The Signal and the Noise

by Nate Silver

  As Blodget says, these mistakes can be exceptionally costly for investors. Suppose that you had invested $10,000 in the S&P 500 in 1970, planning to cash it out forty years later upon your retirement in 2009. There were plenty of ups and downs during this period. But if you stuck with your investment through thick and thin, you would have made a profit of $63,000 when you retired, adjusted for inflation and not counting the original principal.95 If instead you had “played it safe” by pulling your money out of the market every time it had fallen more than 25 percent from its previous peak, waiting until the market rebounded to 90 percent of its previous high before reinvesting, you would have just $18,000 in profit—a meager return of 2.6 percent per year.96 Many investors, unfortunately, behave in exactly this fashion. Worse yet, they tend to make their initial investments at times when the market is overvalued, in which case they may struggle to make a positive return of any kind over the long term.

  The next time the market is in a bubble, you will see signals like the flashing lights in a casino drawing you ever closer: the CNBC ticker full of green arrows . . . Wall Street Journal headlines about record returns . . . commercials for online brokerages that make a fortune seem only a mouse-click away. Avoiding buying during a bubble, or selling during a panic, requires deliberate and conscious effort. You need to have the presence of mind to ignore it. Otherwise you will make the same mistakes that everyone else is making.

  Daniel Kahneman likens the problem to the Müller-Lyer illusion, a famous optical illusion involving two sets of arrows (figure 11-11). The arrows are exactly the same length. But in one case, the ends of the arrows outward, seem to signify expansion and boundless potential. In the other case, they point inward, making them seem self-contained and limited. The first case is analogous to how investors see the stock market when returns have been increasing; the second case is how they see it after a crash.

  FIGURE 11-11: MÜLLER-LYER ILLUSION

  “There’s no way that you can control yourself not to have that illusion,” Kahneman told me. “You look at them, and one of the arrows is going to look longer than the other. But you can train yourself to recognize that this is a pattern that causes an illusion, and in that situation, I can’t trust my impressions; I’ve got to use a ruler.”

  The Other 10 Percent

  The cognitive shortcuts that our mind takes—our heuristics—are what get investors into trouble. The idea that something going up will continue to go up couldn’t be any more instinctive. It just happens to be completely wrong when it comes to the stock market.

  Our instincts related to herding may be an even more fundamental problem. Oftentimes, it will absolutely be right to do what everyone else is doing, or at least to pay some attention to it. If you travel to a strange city and need to pick a restaurant for dinner, you probably want to select the one that has more customers, other things being equal. But occasionally it will backfire: you wind up at the tourist trap.

  Likewise, when we were making forecasts in Bayesland, it usually behooved us to pay some attention to what our neighbors and adjust our beliefs accordingly, rather than adopt the stubborn and often implausible notion that we knew better than everyone else.

  I pay quite a bit of attention to what the consensus view is—what a market like Intrade is saying—when I make a forecast. It is never an absolute constraint. But the further I move away from that consensus, the stronger my evidence has to be before I come to the view that I have things right and everyone else has it wrong. This attitude, I think, will serve you very well most of the time. It implies that although you might occasionally be able to beat markets, it is not something you should count on doing every day; that is a sure sign of overconfidence.

  But there are the exceptional cases. Fisher Black estimated that markets are basically rational 90 percent of the time. The other 10 percent of the time, the noise traders dominate—and they can go a little haywire.97 One way to look at this is that markets are usually very right but occasionally very wrong. This, incidentally, is another reason why bubbles are hard to pop in the real world. There might be a terrific opportunity to short a bubble or long a panic once every fifteen or twenty years when one comes along in your asset class. But it’s very hard to make a steady career out of that, doing nothing for years at a time.

  The Two-Track Market

  Some theorists have proposed that we should think of the stock market as constituting two processes in one.98 There is the signal track, the stock market of the 1950s that we read about in textbooks. This is the market that prevails in the long run, with investors making relatively few trades, and prices well tied down to fundamentals. It helps investors to plan for their retirement and helps companies capitalize themselves.

  Then there is the fast track, the noise track, which is full of momentum trading, positive feedbacks, skewed incentives and herding behavior. Usually it is just a rock-paper-scissors game that does no real good to the broader economy—but also perhaps also no real harm. It’s just a bunch of sweaty traders passing money around.

  However, these tracks happen to run along the same road, as though some city decided to hold a Formula 1 race but by some bureaucratic oversight forgot to close one lane to commuter traffic. Sometimes, like during the financial crisis, there is a big accident, and regular investors get run over.

  This sort of duality, what the physicist Didier Sornette calls “the fight between order and disorder,”99 is common in complex systems, which are those governed by the interaction of many separate individual parts. Complex systems like these can at once seem very predictable and very unpredictable. Earthquakes are very well described by a few simple laws (we have a very good idea of the long-run frequency of a magnitude 6.5 earthquake in Los Angeles). And yet they are essentially unpredictable from day to day. Another characteristic of these systems is that they periodically undergo violent and highly nonlinear* phase changes from orderly to chaotic and back again. For Sornette and others who take highly mathematical views of the market, the presence of periodic bubbles seems more or less inevitable, an intrinsic property of the system.

  I am partial toward this perspective. My view on trading markets (and toward free-market capitalism more generally) is the same as Winston Churchill’s attitude toward democracy.100 I think it’s the worst economic system ever invented—except for all the other ones. Markets do a good job most of the time, but I don’t think we’ll ever be rid of bubbles.

  But if we can’t fully prevent the herd behavior that causes bubbles, can we at least hope to detect them while they are occurring? Say you accept Black’s premise that the market is behaving irrationally 10 percent of the time. Can we know when we’re in that 10 percent phase? Then we might hope to profit from bubbles. Or, less selfishly, we could create softer landings that lessened the need for abhorrent taxpayer bailouts.

  Bubble detection does not seem so hopeless. I don’t think we’re ever going to bat 100 percent, or even 50 percent, but I think we can get somewhere. Some of the bubbles of recent years, particularly the housing bubble, were detected by enormous numbers of people well in advance. And tests like Shiller’s P/E ratio have been quite reliable indicators of bubbles in the past.

  We could try to legislate our way out of the problem, but that can get tricky. If greater regulation might be called for in some cases, constraints on short-selling—which make it harder to pop bubbles—are almost certainly counter-productive.

  What’s clear, however, is that we’ll never detect a bubble if we start from the presumption that markets are infallible and the price is always right. Markets cover up some of our warts and balance out some of our flaws. And they certainly aren’t easy to outpredict. But sometimes the price is wrong.

  12

  A CLIMATE OF HEALTHY SKEPTICISM

  June 23, 1988, was an unusually hot day on Capitol Hill. The previous afternoon, temperatures hit 100 degrees at Washington’s National Airport, the first time in decades they reached triple-digits so early in the summer.1 Th
e NASA climatologist James Hansen wiped his brow—the air-conditioning had inconveniently* ceased to function in the Senate Energy Committee’s hearing room—and told the American people they should prepare for more of the same.

  The greenhouse effect had long been accepted theory, predicted by scientists to warm the planet.2 But for the first time, Hansen said, it had begun to produce an unmistakable signal in the temperature record: global temperatures had increased by about 0.4°C since the 1950s, and this couldn’t be accounted for by natural variations. “The probability of a chance warming of that magnitude is about 1 percent,” Hansen told Congress. “So with 99 percent confidence we can state that the warming trend during this time period is a real warming trend.” 3

  Hansen predicted more frequent heat waves in Washington and in other cities like Omaha—already the change was “large enough to be noticeable to the average person.” The models needed to be refined, he advised, but both the temperature trend and the reasons for it were clear. “It is time to stop waffling so much,” Hansen said. “The evidence is pretty strong that the greenhouse effect is here.”4

  With nearly a quarter century having passed since Hansen’s hearing, it is time to ask some of the same questions about global warming that we have of other fields in this book. How right, or how wrong, have the predictions about it been so far? What are scientists really agreed upon and where is there more debate? How much uncertainty is there in the forecasts, and how should we respond to it? Can something as complex as the climate system really be modeled well at all? Are climate scientists prone to the same problems, like overconfidence, that befall forecasters in other fields? How much have politics and other perverse incentives undermined the search for scientific truth? And can Bayesian reasoning be of any help in adjudicating the debate?

  We should examine the evidence and articulate what might be thought of as healthy skepticism toward climate predictions. As you will see, this kind of skepticism does not resemble the type that is common in blogs or in political arguments over global warming.

  The Noise and the Signal

  Many of the examples in this book concern cases where forecasters mistake correlation for causation and noise for a signal. Up until about 1997, the conference of the winning Super Bowl team had been very strongly correlated with the direction of the stock market over the course of the next year. However, there was no credible causal mechanism behind the relationship, and if you had made investments on that basis you would have lost your shirt. The Super Bowl indicator was a false positive.

  The reverse can sometimes also be true. Noisy data can obscure the signal, even when there is essentially no doubt that the signal exists. Take a relationship that few of us would dispute: if you consume more calories, you are more likely to become fat. Surely such a basic relationship would show up clearly in the statistical record?

  I downloaded data from eighty-four countries for which estimates of both obesity rates and daily caloric consumption are publicly available.5 Looked at in this way, the relationship seems surprisingly tenuous. The daily consumption in South Korea, which has a fairly meat-heavy diet, is about 3,070 calories per person per day, slightly above the world average. However, the obesity rate there is only about 3 percent. The Pacific island nation of Nauru, by contrast, consumes about as many calories as South Korea per day,6 but the obsesity rate there is 79 percent. If you plot the eighty-four countries on a graph (figure 12-1) there seems to be only limited evidence of a connection between obesity and calorie consumption; it would not qualify as “statistically significant” by standard tests.*

  FIGURE 12-1: CALORIE CONSUMPTION AND OBESITY RATES IN 84 COUNTRIES

  There are, of course, many conflating factors that obscure the relationship. Certain countries have better genetics, or better exercise habits. And the data is rough: estimating how many calories an adult consumes in a day is challenging.7 A researcher who took this statistical evidence too literally might incorrectly reject the connection between calorie consumption and obesity, a false negative.

  It would be nice if we could just plug data into a statistical model, crunch the numbers, and take for granted that it was a good representation of the real world. Under some conditions, especially in data-rich fields like baseball, that assumption is fairly close to being correct. In many other cases, a failure to think carefully about causality will lead us up blind alleys.

  There would be much reason to doubt claims about global warming were it not for their grounding in causality. The earth’s climate goes through various warm and cold phases that play out over periods of years or decades or centuries. These cycles long predate the dawn of industrial civilization.

  However, predictions are potentially much stronger when backed up by a sound understanding of the root causes behind a phenomenon. We do have a good understanding of the cause of global warming: it is the greenhouse effect.

  The Greenhouse Effect Is Here

  In 1990, two years after Hansen’s hearing, the United Nations’ International Panel on Climate Change (IPCC) released more than a thousand pages of findings about the science of climate change in its First Assessment Report. Produced over several years by a team of hundreds of scientists from around the globe, the report went into voluminous detail on the potential changes in temperatures and ecosystems, and outlined a variety of strategies to mitigate these effects.

  The IPCC’s scientists classified just two findings as being absolutely certain, however. These findings did not rely on complex models, and they did not make highly specific predictions about the climate. Instead, they were based on relatively simple science that had been well-understood for more than 150 years and which is rarely debated even by self-described climate skeptics. They remain the most important scientific conclusions about climate change today.

  The IPCC’s first conclusion was simply that the greenhouse effect exists:

  There is a natural greenhouse effect that keeps the Earth warmer than it otherwise would be.8

  The greenhouse effect is the process by which certain atmospheric gases—principally water vapor, carbon dioxide (CO2), methane, and ozone—absorb solar energy that has been reflected from the earth’s surface. Were it not for this process, about 30 percent9 of the sun’s energy would be reflected back out into space in the form of infrared radiation. That would leave the earth’s temperatures much colder than they actually are: about 0° Fahrenheit or –18° Celsius10 on average, or the same as a warm day on Mars.11

  Conversely, if these gases become more plentiful in the atmosphere, a higher fraction of the sun’s energy will be trapped and reflected back onto the surface, making temperatures much warmer. On Venus, which has a much thicker atmosphere consisting almost entirely of carbon dioxide, the average temperature is 460°C.12 Some of that heat comes from Venus’s proximity to the sun, but much of it is because of the greenhouse effect.13

  There is no scenario in the foreseeable future under which the earth’s climate will come to resemble that of Venus. However, the climate is fairly sensitive to changes in atmospheric composition, and human civilization thrives within a relatively narrow band of temperatures. The coldest world capital is Ulan Bator, Mongolia, where temperatures average about –1°C (or +30°F) over the course of the year;14 the warmest is probably Kuwait City, Kuwait, where they average +27°C (+81°F).15 Temperatures can be hotter or cooler during winter or summer or in sparsely populated areas,16 but the temperature extremes are modest on an interplanetary scale. On Mercury, by contrast, which has little atmosphere to protect it, temperatures often vary between about –200°C and +400°C over the course of a single day.17

  The IPCC’s second conclusion made an elementary prediction based on the greenhouse effect: as the concentration of greenhouse gases increased in the atmosphere, the greenhouse effect and global temperatures would increase along with them:

  Emissions resulting from human activities are substantially increasing the atmospheric concentrations of the greenhouse gases carbon dioxide,
methane, chlorofluorocarbons (CFCs) and nitrous oxide. These increases will enhance the greenhouse effect, resulting on average in additional warming of the Earth’s surface. The main greenhouse gas, water vapor, will increase in response to global warming and further enhance it.

  This IPCC finding makes several different assertions, each of which is worth considering in turn.

  First, it claims that atmospheric concentrations of greenhouse gases like CO2 are increasing, and as a result of human activity. This is a matter of simple observation. Many industrial processes, particularly the use of fossil fuels, produce CO2 as a by-product.18 Because CO2 remains in the atmosphere for a long time, its concentrations have been rising: from about 315 parts per million (ppm) when CO2 levels were first directly monitored at the Mauna Loa Observatory in Hawaii in 1959 to about 390 PPM as of 2011.19

  The second claim, “these increases will enhance the greenhouse effect, resulting on average in additional warming of the Earth’s surface,” is essentially just a restatement of the IPCC’s first conclusion that the greenhouse effect exists, phrased in the form of a prediction. The prediction relies on relatively simple chemical reactions that were identified in laboratory experiments many years ago. The greenhouse effect was first proposed by the French physicist Joseph Fourier in 1824 and is usually regarded as having been proved by the Irish physicist John Tyndall in 1859,20 the same year that Charles Darwin published On the Origin of Species.