any loss, simply that these losses are due tothe market, not to our inability to cut losing trades early. In addition, this strategy is a perfect example of the relatively benignimpact of other traditional risks. With 118 positions a yearÐthatis, 250 open daysÐwe are trading on average every other day,holding a position for 24 hours. In that context, it is unlikely thatdividends, interest rates, or borrowing rates for RD or SC will everbe a problem.
CHAPTER 10
PAIR TRADING AND TECHNICAL TRADING
481
DJI Pairs
In this example, we will examine a more systematic approach to pairtrading, not relying anymoreÐeven if we did not use itÐon any sort ofknowledge about the stocks involved. Like RD/SC, this model iswidely used in practice but allows many more variations.The idea is to compute a short-term correlation between a numberof stocks typically included in an index. From there we systematicallytrade the pairs with the highest correlation regardless of any industryrepresentation. As an illustration, Table 10-5 shows the three-monthcorrelation of all pairs of stocks included in the Dow Jones IndustrialAverage index between August and November 1999. The bold ®guresrepresent the extremes:. Philip Morris (MO) and IBM (IBM): 0.95. Hewlett Packard (HWP) and IBM: 0.93
. United Technologies (UTX) and Disney (DIS): 0.92. MO and Goodyear (GT): 0.91
. Exxon (XON) and Chevron (CHV): 0.9019
And on the other side:. Wal-Mart (WMT) and IBM:
0.910.89. IBM and Merck (MRK):0.88. WMT and HWP:0.86. General Electric (GE) and Goodyear (GT):. WMT and MO:
0.84
Based on these ®gures we decide to trade systematically the ®ve ®rstpairs, MO/IBM, HWP/IBM, UTX/DIS, MO/GT, and XON/CHVÐthe same way we traded SC/RD, using a normalized measure of thedeviation from a 30-day moving average of the ratio as a tradingsignal. For example, the charts in Figures 10-5 and 10-6 show theratio IBM/HWP, its 30-moving average, and the corresponding normalized deviation norm. Next we trade every pair in a manner identical to the way we traded SC and RD. We ®x the threshold at 1.5standard deviations and enter the arbitrage with a ®xed-quantityhedge based on the 30-day moving average of the ratio betweenthe two stocks. The chart in Figure 10-7 plots the resultsÐthat is,
19
Exxon merged in December 1999 with Mobil to form Exxon Mobil (XOM).
TABLE 10-5AAAAALDAXPBAC
ALD
AXP
BA
C
CAT
0.75
-0:27
0.49
0.35
0.73
0.70
0.65
0.73
0.47
0.59
0.30
0.80
0.78
0.67
0.27
0.04
0.29
0.29
0.19
0.52
0.67
0.57
0.25
0.77
0.37
0.27
0.72
0.55
0.82
0.24
0.24
0.39
0.76
0.54
0.53
0.76
0.68
0.52
0.24
0.78
0.85
0.81
0.17
0.20
0.26
0.20
0.03
0.65
0.84
0.67
0.20
0.79
0.42
0.05
0.75
0.64
0.74
0.08
0.85
0.04
0.02
0.05
0.19
0.56
0.77
0.82
0.48
0.54
0.66
0.37
0.71
0.53
0.46
0.22
0.20
0.58
0.73
0.63
0.27
0.38
0.52
0.17
0.76
0.13
0.07
0.51
0.56
0.62
0.58
0.24
0.37
0.24
0.50
0.43
0.31
0.12
0.28
0.38
0.48
0.55
0.38
0.29
0.16
0.09
0.48
0.28
0.32
0.67
0.38
0.46
0.14
CATCHVDDDISEKGEGMGTHWPIBMIPJNJJPMKOMCDMMMMOMRKPGSTUKUTXWMTXON(Source: Compiled by author from Bloomberg data.)
CHV
DD
DIS
EK
GE
GM
GT
HWP
IBM
IP
JNJ
JPM
KO
MCD
MMM
MO
MRK
PG
S
T
UK
UTX
WMT
XON
0.01
0.06
0.25
0.73
0.83
0.84
0.65
0.61
0.77
0.57
0.74
0.68
0.55
0.35
0.18
0.72
0.74
0.75
0.31
0.37
0.67
0.19
0.80
0.13
0.65
0.83
0.82
0.47
0.51
0.20
0.75
0.70
0.55
0.36
0.12
0.48
0.53
0.31
0.62
0.66
0.47
0.21
0.86
0.65
0.43
0.86
0.51
0.76
0.56
0.71
0.06
0.30
-0.07
0.50
0.57
0.38
0.53
0.33
0.58
0.60
0.21
0.57
0.35
0.27
0.13
0.57
0.35
0.43
0.69
0.34
0.90
0.64
0.33
0.47
0.21
0.67
0.48
0.35
0.27
0.17
0.43
0.48
0.38
0.42
0.48
0.31
0.30
0.79
0.59
0.54
0.72
0.32
0.63
0.56
-0.54
-0.30
0.74
0.81
0.69
0.28
0.02
0.43
0.46
-0.39
0.70
0.72
0.58
0.14
0.81
0.41
0.26
0.92
-0.69
0.82
0.73
0.60
0.77
0.75
0.86
0.38
0.57
0.28
0.26
0.25
0.23
0.88
0.74
0.57
0.62
0.03
0.37
0.55
0.80
0.29
0.85
0.84
0.74
0.80
0.31
0.56
0.31
0.15
0.51
0.00
0.82
0.84
0.79
0.67
0.03
0.26
0.56
0.89
0.44
0.57
0.52
0.64
0.45
0.72
0.55
0.45
0.48
0.17
0.61
0.74
0.82
0.37
0.35
0.42
0.23
0.77
0.17
0.87
0.86
0.14
0.28
0.00
0.09
0.46
0.36
0.91
0.75
0.56
0.83
0.30
0.05
0.79
0.81
0.65
0.93
0.07
0.30
0.13
0.16
-0.22
0.53
0.92
0.80
0.33
0.77
0.25
-0.10
0.79
0.86
0.73
0.18
0.54
0.14
0.12
0.22
0.38
0.95
0.88
0.50
0.69
0.07
0.32
0.65
0.91
0.57
0.49
0.75
0.65
0.34
0.48
0.18
0.18
0.56
0.18
0.49
0.74
0.26
0.25
0.49
0.71
0.75
0.05
0.28
0.48
0.68
0.71
0.10
0.42
0.59
0.13
0.55
0.12
0.88
0.16
0.67
0.09
0.20
0.60
0.36
0.64
0.78
0.51
0.19
0.55
0.09
0.53
0.06
0.19
0.50
0.39
0.65
0.70
0.57
0.09
0.52
0.01
0.27
0.20
0.46
0.24
0.00
0.03
0.39
0.43
0.10
0.38
0.23
0.27
0.51
0.49
0.43
0.65
0.26
0.64
0.87
0.54
0.78
0.21
0.24
0.71
0.89
0.57
0.66
0.68
0.03
0.27
0.54
0.90
0.52
0.39
0.24
0.34
0.12
0.60
0.01
0.49
0.31
0.86
0.66
0.78
0.63
0.56
0.04
0.43
0.33
0.32
0.41
0.64
0.800.50
CHAPTER 10
PAIR TRADING AND TECHNICAL TRADING
Figure 10-5 IBM/HWP(Source: Compiled by author from Bloomberg data.)
Figure 10-6
IBM/HWP Norm Aligned
483
484
COMMON ARBITRAGE SITUATIONS
Figure 10-7 DJI Pair Results
the accumulated pro®t for each pair over the period.20 Interestingly,the ®ve pairs seem to be pro®table, although this may be a result ofthe methodology because we computed each correlation at the end ofthe interval. There are, nevertheless, some interesting insights to begained from this chart and Table 10-6, which is only a summary ofthe numerical gains for each pair. In particular, it is interesting tonote that the magnitude of the pro®t associated with each pair isunrelated to the correlation of the two stocks. For example, despitea high correlation, MO/IBM and UTX/DIS do not seem to present asigni®cant opportunity, whereas XON/CHV, on the contrary, is themost pro®table. In addition, despite being pro®table, MO/IBM,UTX/DIS, and to some extent MO/GT, are relatively disappointingbecause their total P&L never goes very high and is at times negative.The only two pairs that seem to perform adequately are HWP/IBM
20
Note the fact that our approach is slightly inconsistent. We select pairs based on athree-month correlation from August to November 1999 and trade them fromDecember 1997 to November 1999. In reality, we should have computed the correlation at the beginning of the periodÐthat is, December 1997 to March 1998. Thisproblem is relatively benign here because the purpose of the exercise is to providea practical illustration of the proposed strategy, and its effect is to show the strategyas more successful than it probably is.
CHAPTER 10
PAIR TRADING AND TECHNICAL TRADING
485
TABLE 10-6PairMO/IBMHWP/IBMUTX/DISMO/GTXON/CHV
Correlation
P&L
0.950.930.920.910.90
$4.55$18.66$5.04$12.30$29.79
and XON/CHV. This is hardly surprising because these two pairs areextracted from identical industries. Therefore, there is a common factor in the stock price of each member of the pair, and our tradingstrategy is only trying to express this particular factor, apparentlywith some success.Therefore, it looks like a systematic approach like the one wejust implemented is no better than a purely intuitive selection inwhich we pick stocks based on some common factor, typicallytheir industrial sector. This is not entirely true, however, becausesuch a rapid conclusion overlooks two important elements in whatwe did.First, a systematic approach based on a statistical analysis of alarge universe of stocks is one more step in the direction of lesshuman intervention. The idea behind the process is that if a givenpair has a good reason to be traded, then the statistical process will®nd it, and indeed this is exactly the case for HWP/IBM and XON/CHV. However, a statistical selection has the added advantage ofinvestigating beyond the obvious. For example, in our case nobodywould have proposed to pair Disney with United Technologies, andstill the pair is pro®tableÐalthough barely. Not only did the statistical approach give ®ve pairs instead of two, it also opened newopportunities. If we think it is appropriate to trade stocks that arehighly correlated, it may also be appropriate to trade stocks that arehighly uncorrelated, taking an opposite position. For example, WMTand IBM have a correlation of 0:91, which suggests that they movein opposite directions quite often. Therefore, when the spreadbetween them gets too thin, we can take a position based on theexpectation that it will widen again very quickly. Such a strategy isindeed pro®table on IBM/MRK, WMT/MO but loses on the otherthree pairs. In essence, being systematic offers a number of advantages, if nothing else because it signi®cantly enlarges the availableuniverse. With no need to thoroughly research every stock, a trader
486
COMMON ARBITRAGE SITUATIONS
can virtually explore thousands of opportunities provided he or shehas the adequate computing power.21By far, however, the most important bene®t of a systematicapproach is diversi®cation. Typically, pair trading based on somesort of correlation analysis is carried out on a large number ofpairs, with a clear limit on each individual position. In contrast, apair trader investigating every pair will carry fewer positions becausehis or her time becomes a scarce resource. The result of a systematicapproach is a portfolio in which the number of sources of uncertaintyis higher, but the combination of these sources still reduces the overall uncertainty because they are not behaving identically. If the selection process is sound and the risk procedure rigorously implemented,there is no reason why a systematic pair trading strategy could notoffer a steady source of income with a limited downside and relatively low risk overall.
Opening and Closing Gaps
We develop here the two ®nal examples of this chapter dedicated tospeculative arbitrage.22 Whereas we concentrated so far on pair tradingin a large sense, we focus here on technical trading. We trade a set ofsecurities based on very simple rules, but we do not hedge the positions in any way, giving rise to an exposure we need to monitor day today.The idea behind each strategy is that in the absence of dramaticinformation, there should be no dramatic move in price. In otherwords, the market is ef®cient enough to operate a correction followinga move that was not necessarily warranted in the ®rst place. The dif®culty here naturally is to de®ne the trading rule such that we capturetruly ``abnormal'' events and leave aside extraordinary moves thatmay be the result of an earnings announcement, for example. We propose here the ®rst steps in that direction, knowing that there is anumber of ways to improve those strategies.
21
In particular, nowadays traders in large institutions have access to virtually everymajor market in the world. A statistical approach has the advantage of being basedÐusuallyÐprimarily on analysis of market data, which means that it can be readilyperformed on any market, in contrast to a ®nancial analysis using fundamentalcorporate data that may or may not be available easily.22These two strategies are inspired by two articles the author published in the magazine Technical Analysis of Stocks and Commodities. See ``Trading the Opening Gap,''November 1999, and ``Trading Against the Gap,'' December 1999.
CHAPTER 10
PAIR TRADING AND TECHNICAL TRADING
487
As an introduction to the concept, consider the histogram in Figure10-8 for the close-to-open returns for General Electric (GE) betweenDecember 1997 and December 1999. A close-to-open return is computed using the following formula:close to open
rt
open

Pt
Pcloset 1
Pcloset 1
where Pt open and Pt close denote respectively the opening and closingprices of GE on date t. In other words, if GE closes today at $73 andopens tomorrow at $731/2, the close-to-open return is 0.68 percent(= $0.5/$73).The histogram shows that the distribution is relatively peaked, thevalues around 0 being frequently represented in the sample. In otherwords, the opening price is frequently very close to the last day'sclosing price. If it is indeed very different, it may be that the marketis incorporating new information or simply overreacting without anything fundamentally new. In this latter case, it is probable that the stockwill correct at some point, the probability of a correction being mostprobably proportional to the close-to-open return observed. This correction in turn can be considered an elementary form of convergence,and we can take advantage of it by trading the stock at open andliquidating the position at the close to diminish risk.This can be done very easily by placing a limit price order beforethe open around the closing price of the previous day. For example, GEclosed on January 21, 1998, at $749/16. The next day, January 22, 1998,we could place a buying order at $73 and a selling order at $76 Ð thatis, at 2 percent above and below $749/16. If we place these orders ``atopen'' only one, if any, will be executed when the market opens. Thethreshold of 2 percent means that we consider that any opening moveabove 2 percent or below 2 percent from the previous day is unlikelyto persist and will probably correct by the end of the day, at which timewe will close the position regardless of what has happened. Againnotice the systematic stop, expressed as a very short holding period,one single trading day. The advantage of choosing this particular valueis that we do not carry any risk overnight.As an illustration, consider Table 10-7 with prices for GE over theperiod January 20 to January 29, 1998. On January 21, 1998, the closeto-open return is 0:49 percent, which is too small for us to take aposition. If we decided to ®x the trading threshold at 1 percent, wewould place every day a selling order at 1 percent above and a buyingorder at 1 percent below the last day's close. In doing that, we wouldtrade only on January 26, 1998, placing a sell order for one share at
488COMMON ARBITRAGE SITUATIONS
Figure 10-8 Close-to-Open(Source: Compiled by author from Datastream data.)
CHAPTER 10
PAIR TRADING AND TECHNICAL TRADING
489
TABLE 10-7Date
Open
Close
Return
Jan. 20, 1998Jan. 21, 1998Jan. 22, 1998Jan. 23, 1998Jan. 26, 1998Jan. 27, 1998Jan. 28, 1998Jan. 29, 1998
73.3875.1974.9475.5674.9474.9476.5676.25
75.5675.5675.1974.0674.6976.2576.2577.13
0.00%0.49%0.82%0.49%1.19%0.33%0.41%0.00%
$74.80 (= $74.06  101 percent) and being executed in reality at $74.94.We would then buy it back the same day at $74.69 for a pro®t of$0.25.23In fact, we are going to extend the strategy beyond GE to all thestocks of the Dow Jones Industrial index. The idea is similar to the goalwe pursued in implementing a systematic pair tradingÐthat is, diversi®cation. If one stock does not correct, for example, chances are thatothers will, essentially decreasing the overall risk. Table 10-8 shows theresults of trading this model from December 1997 to December 1999,on each individual stock, for a threshold set at 2.5 percent.24 The totalP&L for the period is $2.59 (+$31.86 for the long, $34.45 for theshort), for a total of 602 positions (244 long, 358 short). Obviouslythis model is much less successful than RD/SC, for example, whichis not surprising considering the hypothetical nature of the underlyingassumptions. Interestingly, however, it does have some success oncertain stocks, so one possible way to re®ne it is to design a ``smart''®lter to extract those stocks that are more likely to be pro®table on agiven day. In addition, despite ending on a small loss, a closer examination shows that is has been pro®table for a signi®cant part of theperiod, as shown in Figure 10-9. This chart is important notablybecause it gives a more detailed view of the strategy, in terms ofpotential opportunity as well as risk. As we indicated, a signi®cant
23
Note that we decided to close the position the same day in this particular example,but in reality, we could choose any other stopÐfor example, a percentage-based stop.Along the same lines, the threshold of 1 percent is entirely variable and should beexperimented with.24Again we keep the position over a single trading day and trade each stock for onesingle share. Note that the test was run after December 1999Ðthat is, after therecomposition of the index to include Microsoft (MSFT) and Intel (INTC).
490
COMMON ARBITRAGE SITUATIONS
TABLE 10-8NameMSFTHDGEHONKOIPUTXDDAAMODISJNJXOMPGMCDGMSBCCWMTBAMMMCATMRKHWPTIBMAXPEKINTCJPM
No. Long No. ShortTotalPositions Positions Positions9126116115971013413944216132931596841311
12205124221210138123227171027151732141910121892210
2132112310331719201825735162114482130530734191826133521
P&LLong
P&LShort
P&LTotal
14.884.697.933.823.133.421.330.383.512.542.482.950:874.311.131.091.510.752.010.1611.573.194.392.891.195.736.51.520.25
0.968.65.065.155.192.534.414.331.171.190.150.752.443.071.581.780.751.743.461.873.0710.411.119.918.455.225.313.83.57
15.8413.2912.998.978.325.955.744.714.683.732.332.21.571.240.450.690.760.991.451.712.072.573.596.727.027.2610.9511.812.323.82
part of the period is above the horizontal axis showing that the accumulated pro®t was positive and for that reason the strategy is certainlyworth more investigation. At the same time several elements raise anumber of concerns. On two daysÐSeptember 21, 1998, and January13, 1998Ðthe strategy is extremely pro®table, which at the very leastrequires a closer look. In addition, from February to December 1999,the P&L is steadily declining, indicating that if the strategy has hadsome success in the past, it seems inadequate over that particular period, possibly due to changing market conditions. We will not pursuethis discussion further here, but clearly there are a number of questions
CHAPTER 10
Figure 10-9
PAIR TRADING AND TECHNICAL TRADING
491
Close-to-Open P&L
that should be answered to gain a better understanding of the modeland its limitations.As we did earlier, it is also interesting here to perform a sensitivityanalysis to get a better sense of the performance of the model under awide range of assumptions. Figure 10-10 presents the accumulatedP&L over the period for different values of threshold. The strategy isepisodically pro®table, notably if we increase the threshold. This is avery intuitive result in the sense that a higher amplitude for a close-toopen move is more likely to be considered by the market as ``abnormal,'' giving rise to a correction very early.In terms of risk management, the strategy presents the advantageof not creating any overnight exposure, but this advantage comes at aprice. Because we place orders systematically on every stock in theDow Jones every morning, we have no control over what will beexecuted. In other words, if we have a threshold of 2 percent and theentire market opens with a move of 2 percent, we will be executed onall orders at the same time, creating a possibly huge exposure on thesame side. To get a sense of the probability of such a worst-case happening, Figure 10-11 gives the nominal exposure through the periodwith the same threshold of 2.5 percent.25 There are indeed two days for25
This exposure is simply the algebraic sum of all the longs minus all the shorts on agiven day.
492
COMMON ARBITRAGE SITUATIONS
Figure 10-10 Close-to-Open Sensitivity
which the exposure is quite signi®cant: September 8, 1998, and January13, 1998. On September 8, 1998, in the midst of the Russian crisis, 20out of 30 stocks opened above +2.5 percent, creating an exposure of$1,017 short. On January 13, 1998, the exact opposite scenario occurred,and 19 stocks opened below 2:5 percent compared to the previousclose, generating a long of $1,163.26 In terms of pro®t, however, bothdays ended up being rather reassuring. On September 8, 1998, thestrategy lost only $0.52 because of a combination of pro®ts and lossesin the 20-stock short. On January 13, 1998, however, the positiongained $24.82 because most of the stocks came back from the lowstoward the end of the day. This was already one of the days we pinpointed earlier, so we know now what happened and why. In conclusion, even if both occurrences turned out to be nonevents from a riskperspective, they highlight the fragile nature of risk management inthis particular model.2726
Note that the risk is not simply that we are executed on all the stocks; rather, that theyall open on the same sideÐthat is, there is a major shift in the entire market.27One way to decrease the exposure would be, for example, to hedge it with Dow Jonesfutures over the course of the day.Note that this model does not ``cost'' much in terms of market exposure if weexclude the two extreme days. Generally the level of exposure is remarkably low,notably when compared to the close-to-close arbitrage that we will consider shortly.
CHAPTER 10
PAIR TRADING AND TECHNICAL TRADING
493
Figure 10-11 Close-to-Open Exposure
As a continuation of the same set of ideas, let's now consider asmall variation of the model in which we trade the close-to-closereturn as opposed to the close-to-open return. This is much moreclassical and in fact it is also a popular model implemented undermany shapes and forms. A quick examination of the histogram inFigure 10-12 of close-to-close returns for GE will give us a sense ofwhat we should expect when comparing it to the close-to-openmodel. The distribution is much wider, indicating that close-to-clos