative values (when price fallsbelow the bottom band) the final value is increased by one and the formula becomes:SEC1BOL=1+(C-MA+2SD)/4SD
(9.5)
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Intermarket Trading Strategies
The divergence is then calculated by taking the 3-day exponential moving averagepercentage difference between the relative position of the related intermarket securityand the security to be traded as follows:DIVERGENCE=EMA(3)[(SEC2BOL−SEC1BOL)/SEC1BOL ∗ 100]
(9.6)
where SEC1BOL=Relative position of the base security in the BollingerBands; SEC2BOL=Relative position of the intermarket security in the BollingerBands; MA=Moving average; SD=Standard deviation; EMA=Exponential MovingAverage.There are some limitations with the underlying Bollinger Band theory that shouldbe understood before applying it to trading:• The formula involves the calculation of the standard deviation which makes the assumption of normality and it is therefore subject to error when the price distributiondeviates significantly from normality.• Because of scaling factors the formula doesn’t work so well with negatively correlated markets.You can find the MetaStock code for all intermarket indicators in Appendix A. Thereare two ways of entering data for the intermarket security (SEC2). The first method(used in the relative strength indicator) is by referencing the symbol and folder in thefirst line of the code. For example in the lineSEC2:=Security(“C:\MetastockData\INTERMARKET\DXY0”,C);C:\Metastock Data\INTERMARKET is the folder in my hard drive where historicaldata for the dollar index is located; DXY0 is the symbol for the Dollar Index; and Cindicates that I want to reference only the closing price.An alternative method (used in the case of the Bollinger Band divergence indicator)is to drag and drop the indicator on the dollar index chart until it changes color to pink(the dollar index and not the indicator). This method cannot be used, however, whenback-testing an indicator. An advantage of using the first method is that there is noneed to have a chart of the intermarket security plotted in order to use the indicator.Tradestation users can only use the second method and a chart of the intermarketsecurity should be always plotted together with the base security.
9.3
INTERMARKET DISPARITY
The disparity index was first introduced by Steve Nison in his book Beyond Candlesticks: New Japanese Charting Techniques Revealed (see Bibliography) and it hassince been incorporated in the majority of popular technical analysis software.
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Intermarket Trading Strategies
Figure 9.1 Composite chart of the Gold ETF (GLD) and the dollar index (DXY) for the2-year period from July 2005 to July 2007. The 3-day moving average of the gold/dollarrelative strength is depicted in the middle window and the 2000-day intermarket momentumoscillator (see Section 9.6) in the top window. Up and down arrows indicate sell and buysignals triggered by the oscillator crossing its 4-day moving average at overbought (over 80)and oversold (less than 50) levels respectively.
average (EMA). This is plotted in the middle window and, to avoid confusing itwith Wilder’s Relative Strength Index, I called it Intermarket Relative Strength.Classic technical analysis trendlines can be drawn by joining tops or bottoms. On27 March 2006 the gold/dollar ratio broke the trendline drawn over the three previouspeaks (the first, shorter trendline on the left of the chart in Fig. 9.1) and the price ofthe gold ETF surged 27 % from 55.7 to 71.1. Similarly, on 27 October 2006 the ratiobroke its 5-month down trendline (second trendline in the middle) which indicated atrend reversal for gold.The relative strength, however, cannot keep rising indefinitely, flagrantly violatinglong-term relationships. To determine overbought and oversold levels, I normalize iton a scale from 1 to 100 using the intermarket momentum oscillator (the formula isincluded in Section 9.6 below).Values over a specific value (e.g. 80) indicate overbought levels and below anotherlower value (e.g. 50) oversold levels. In Fig. 9.1, I marked some possible buy and
Intermarket Indicators
125
Figure 9.2 Composite chart of the gold (GLD) and silver (SLV) ETF. The 20-day intermarketBollinger Band divergence indicator is depicted in the top window. Horizontal lines are drawnat the 1