) and divide by (n1):21 741We can see that by reversing the order of the returns of Stock B, so thatit declines as Stock A’s returns increase, we get a negative covariance, implying stocks that move in opposite directions. Although we can see the difference in the direction of movement, it is difficult to know what exactly thevalues of 7 or 7 stand for in the world of all stocks.Covariance of Stock A and Stock B:
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Understanding Correlations
The correlation coefficient standardizes this term to a value between 1and 1. A correlation coefficient of 1 implies stocks that are perfectly negatively correlated, while a correlation coefficient of 1 implies stocks thatare perfectly positively correlated. A correlation coefficient of zero impliesno correlation. It is rare in the real world to find two stocks that have a perfect 1 or 1, but it is still much simpler to decipher a reading in this rangethan to decipher a reading of 7 versus a reading of 26.The next step in the calculation is to divide the covariance term by theproduct of the standard deviations of the two stocks. In the case of the firstdistribution of Stocks A and B, we get:Correlation Coefficient:
7 .9763.92  1.83
In the second distribution, we get:7 .9763.92  1.83As you can see, the stocks that move in the same direction in terms ofincreasing returns have a high correlation coefficient (.976) close to 1. Thiswould be true for stocks that also show an equivalent pattern of decreasingreturns in the same periods. Instead of the variances in each period starting outnegative (in relation to the mean) and turning positive at the same time, wewould see these values begin positive (in relation to the mean) and turn negative in the same periods. Because we multiply these numbers together andthen sum them, we will still get positive values for stocks moving in the samedirection since multiplying two negatives gives us a positive number.When we reverse the order of Stock B’s returns to decrease as Stock A’sreturns increased, we end up with a correlation coefficient of (.976), whichis close to a perfect negative correlation of 1.Now let’s try one more example. Instead of simply reversing the order ofStock B, let’s use the same returns in no particular order. We’ll assign valuesto the returns in periods one through four of 5 percent, 4 percent, 1 percent,and 2 percent. Let’s go through the calculations once again.Correlation Coefficient:
Period
A
B
(A  )
(B  )
(A  )  (B  )
1
8
5
8  12  4
5  3  2
4  2  8
2
10
4
10  12  2
431
2  1  2
3
13
1
13  12  1
1  3  2
1  2  2
4
17
2
17  12  5
2  3  1
5  1  5Sum  1
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By placing the returns from Stock B in no particular order compared toStock A, we now get the following covariance and correlation coefficient.1 .33341.333 .05Correlation coefficient:3.92  1.83
Covariance of Stock A and Stock B:
As you can see, a number close to zero indicates very little correlation atall between the two stocks. This can be seen in the returns, where Stock A’sreturns are increasing and Stock B’s returns first decrease, then increase,but show little similarity to Stock A.Now let’s say you were analyzing groups of stocks for the possibility oftrading them in pairs and you got the preceding results of .976, .976, or.05 for your correlation coefficients of various comparisons. Which pair ofstocks would you be more likely to choose, all else being equal? The highcorrelation of .976 would indicate that these two stocks are highly correlatedwith one another and that a temporary move in the spread between the twobeyond historical values is more likely to correct itself than for either of theother two combinations.A strong negative correlation might indicate that two stocks which arecurrently moving in the same direction could be due for divergence. In thiscase, the correlation coefficient would suggest that over the period of timefor which you have collected data the stocks moved in opposite directions.If they have now converged, it may be an opportunity to trade the two on theexpansion away from this convergence. Stocks that might exhibit this typeof relationship could be gold stocks and banking stocks, which tend to movein opposite directions based on the strength of the economy.One of the biggest factors to consider when calculating this coefficientis the time period and frequency of the sample data. If a trader is taking onlyquarterly results, the coefficient will measure only the end point at whichthese stocks finish four times per year. This would certainly allow for a greatdeal of movement in the interim periods and could be very costly for a traderwith a rather short time horizon. Daily data is more accurate; however, it isalso very labor intensive to compile and may show more extreme fluctuationthan two stocks have exhibited over time, depending on the time period thatis chosen. For instance, a trader who chooses a single month’s worth of dailyclosing prices for his or her data sample may end up with a skewed pictureof the relationship between two companies. If Stock A releases earningsmid-month and Stock B experiences little movement that month, the picturemay be misleading.
Understanding Correlations
57
The best way to address time and frequency of data sample collectionwould be for a trader to define the time horizon of his proposed trade andthen pick a reasonable frequency by which to measure the two stocks’returns. The next step would be to go back far enough in time to smooth outthe results of outlying blips in the data stream. If a trader is looking at a quarterly time horizon, he may want to take weekly data and go back 5 to 10years to get an idea of just how correlated the stocks are. If a trader is looking at a time horizon of just a few days for his trade, it will be difficult to geta reliable coefficient; however, looking at daily data for the past few monthsmay be more appropriate. The idea is to match time horizons and thenextend back far enough historically to get a reliable number.As mentioned earlier, the calculation for correlation coefficient can bedone quickly and easily on Excel or another statistical program. However, athorough understanding of how this is calculated can give a trader a betterunderstanding of the data he is seeing and the ability to “eyeball” a set ofreturns . . . and get an idea ahead of time, whether he has found candidatesfor his pairs trading strategy before spending the time to enter the data.
CHAPTER 9
CorrelationSimplifiedWhat Is a Correlation?Where to Find CorrelationsBuilding a CorrelationUsing Excel
WHAT IS A CORRELATION?As previously explained, the correlation is the glue that holds a pair together.On a commonsense level, we might expect ExxonMobil (NYSE: XOM) andChevronTexaco (NYSE: CVX) to have a higher correlation than ExxonMobiland Microsoft (NASDAQ: MSFT). Why you ask? Exxon and Chevron areboth major oil and gas integration and refinery companies, while Microsoftis the root of all evil, er, um, sorry, I mean Microsoft is a software company.(Really, just kidding there.) All right, back on track, the main principle hereis that comparable business models have higher correlations. Although thereare a few exceptions, most companies will have the highest correlationswith similar companies in their respective sectors; that is, trucking stockswill closely follow trucking stocks, while insurance stocks may faithfullypursue other insurance stocks.
WHERE TO FIND CORRELATIONSWhile I highly recommend working through the previous chapter, I also havea shortcut. First, if you are willing to pay for data, the best resource availableis http://www.market-topology.com. This site has already neatly mapped outthe correlations for not only U.S. markets, but foreign markets as well. I amnot completely sure what time periods market-topology.com is using for itscorrelation data, though I have noticed that the correlation numbers areidentical to those retrieved on a Bloomberg terminal.59
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If you have access to a Bloomberg terminal (cost: around $1,400 permonth), the command to find historical spread information along with correlation numbers is: Ticker EQUITY Ticker EQUITY HS GO. Using actualcompany tickers, the historical spread function would be entered as XOMEQUITY CVX EQUITY GO. Then, once the historical spread screen is displayed, hit “2” GO; you will then see the correlation number on the lowerleft-hand corner of the screen. Because Bloomberg never seems to change,I have a feeling that this spread command will be accurate for several yearsto come. (That’s a good thing.) But what if you don’t want to pay for the correlation data or do not have access to a Bloomberg terminal? No problem,we can build our own using an Excel spreadsheet.
BUILDING A CORRELATION USING EXCELUsing the spreadsheet that we already created, the Excel syntax for calculating correlations is CORREL. Let’s walk through how to calculate theaforementioned relationship.A brief explanation of Excel syntax is needed before we go too far. Anytime you are putting a mathematical formula in a cell, if you click in the chosen cell, you will then see the label bar activated on the top of the screen.You can type the formula in either the actual chosen cell or the formula fieldat the top of the screen. Excel reads figures as a mathematical formula onlyif there is an equal sign (⫽) at the beginning of the syntax. After the equalsign, verbal functions must then come first before any actual cell values ormathematical equations. As an example of a verbal Excel function, when wetype in AVERAGE before our designated numbers, the spreadsheet willknow to automatically total all numbers in the specified period and divide bythe total amount of cells read. After the function comes the actual math syntax. In general, Excel reads math much like college algebra. For example,[A1 ⫹ (A1*B1)] would mean that the spreadsheet would first multiply A1and B1 and then add cell A1. When we put in syntax such as ⫽AVERAGE(A1:A100), we are asking Excel to return the mean of all cells summed fromA1 to A100. If you find yourself confused at any time, simply click on theHelp option on the toolbar and select the first option Microsoft Excel Help.You can type in key words like standard deviation, and Excel will bring upseveral options of topics to choose from.Step 1. In cell A3 on the Main page, type in: Close Correlation. You willnotice that the text we have just typed overlaps into cell B3. To separate
Correlation Simplified
61
FIGURE 9.1 Close Correlation
cell B3, grab the cell divider on the top of the screen and widen the cellso that the text “Close Correlation” is only in cell A3 (see Figure 9.1).Step 2. Highlight cell B3 and type ⫽CORREL(‘Stock 1’!E2:E190,‘Stock2’!E2:E190). What we are asking Excel to do is to go into the Stock 1spreadsheet and compare all the closing data to the closing data in theStock 2 spreadsheet. (Notice that the syntax for making a formula in onespreadsheet look in another spreadsheet is denoted as ‘Stock1’!E2:E190.) Our resulting study has now allowed us to see that the correlation between Novellus (NASDAQ: NVLS) and KLA-Tencor (NASDAQ:KLAC) for our given time period is ⫹.82! (As an arbitrary number, we areusing only 188 days of data, just to make our initial analysis a littleeasier.) This is a very high correlation and denotes that our pairdefinitely has a tradable relationship. What this does not mean is that thepair will always diverge and converge. Even though our present dataindicates that the two stocks have historically (in the period we
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measured) traded very similar to one another, the pair could still fallapart at any moment in the future. How? As we very well know, thesemiconductor market is extremely fickle, with technology continuallyshaping how chip makers do business. Both Novellus and KLA-Tencorface technology risk, research risk, political risk, event risk, market risk,and generally just about any other type of risk we can think of. Thus, ifone company finds itself the unfortunate recipient of (just for the sake ofexample) geographical risk, the pair could quickly blow up. For example,several semiconductor companies found themselves under the scrutiny ofbears when the SARS outbreak in 2003 caused several domestic chip makers to halt production in Asian countries. If the correlation is true to itsnature, then the two stocks will come back together once the geographicalproblem has been fixed. However, there is always the chance that whatever
FIGURE 9.2 Spreadsheet Example of Correlations
Correlation Simplified
63
event drove the two stocks apart in the first place has now altered the business models to a point where the correlation will begin to break down.Next, we will take a look at the daily change correlation to see how accurately the two stocks trade together on an end-of-day change basis. To dothis, we will first need to set up a column to calculate each day’s changefrom the previous session.Using Excel:Step 1. In the sheet Stock 1, label cell H1: Change.Step 2. In cell H2, put in the formula: ⫽G2-G3. This will calculate thechange between the present day’s closing price and the closing price ofthe previous day.Step 3. Repeat for Stock 2.Step 4. Once you have the changes in each cell, you will need to make surethat all the cells in column H have the same formulas. To do this, simplyhighlight cell H2 and press Control C (Command C for Mac users). Onceyou have done this, highlight (using your mouse) all of the cells vertically incolumn H starting with cell H3 to the bottom of the sheet—or at least tothe bottom of the data. Press Control V (Command V for Mac users). Thisshould paste the change formula respectively into each cell.Step 5. In the main sheet, in cell A4, type in: Change Correlation. Then incell B4, add: ⫽CORREL(‘Stock 1’!H2:H190,‘Stock 2’!H2:H190). This will
FIGURE 9.3 KLAC-NVLS
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TRADING PAIRS
calculate the correlation of the day-to-day change between the twostocks. Figure 9.2 shows what your spreadsheet should now look like. Ifyou prefer all the data from our time range, you can put in ⫽CORREL(‘Stock 1’!H2:H397, ‘Stock 2’cH2:H397). However, in the first CORRELexample under Step 5 we are using much less data, again, just for theease of analysis.So what does this data mean? What these two correlations are telling usis that most likely KLAC/NVLS is a very viable pair to trade. Why?First, the actual correlation between the two stock prices is (rounded)0.82, and the change correlation is 0.90 for the period of our study. If thechange correlation has a higher value than the EOD correlation, then weknow that the two stocks are not only a good pair to trade on an EOD basis,but will also have some intraday opportunity as well. You can see that ourcorrelation data has given us some food for thought.Given the high correlation of our two stocks, we can also infer that thecharts of the two stocks should look extremely similar. Figure 9.3 demonstrates exactly that. Take a close look and you will see that there is a remarkable similarity between the two. I’m not sure about you, but I smell opportunity here. When two stocks have a distinct relationship, then the “rubberband” theory is clearly in effect.
CHAPTER 10
UnderstandingStockCorrelationsin Relationto IndicesWhy an Index?What Is Beta?How to Apply BetaWhere to Find Beta
WHY AN INDEX?In Chapter 1, I mentioned that an index is similar to a highway runningthrough a small town. More than likely, many of the smaller roads in a townwill parallel the larger road’s general direction. This causes city planners torethink the development of newer suburbs in an effort to make the city’sstreets congruous with the larger, immobile interstate. This principle is witnessed in the market, as investors realize that they are less able to have animpact on a large index, than on a single stock. Thus, as investors, we areforced to base our decisions (the planning of our portfolio development) inaccordance with the greater direction of the corresponding index. Investorsmay then find information regarding a stock’s movement within an index byusing beta.
WHAT IS BETA?Beta is the measurement of a stock’s volatility in relation to a larger index,usually the Standard & Poor’s (S&P) 500. Moreover, beta is said to be a measurement of market risk. Investopedia.com defines risk as: “The chance thatan investment’s actual return will be different than expected. This includes65
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the possibility of losing some or all of the original investment. It is usuallymeasured using the historical returns or average returns for a specific investment.” Investorwords.com defines market risk as: “Risk which is common toan entire class of assets or liabilities. The value of investments may declineover a given time period simply because of economic changes or otherevents that impact large portions of the market. Asset allocation and diversification can protect against market risk because different portions of themarket tend to under-perform at different times. This is also called systematic risk.” In general, the S&P 500 is said to have a beta of ⫹1; thus, any stockwith a beta of greater than 1 should (in theory) have greater volatility thanthe broader market. In brief, the greater a stock’s beta, the more amplified itsprice movement will be compared to the S&P 500, and the more market riska security may face. For example, a stock with a beta of ⫹1 would likely havepercentage moves similar to the S&P 500. However, a stock with a beta of⫹1.5 would increase 50 percent when the S&P 500 was up 25 percent. Thekey in comparing beta is to understand that percentage moves are the greatequalizer. Thus, even though the daily change in the Dow may be ⫹200 pointsand the daily change for Microsoft may only be ⫹1.3 points, if the percentage moves are similar, then the beta correlation will likely be near ⫹1.
HOW TO APPLY BETAIf we look at Microsoft and Oracle, we know that there is a definite relationship between the two companies. The correlation coefficient displays arelationship of ⫹0.82. The relationship discovered when looking onYahoo.com is that Microsoft has a beta of 1.74, while Oracle has a beta of1.88. Both stocks have high betas compared to the S&P 500! Taking this onestep further, if we run a correlation study on both Microsoft and Oracle separately against the S&P 500, we end up with 0.87 and 0.66, respectively.These numbers validate our thoughts on beta, as the lesser-correlated Oracle has a higher beta, thus indicating greater volatility compared to everydaymovements of the S&P 500. No matter how you slice it, though, becauseMicrosoft and Oracle both have betas above 1, they are both more volatilethan the S&P 500. For example, if S&P 500 moves (random number for thesake of argument) 0.03 percent in one day, Oracle should (in theory) close1.88 times (on a percentage basis) above the closing price of the S&P 500.However, given that day-to-day order flow and news events can cause stocksto trade more erratically than the indices, the beta measure of intradayvolatility does not always work. In fact, it’s probably a good idea to never
Understanding Stock Correlations in Relation to Indices
67
FIGURE 10.1 Yahoo.com and Beta
institute this theory in an actual trading system without some other type ofdata to improve the trading theory. And in the context above, that is exactlywhat it is—a theory. While it does not work very well by itself in reality, it isimportant to understand.
WHERE TO FIND BETAFigure 10.1 displays the same Yahoo.com Key Statistics page that we lookedat in Chapter 3. Beta is the first item down in the far right column.
CHAPTER 11
Basic StatisticsFrequency DistributionMean/Median/ModeMean DeviationVarianceStandard Deviation
lthough some statistics were discussed in Chapter 8, it is importantenough to delve a little deeper into. A basic understanding of statisticswill be the second layer of our pairs foundation, on which we build ourknowledge. So what is statistics? Statistics is the study of numerical data in anattempt to find systematic patterns. Hyperdictionary.com defines statistics as:“The practice, study or result of the application of mathematical functions tocollections of data in order to summarize or extrapolate that data.” As a result,we will be using simple descriptive statistics in an effort to uncover reliablepairs data in hopes of finding possible trading patterns.
A
FREQUENCY DISTRIBUTIONTo begin our tour in statistics, we will look at a frequency distribution, whichis basically a table in which all data has been grouped in specific classescalled categories. The frequency distribution has nonoverlapping data thatcan be seen and analyzed.The following steps show how to create a frequency distribution:Step 1. Define the classes in which the data will be sorted. A class is alevel of prices that have definite upper and lower limits that do not overlap with other levels. This principle is known as making prices mutuallyexclusive, so they cannot show up in two separate classes.Step 2. Assign the observations (stock prices) to their classes. Once allthe prices are assigned to their respective classes, we may then find the69
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TRADING PAIRS
midpoint for further data analysis. For the midpoint, subtract the lowestvalue of all classes from the highest value.Step 3. Count the number of observations in each class.How do we define the classes? When we have the total amount ofobservations in the entire population, we will attempt to find out what ourclass interval is. A class interval is the total distance from the smallest tolargest values in any one class. To pick the size of the class interval, usethis formula: Class interval ⫽ (Highest value ⫺ Lowest value) / Number ofclasses. But how many classes are there? To find the total number ofclasses, we will use the formula: 2^k ≥ n. In the aforementioned equation,k stands for the power to which 2 is raised and is the smallest integer thatis greater than n, otherwise known as the total amount of observations.Hence, in a data set with 100 prices, our class size would be 7. This isbecause 2^6 ⫺ 64 is less than 100, while 2^7 ⫽ 128, which is greater than100. We would then have seven total classes. Next, using our previous formula, we would then have Class interval ⫽ (100 ⫺ 1) / 7, which equals14.14, or simply 14.Setting up a frequency distribution allows us to actually see the patternof the data we are analyzing. Let’s construct a frequency distribution withthe following closing prices: 5, 4, 6, 8, 12, 5, 6, 4, 9.First, we have nine total observations. Thus, we find that k ⫽ 4, as 2^4 ⫽ 16,and is the smallest integer equaling a sum greater than 9. Now, we know thatwe have four classes. To figure out the intervals within the four classes, wewould use: (12 ⫺ 4) / 4, which equals 2. As a result, our classes and observations are:4⫺56⫺77⫺88 ⫺ 9⫹
4213
Using the frequency table that we have just created, we can then visuallysee how our data is skewed. The actual visual representation is called a histogram and is represented as a line that looks like an upside-down “U” on achart. By skewed I mean what type of curve the data presents. Normal datais said to be “bell shaped” with the mean, median, and mode all in the center of the curve. A normal curve is a perfect upside-down U. Skewed datalooks like a U stretched either to the right or left, and represents that thereare more (or more extreme) values on one side of the data set. (EN 11.1)
Basic Statistics
71
MEAN/MEDIAN/MODEStudying the mean, median, and mode, we will find basic relationships ofwhere our pair has been trading.• Arithmetic mean: The sum of all values divided by the total of all values,otherwise known as the average. Initially, we will be using only the arithmetic mean for our analysis.• Median: The midpoint of all data when it is arranged in numerical order. Forexample, for four different closing prices of: $27, $28, $32, and $33, themedian would be $30.• Mode: The number in the data set that appears most frequently. In the set ofclosing prices: $23, $23, $23, $27, $45, $68, the mode is $23.
MEAN DEVIATIONThe mean deviation and standard deviation are both measurements of dispersion that are meant to depict how the data is spread within a population.(By population, I am referring to all of the data we have to work with, not aselect group within, which is known as a sample.) The mean deviation (alsoknown as mean absolute deviation [MAD]) is an average of the absolute values of the deviations from the arithmetic mean. All deviations from the meanare in percentages and equal zero. Thus, the mean deviation only usesabsolute values to get around the “zeroing out” problem.To put this in mathematical terms, using the above numbers we can calculate the mean deviation from the average stock price. Our prices are $23,$23, $23, $27, $45, $68. Our mean or average price is $34.83.To calculate the mean deviation, we subtract the mean from each value,sum the values and then divide by the total number of original observations.
VARIANCEThe variance is the mean of the squared deviations from the mean. The reason that we square the deviations is that when the numbers are not squared,the total of all deviations equals zero. By squaring the deviations, we thenhave positive numbers to work with. Don’t worry too much about variance,as we will not be using it; however, just for the math buffs, Figure 11.1shows the formula for a population variance. For sample variance look atFigure 11.2.
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2
n a x ⫺ a a xb2
n2FIGURE 11.1 Population Variance
2
n a x2 ⫺ a a x bn(n ⫺ 1)FIGURE 11.2 Sample Variance
STANDARD DEVIATIONOne step further is the standard deviation, which is the probability of deviation known as the square root of variance. In layman’s terms, the standarddeviation allows us to measure the data observations from the entire population, and map them in regard to the statistical mean. The actual formula fora population standard deviation is shown in Figure 11.3. For a sample standard deviation see Figure 11.4. Don’t worry, we will let Excel do our calculations for us, however, for the time being it is important to understand whata standard deviation is.How is the data measured? The empirical rule states that in a normal distribution:• 68 percent of the data will rest within ⫹/⫺ one standard deviation of themean.• 95 percent of the data will lie within ⫹/⫺ two standard deviations of themean.• 99.7 percent of the data will sit within ⫹/⫺ three standard deviations ofthe mean.Thus, once the standard deviation for a data set is known, the rangethat the data should fall within can be measured. Using the same prices—$23, $23, $23, $27, $45, $68—we know that the mean is $34.83. By plugging
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Basic Statistics
2
n a x ⫺ a a xb2
R
n2
FIGURE 11.3 Population Standard Deviation
2
n a x2 ⫺ a a x bR
n(n ⫺ 1)
FIGURE 11.4 Sample Standard Deviation
the numbers into our formula for a population standard deviation, wecome up with a population standard deviation of 18.36. What does thismean? The empirical rule would state that 68.3 percent of all prices residewithin one standard deviation of the mean. Thus, 68.3 percent of all priceslye within one standard deviation of $34.83. If one standard deviationequals 18.36, then 68.3 percent of all prices should rest between $16.47 and$53.19. (Simply the standard deviation added and subtracted from themean.) Our logic may then follow that 95 percent of the prices are situatedwithin $0 (the value is zero, as stock prices cannot be negative) and $71.55.If we lived in a vacuum of pure statistics, we could then buy the stock anytime the price traded near $0 or short sell it when the price nears $71.55.Although obviously the market is not quite that simple, you can still see thatthis is getting exciting!So now you’re sitting there saying “All right bub, enough of this statisticsstuff, just show me how it works—show me the money.” Before we begin, Iwould like to go over the following 10 statistical principals, just kidding, hadyou going there for a second. Instead, we’ll now take the basic statisticalinformation that we have and put it into practice with Excel.
CHAPTER 12
Excel andStatisticsSetting Up the SpreadsheetAverage, Median, Mode, andStandard DeviationUnderstanding the Present DataHow Do You Know Which Stockto Buy or Short?Charting the Data
SETTING UP THE SPREADSHEETAll right, back to our trusty spreadsheet! At this point we should alreadyhave data imported into our spreadsheet, so now we just need to beginapplying our basic statistical functions to commence analyzing our pair.Step 1. Bring up your spreadsheet and label cell A8 Mean, A9 Median, andA10 Mode. Then label B6 Differential, C6 Ratio, D6 Closing, and D7Spread.Step 2. Label cell A12 Average Deviation, A13 Standard Deviation, and A14Population Standard Deviation.Step 3. Right click on the Stock 1 spreadsheet tab and then insert a newworksheet. Label the worksheet Pair Data.Step 4. In the Pair Data worksheet, label cell A1 Pair Data, then label thefollowing cells: A4 Date, B4 Differential, C4 Ratio, and D4 CloseSpread. (You may have to widen the cells, via drag and drop, to fit thetext.)Step 5. Next, click in cell A5 and hit the  key. Then, click on the Stock 1worksheet tab, click once in cell A2, and hit Enter. What we have done isasked the Pair Data sheet cell A5 to always correspond the first date in75
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the sheet with that of Stock 1. And because we will update the data inthe Stock 1 sheet sometime in the future, we want the dates and datain the Main Sheet and Pair Data sheet to automatically updatethemselves. Next, copy and paste the Pair Data cell A5 all the waydown the A column to cell A195. If you are using all of the data, thenpaste the data all the way through cell A400.Step 6. Type in the following formulas in each corresponding cell:B5: (‘Stock 1’!E2-‘Stock 2’!