the experiment in Figure 6.1 and Table 6.2.Value Line Group 1, consisting mainly of growth stocks, quickly outpaced thethree value stock categories. By March 2002, the growth stocks had returnedalmost 28 times the return of the best-performing “value” group, “low
70,000
Growth of $100 Invested(Dividends Reinvested)
60,00050,00040,00030,00020,00010,00001965 1969 1973 1977 1981 1985 1989 1993 1997 2001April Totals for Each YearGROUP 1LOW P/SLS
Figure 6.1
LOW P/ELOW P/BK
Value versus Growth
172 Practical SpeculationTable 6.2
Value versus Growth (Dividends Reinvested)
Starting Value
Group 1100
Low Price/Sales100
Low P/ E100
Low Price/ Book100
January 1970January 1980January 1990March 2002
2162,78216,54046,885
1918151,3261,698
2051,4503,0341,555
1881,0861,2961,250
price/sales.” (How Value Line came to be capable of such calculations is discussed in Chapter 10.)Certain aspects of Graham’s life do have a mythical quality. After thetragic suicide of Graham’s son in France, Graham traveled from his home inCalifornia to collect the deceased’s belongings. On arriving, he fell in love withhis late son’s girlfriend, Marie Louise. As Graham was already married, hesuggested to his fourth wife, back home in California, that she share him withhis new amour. Much to Graham’s wife’s distress, she thenceforth saw herhusband only six months out of every year. The tale has odd echoes of Zeus’philandering and Persephone’s annual six-month descent into the underworldto be with her husband, Hades, lord of the dead, during the winter months.Belief in Zeus and the feats of Hercules eventually dwindled into insignificance. We suspect that the legendary father of value investing will betreated no better by the gods.
7
NEWS FLASH:COMPUTER WRITESSTOCK MARKET STORY!
The foundation of all morality is to have done, once andfor all, with lying; to give up pretending to believe that forwhich there is no evidence, and repeating unintelligible propositions about things beyond the possibilities of knowledge.—Thomas Henry Huxley1
W
e are all familiar with the truth of the proverb that one lie begets another. Assertions have implications. When implications turn out tobe false, obfuscation, or “further-putting-into-perspective,” is necessary to extend the original lie.Nowhere is this principle better seen than in the typical story on dailymarket moves in the financial media. These stories are generated with a simple formula:Stocks (rose/fell) on (earnings/interest-rate) (optimism/pessimism)173
174 Practical SpeculationThe possible combinations are limited, but well within the capabilities ofreporters without much trading experience or statistical knowledge:Stocks rose on earnings optimism. Stocks fell on earnings pessimism.Stocks rose on interest-rate optimism. Stocks fell on interest-rate pessimism.A fancy report will combine the two:Stocks fell on expectations that rising borrowing costs will cut into corporate earnings.Stocks rose on expectations that lower borrowing costs will boost corporate earnings.The assumption about the earnings-market return relation in this formulais, as readers know by now, completely fallacious. As shown in Chapter 2, thetime to get ready to buy is exactly when earnings look worst, and the time tosell is when earnings look best. But there is another aspect to these formulaicstories: Although human beings write these reports according to the blueprint,the stories could just as well be done with a computer. In fact, we havepatented a Market News-O-Matic program and debut it later in this chapter.But back to the blueprint. Once the ball is rolling, the reporter is bound tocontinue down the fallacious track to fulfill the market’s never-ending needfor promotional material and contributions from the public. The next step,therefore, is to introduce a money manager. She just sold her position in anindustry based on lowered earnings expectations. (You must know about herso that you can buy her fund, or sell that stock yourself, or possibly hire thatprescient fund manager in the future.) If all the fund managers in the reporter’s Rolodex are busy on TV, the statement can always be attributed to“some investors.”Next, the reporter will attempt to find a quote pertinent to the chosentheme from one of the Federal Reserve officials or government economistswho are always giving a speech somewhere on any given day. If the Fed chairman himself is speaking, the story practically writes itself. “Declines deepenedafter Federal Reserve Chairman Alan Greenspan said consumer spending,which makes up two-thirds of demand in the U.S. economy, won’t increase asmuch as it has following past recessions,” ran one story from a major wire service. This statement “cast doubt on how much an economic recovery will fuelcorporate profit growth.” Bingo! The reporter has succeeded in working thechairman’s words into support for the earnings fallacy embedded in his story’slead paragraph.
Chapter 7 • News Flash: Computer Writes Stock Market Story!
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Next comes an enumeration of a list of companies whosestocks declined that day after analysts cut forecasts on their earnings. Propagandists call this card stacking; the reporter, apparentlyheedless of the worthlessness of anecdotal evidence, presents this list as confirmation of his theme.The reporter’s unconscious work on behalf of the market is now complete. He has allowed a manager to tout her fund. He has provided, based ona series of extrapolations that are possibly incorrect, an analysis of a statementby the chairman of the Federal Reserve. He has completely tied up the investor in specious conclusions. More important, he has encouraged investorsto be fearful and to overtrade. For good measure, he has publicized names ofbrokerages available to assist investors in their overtrading.
Harm DoneSuch stories are completely worthless to anybody who trades. They are purelydescriptive, anecdotal, and backward-looking. They are harmful to anybodywho trades on the assumptions they contain. But the damage does not endwith the hapless investor. If current earnings strength is the key to marketmoves, by natural extension the main job of corporations is to construct anddeliver a steady stream of favorable earnings comparisons. Can anyone doubtthat the string of 35 positive earnings comparisons in General Electric, withthe skepticism it engenders about the underlying process, as well as the massive attempt by companies like Enron to sell debt (which is good for corporateearnings per share but bad for survivability), has poisoned the atmosphere ofthe early Naughties?You might think that there would be checks and balances on such propaganda because of the obvious harm. Scholars might undertake an academic study of the phenomenon, and some enterprising reporter mightpublicize the results to puncture the ballyhoo. But most academics haveaxes of their own to grind. Even to read the most basic academic journalrelating to economics or finance these days requires membership in apostadvanced-calculus, postadvanced-econometrics, postcanned-computerprogram-using club that only professional economists who registered forall these courses in their postdoc education could hope to unravel. Even ifacademics communicated their conclusions in language that laypeoplecould decipher, the information would not be of much use. By the time a
176 Practical Speculationstudy goes through the usual rounds of peer review and publication in an academic quarterly, a few years will have passed,and the cycle is likely to have changed.Part of the harmfulness of a lie is that it crowds out other statements thatmight add to knowledge. Many investors undoubtedly know that selling stockson bad news, earnings-related or otherwise, and buying on good news will getthem in trouble. Since the main thing investors and editors are attuned to hearing is the earnings-market return myth, any commentators who might know what factors really did create the market movethat day are left twisting in the wind. By focusing everyone’s attentionon a bogus explanation, the investor is led away from finding out the truthfrom some other source.Stock moves from day to day are in the main randomly related toephemeral factors of the day. They tend to go down after there has been excessive optimism over the previous several days, and they tend to go up after therehas been excessive pessimism. These swings in optimism and pessimismhave little, if anything, to do with earnings. However, it would be completelydysfunctional for reporters to attribute the swings to excesses in anything likepublic sentiment. Such a report might lead to the thoughtful decision that perhaps the solution would be less trading. Even worse, investors might pay lessattention to what the channels of communications are transmitting. Thatwould be bad for the ecosystem of the newspaper and TV and Internet purveyors as it would cut down on advertising revenues from brokerages and stockexchanges. Moreover, it might keep the public from making its maximum contribution to the market’s vast machinery of brokers, specialists, analysts, andinvestment bankers.The bottom line for investors is that no matter whether news reports saystock is going up on earnings optimism or down on earnings pessimism,these assertions amount to nothing more than an invitation to trade the wrongway. If an investor had a guardian angel, he might hear a whispered: “Listen! Alot of ephemeral things go on. The thing to know is that stocks are a claim oninfinite future earnings. What happens today should not affect your view of astock, because you are buying it for its long-term discounted value. Do not letthe market take you and your loved ones away to the poorhouse.”
The Market News-O-MaticAfter studying the subject from a wide variety of statistical, economic, andpsychological angles, after reading more than a thousand academic articles on
177
n=5
n=4
n=3
n=2
n=?
Yes
Input interest-rateoptimism/pessimism
Input Federalnews (y/n)
> one-daymove?
Calculate1. up/down2. change3. percent change
Input Dow price(today, yesterday)
No
No
Earningsnews?(y/n)Yes
Figure 7.1
Print out
Writeforecast
Input 52-week high/52-week lowDow price
Write firstparagraph
Yes
Earningsnews?(y/n)
Input earningsnews (y/n)
No
Market News-O-Matic
Interest-ratemovement?(y/n)
Write earningsnews paragraph
Input earningsnews (y/n)
Write firstparagraph
Yes
Input made-upreason
R = “You can’t really look at values, youcan’t really look at fundamentals. It’s allabout psychological reaction today.”
R = Not all stocks advanced; however,“It’s a market of stocks, not a stockmarket.”
ALL-PURPOSER = “Of course, all bets are off if thewar does not wrap up quickly.”
R = “Retail stocks were lifted by betterthan expected same-store estimates.”
R = “More than 60% of all companieshave beat their forecasts.”
BULLISHR = “Any hint of good news is goingto be taken very well by the market.”
R = “As long as we see more than50% of all stocks more than 30%from their one-year highs, this is justa bear market rally.”
R = “Most analysts agree thatthe economic recovery forecastfor the next few months will notlift all boats.”
BEARISHR = “Everyone is afraid to buybefore the employment number.”
Made-Up Reasons(from real news stories)
178 Practical Speculationthe subject, after running and vetting our ideas by the greatest minds in thefield, after spending thousands of our own hours calculating the numbers byhand, rechecking the original sources, and directing and supervising our multifarious talented staff in similar pursuits, we can recommend an effective antidote to financial news coverage: From time to time, investors should makeup stock stories themselves for their educational amusement.We drew our inspiration from Alan Turing, the genius British codebreakerwho proposed a test for artificial intelligence. The test is, “Can a computer beprogrammed to produce a product that could be completely indistinguishablefrom a human effort?”In the case of stock market reporting, the answer is yes (see Figure 7.1).Our program proceeds through a simple series of steps. Say the marketis up. There can be two reasons. Either it is earnings optimism or interestrate optimism. If a major company reported good earnings and its stockwent up, then attribute it to the latter. If, on the contrary, the major companyreported good earnings and its stock went down, then attribute the market’sup move to interest-rate optimism. Throw in some benign commentsfrom Doc Greenspan or one of the minions dispatched daily to feather thenests of the Fed’s clients at the government dealers and brokers, and youhave a story.Readers should test their understanding and creativity by trying this outat home. For practice, apply the preceding basic formula to a down day. If possible, attribute the decline to poor earnings reports from one or more companies. If you can find no plausible examples of poor earnings, go to Plan B,which is to talk instead about interest-rate pessimism. Be sure to throw in acomment or two from Alan Abelson’s list of reasons to be bearish and woeful(see Chapter 4).With the current vogue for downsizing in our economy, it is nice to knowthat you have within you the makings of another career, that of a newspaperreporter.The following is a sample story generated by the Market News-O-Matic:Today’s Market: U.S. Stocks [Rise/Fall] on Earnings [Optimism/Pessimism]By Victor NiederhofferJunior Staff Writer[First Paragraph](New York, Niederhoffer News)—U.S. stocks [rose/fell] as unexpectedly [strong/weak] earnings from [company] fueled [optimism/pessimism] for a rebound inearnings by year-end.
Chapter 7 • News Flash: Computer Writes Stock Market Story!
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[Price Paragraph]The Dow Jones Industrial Average [rose/fell] [# points], or [percent change] to[price]. The Standard & Poor’s 500 Index rose [rose/fell] [# points], or [percentchange] to [price]. The technology-laden Nasdaq Composite Index rose [rose/fell][# points], or [percent change] to [price].[Fed Paragraph]Stocks [pushed higher/lost ground] in the afternoon after Federal Reserve Chairman Alan Greenspan said that [technology is improving productivity and creatinga virtuous circle of sustainable economic growth/too many people have made toomuch money from stocks, and that the resulting demand for goods threatens tounbalance the economy].[Earnings Paragraph][Company] [jumped/fell] [# points], or [percent change] after beating analysts’ average estimate by [# cents/dollars] per share.[Money Manager Puff Paragraph]“Stocks had sold off because of bad earnings, and now they are recovering,” said[name of money manager], who oversees [$ amount] at [name of establishment]and recently [bought/sold] shares of [company mentioned above].[Below Their Highs Paragraph]A study released by [name of firm] showed that [percent] of all New York Stock Exchange issues are trading below their 52-week highs.[Nonfalsifiable Prediction Paragraph]“The main event is still earnings. If earnings are [good/poor], the market will respond [positively/negatively],” said [money manager name], who oversees [$ amount]at [name of firm]. “Of course, all bets are off if the war in Afghanistan against Osamabin Laden drags on.”[Up/Down, Volume Paragraph][#] stocks [rose/fell] for every [#] that [fell/rose] on the New York Stock Exchange.Some [#] shares changed hands, [percent change] [above/below] the three-monthaverage.[Made-Up Reason Paragraph]“You can’t really look at values, you can’t really look at fundamentals. It’s all aboutpsychological reaction today,” [money manager name], who oversees [$ amount]at [name of firm].
180 Practical Speculation[Chronic Bear Paragraph]Most observers agree that the economic recovery forecast for the next few monthswill not lift all boats. David Tice, manager of the Prudent Bear Fund, expects newlows in the market next year. Tice took profits recently in National Semiconductorand Intel, which have risen [percent] in the past month on optimism for an improving global economic outlook.
Part TwoPracticalSpeculation
“First, Build a Palace for Your King”: A Survival Lessonfrom a Chess MasterPart One described what is wrong with common approaches to investing. Wedebunked the myths and propaganda surrounding the earnings-return relation and technical analysis, presented a case study of chronic negativism, deflated the ballyhoo about value stocks, ran the media’s market coverage undera whole-body scan, and quantified the effects of hubris and humility on individual stocks. But we aren’t the sort of people who only tear down and neveroffer anything constructive.181
182 Practical SpeculationIn Part Two, we provide a series of approaches that together can serve asa foundation for investors. We begin with the one thing that comes beforeeverything else in the quest for investment success: survival.We are as bullish as ever on stocks. The upward sweep of research andprogress will conquer the icy, old-hearted mien that descended on the marketat the beginning of the century. However, the vicious declines of 2000–2002,as well as Vic’s own disaster in 1997, have prompted us to rethink how weprepare for risk.Like all simplifications, our approach is not a panacea. But it is based on adeep philosophical idea from a master of strategy in an area where the greatestminds have been at work for more than 1,000 years. What is more, it has beentested on the firing lines in millions of confrontations. It was in the chess strategy of David Bronstein, a Russian player whom some consider the greatestchess genius who has ever lived, that we found our Holy Grail for trading. Inhis classic work, The Modern Chess Self-Tutor, Bronstein set forth a combination of defense and offensive strategy that is elegant yet revolutionary:At the start of the game, you should not be thinking either about mate, or aboutrapidly gaining a big material advantage. A systematic approach consists in proceeding to one’s aim in stages, and since the system is confrontational, you mustall the time reckon with your opponent’s ideas and counter-actions, and should beconcerned not only about giving mate, but also about ensuring the safety of yourown king. First you must build a shelter for your king . . . a securely defendedcommand post.”1
The advice may have carried a secret poignancy for Bronstein. A Sovietcitizen, he tied for the 1951 world chess championship with the government’sfavorite, Botvinnik. Because Bronstein’s father was a dissident, it has alwaysbeen suspected that his family’s safety would have been in grave jeopardy hadhe won outright.Let’s apply Bronstein’s strategy to investing. At the start of the game, attend to your defenses. Reckon with the market’s tendency to swing violentlyagainst you, and make sure you are not in over your head. Protect yourself andyour family. Take account of the possibility that a long-term illness could keepyou from working or require substantial treatment outlays for a family member. Set aside enough for college educations. Squirrel away enough to maintain the home.We offer no hard-and-fast rules about how much to set aside. But consider Bronstein’s advice:Players who by nature are accurate and cautious can be advised to construct not ashelter, but a virtual palace with double pawn walls and a personal guard.
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Checkmate (Artist: Charles Munro, 1987).Once your king is secure, the offense then can be mounted in three stages:1. First, attack to weaken the adversary’s pawn screen.2. Then, attack with pawns to create a breach in the defenses.3. Finally, mount an invasion with long-range pieces.Applying this approach to markets, it is much more important to gain asteady, reasonable advantage than to risk a wipeout by going for a startlingand enervating win. That is why people who can eke out 2 percent a year morethan the averages have billions of dollars under management. It is not justchance. Therefore, when your financial defenses are in place, start out bymaking small, short-term “swing” trades, buying when the market is oversoldand selling when it becomes overbought.After making good profits and adding to your speculative capital with theswing method, start taking long-range buy-and-hold positions. You will thusbe able to participate in the market’s million percent-a-century returns withoutrisking your survival when the inevitable storms of life and the market come.
184 Practical SpeculationBronstein’s advice on the dangers of being too shortsighted and too aggressive can be applied to putting together a portfolio:You should not bring into play only your favorite piece, but should seek a plan ofaction by which the pieces make moves in turn, creating a united group in attackand defense. . . . You must ask each piece what it can usefully achieve on its own,what help it requires from the other pieces, and in what it itself is prepare to helpthem.
Translated into trading terms, a stock that is sensitive to the market’sfluctuations might balance a long-term sleeper speculation.There it is, in all its brilliance and simplicity. Defend first. Don’t give yourenemy any targets. Make the opponent extend himself if he is going to attackyour very formidable house.To keep ourselves honest and to benefit from the widely dispersed knowledge outside the noisy realm of talking heads and self-promoting marketgurus, we circulated our Bronstein strategy among our friends. A scholarlyday trader, Bipin Pathak, objected that the approach counseled trading toavoid loss instead of trading to win.Our answer: You can’t win if you’re dead. The player, as Bronstein emphasizes, should never lose sight of the main goal: to win. One great longterm winner will make up for numerous small losses, but to survive in theinterim, you need a stable base.Nigel Davies, a chess grandmaster living in London, shared an insightinto tournament play that is apropos here:One of the peculiarities of the laws of chess is that they permit you to make an“agreed draw” at any time. You make your move, verbally offer a draw, press yourclock and your opponent then thinks it over. This has led to the practice of someplayers making draws in very few moves, which are known as “Grandmasterdraws” because of their prevalence in games between Grandmasters. They are notpopular with tournament organizers, the public or anyone else for that matter.But they can be very useful weapons.When I was playing more regularly in round-robin tournaments I would immediately mark down all the games with Black against strong players as beingthose in which a draw is okay On those days I would play very carefully and perhaps make a draw offer around move 10–15. If my opponent wanted to fight thenhe’d be taking a risk, if not you get the day off and save your energy for the nextgame. Like any self-respecting predator I try to pick out the weaklings.In my experience, players who make a few draws in a tournament will veryrarely have a really bad result. But those who go all out in every game will putmuch more pressure on themselves, and sometimes make a REALLY bad result.
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The idea is not to seek to eliminate risk entirely by shooting only for drawsor staying out of the market. The millennial market shakeup left too many people terrified of risk. They are like our grandfathers and fathers after crashes ofthe 1920s and 1970s, taking 2 percent profits on their stocks and selling whenthey have a 10 percent loss—if they dare to venture into the market at all.Yet investors now depend more than ever on the market to meet their financial goals. Work, family life, and retirement savings are inextricably boundto the market in an ecological web of spending, confidence, and capital investment. Adapting Bronstein’s survival principle has improved our own game inchess, life, and the market.Chess players, recall, have only eight pawns and eight pieces—and yet thegame is mind-bendingly complex, particularly since the opponents seek toblock each other at every turn. Stock investing, by contrast, has thousands ofplayers and practically infinite combinations. Where to start? In the followingchapters, we describe how to use quantitative methods to look for cases wherethe market overestimates risk.
8
HOW TOAVOID SPURIOUSCORRELATIONS
I can only say that there is a vast field of topics that fallunder the laws of correlation, which lies quite open to the research of any competent person who cares to investigate it.—Francis Galton1
M
ost of our knowledge is based on analyzing how two things relate toone another. Folk wisdom cautions, “All that glitters is not gold.” InEconomics 101, we learn that prices fall when the quantity supplied rises. Inthe field of investments, people base their expectations on links—perceived oractual—between two things.Here is a list of the things commonly thought to influence the movementsof stocks. Some of these variables are direct: When they’re high, stocks are expected to rise. Others are indirect, or inverse: When they’re high, stocks areexpected to fall. We culled the items on the list from several standard investment texts and hundreds of articles on the Internet.187
188 Practical SpeculationDirect Relations• Better-than-expected earnings.• Change in investor sentiment toward neglected firms (in January).• Dividend yield.• Earnings growth.• Earnings yield.• Insider buying or selling.• Level of CEO ownership.• Liquidity.• Debt level.• Debt rating.• Research and development expenditures.• Risk.• Sales growth.• Short-term interest rates greater than long-term rates.• Similarity to takeover targets in an industry.• Stock buybacks.Inverse Relations• Accrued earnings minus cash earnings.• Excluded expenses in pro forma quarterly earnings reports.• Float.• For mutual funds, top rating of fund or manager.• Inventory increases.• Membership in industry with superior recent performance.• Price to book, sales or earnings.• Return over previous 36 months.• Rising interest rates.• Size (depending on latest trend).Research and practice related to these relations can be found inabundance on the search engine google.com. Most of the academicstudies use arcane statistical analysis, retrospective data files, andold data; none takes into account the ever-changing cycles of themarketplace. The practitioners don’t take account of uncertainty or luck. Fewof these assumptions are ever put to the test. The sad fact isthat most relations are wills-o’-the-wisp, persisting just longenough for the public to lose money.
Chapter 8 • How to Avoid Spurious Correlations
189
The only way to separate ephemeral relations from theones you can trade on is to put the assumptions to the test. Ourhero, Francis Galton, the father of statistical analysis, oftencounseled: “Count! Count! Count!” The best method of counting, for all scientists, scholars, and investors, is to draw a scatter diagram, aplot of the values of two things on a graph.Figure 8.1 shows the scatter diagram used in Chapter 2 to illustrate theinverse relation between earnings in one year and stock market returns inthe next. The line slopes slightly downward from left to right, indicating anegative relation. Thus, contrary to popular belief:• Rising earnings in one year lead to lower stock prices in the next.• Falling earnings in one year lead to higher stock prices in the next.If the line had sloped upward, it would have suggested the opposite: thatrising earnings in one year lead to higher stock market prices in the next,while falling earnings lead to lower stock prices.The importance of scatter plots is widely recognized. A host of seminarsoffer training in using scatter plots as a decision-making tool for businesspeople, government administrators, and researchers of all stripes. The vaunted
Change in Next Year’s S&P 500 Index
0.50.40.30.20.10.0–0.1–0.2–0.3–0.5
0.0Change in Current Year’s Earnings
0.5
y = 9.6% – 1⁄5 (x)R2 = 0.5%
Figure 8.1 Change in Current Year’s Earnings as Predictor of Change inNext Year’s SPX, 1937–2001. Source: Standard & Poor’s Security PriceIndex Record.
190 Practical SpeculationSix Sigma approach to management excellence, widely held to be behind thesuccess of such companies as General Electric, the world’s biggest companyby market value and sales, includes the use of scatter plots, as the followingInternet notice from Applied Performance Strategies Inc. describes:Six Sigma Green Belt TrainingParticipants are introduced to the Six Sigma business methodology and given theopportunity to use the statistical tools required to successfully participate in a SixSigma event. The workshop is designed around a process simulation to help learnthe Define, Measure, Analyze, Improve, and Control methodology. Statisticaltools include process flowcharting, SOPs, response and variables diagrams,Input-Process-Output (IPO) process, histograms, scatter diagrams, [emphasisadded] Pareto diagrams, control charts, run charts, design of experiments, measurement systems, and FMEAs.
Some schools, realizing how critical data analysis is to their students’ future careers, teach scatter plots early on. Fifth-graders at the Humboldt CountySchool District in Nevada learn to “collect, organize, read, and interpret datausing a variety of graphic representations including tables, line plots, scatterplots, [and] histograms; [and] use data to draw and explain conclusions andpredictions.”Like all good things, the tools available to make scatter diagrams are constantly improving. The best by far that we have found is contained in theNumber Cruncher Statistical System, a statistical analysis software package.Number Cruncher’s scatter program software contains so many good featuresthat it made Vic—who is very difficult to please—want to dance. Included aresuch things as trend lines, polynomial spline, lowest curve fitting, sunflowerand box plots, overlays, connecting points, transformations to log or exponential scales, symbols for groups, confidence bands, three-variable plots, threedimensional charts, and colors and font sizes of all descriptions.
How to Build a Scatter DiagramNow, let’s build a scatter diagram from scratch. Computer programs such asExcel, Minitab, or the “freeware” R will do the work, but it’s all to the good ifyou know how it’s done. Understanding the method may give you new insights and help you spot errors.Say you decide to study the relation between changes in interest rates inone year and stock market returns in the next. The first step is to collect observations on two things. We assembled 39 years of data on each variable and
% Change in S&P 500 in Current Year
Chapter 8 • How to Avoid Spurious Correlations
403020100–10–20–30050% Change in T-bill in Previous Year
y = 2.3% – 1⁄10 (x)R2 = 2.3%
100
191
Date