Great trend followers approach trading as science and their foundation is the scientific method. At best, they view the world like physicists. And the following physics definition is dead-on applicable to trading success: “The science of nature, or of natural objects; that branch of science which treats of the laws and properties of matter, and the forces acting upon it; especially, that department of natural science which treats of the causes that modify the general properties of bodies; natural philosophy.”²

If you can’t measure it, you probably can’t manage it . . . 
Things you measure tend to improve.

Ed Seykota³

From error to error, one discovers the entire truth.

Sigmund Freud

Excellence in physics, or trend following, requires a solid grounding in numbers. Both disciplines work off models that describe relationships, and their common language, math, is finite. Physics and trend following thus work best when they constantly test models with real-world applications.

Trading your money necessarily means dealing with numbers and varying quantities—like a physics experiment. But the connection goes deeper. Physics is at its core about developing mathematical models of our world. Those models may describe different types of complexity such as the movement of molecules in a gas or the dynamics of stars in a galaxy. And it turns out similar models can be applied to analogous complex behavior in financial markets.⁴

When I use the term science of trading, it is not a reference to the engineers or scientists who develop elegant and complex academic models prone to fragility (trend following is in the antifragile headspace). Keeping it simple is hard because it is hardest to do what is obvious. Famed physicist, Nobel Prize winner, and Manhattan Project scientist Richard Feynman beautifully sums up the needed mindset in his classic 1960s lecture:

In general, we look for a new law by the following process. First, we guess it (audience laughter), no, don’t laugh, that’s really true. Then we compute the consequences of the guess, to see what, if this is right, if this law we guess is right, to see what it would imply and then we compare the computation results to nature, or we say compare to experiment or experience, compare it directly with observations to see if it works. If it disagrees with experiment, it’s wrong. In that simple statement is the key to science. It doesn’t make any difference how beautiful your guess is, it doesn’t matter how smart you are, who made the guess, or what his name is. If it disagrees with experiment, it’s wrong. That’s all there is to it.

Although few would admit it, the truth is that the typical trader wants to be right on every single trade. He is desperately trying to create certainty where it just doesn’t exist.

Mark Douglas

He added:

It is much more likely that the reports on flying saucers are the result of the known irrational characteristics of terrestrial intelligence, rather than the unknown rational efforts of extraterrestrial intelligence. It’s just more likely, that’s all. And it’s a good guess. We always try to guess the most likely explanation, keeping in the back of our mind that if it doesn’t work, then we must discuss the other possibilities.⁵

It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge . . . The most important questions of life are, for the most part, really only problems of probability.

Pierre-Simon 
Marquis de Laplace⁶

Critical Thinking

Trend followers, like physicists, approach the investing landscape with an open mind. They examine, experiment and A/B test to find solid ground. Like physicists they think critically and develop the ability to ask the right questions, including:

• Digging deep to face the real problem, instead of mindlessly going for the easy superficial query.
• Being completely honest regarding the real reason you might want an answer.
• Discovering how to interpret information before asking the question—in other words, questions that offer the opportunity to make a midcourse correction.
• Facing cold, hard facts about human nature.
• Facing the reality of where the new answer might lead.
• Facing subjective takes on the world and factoring in objective data.
• Seek questions that engender important details that might be missed because people did not ask.⁷

Charles Faulkner prioritized his favorites: “The questions that are most critical—in both senses of that word—are the ones that question our assumptions, our assumptions of what is or is not a fact or a 
truth or possible. After this comes questions that assist statistical 
thinking.”

You must be determined to know what is real. You do not avoid asking a question if you’re suspicious you might not like the answer. You do not ask self-serving questions that reinforce an opinion you already have. You do not ask mindless questions or accept mindless answers. You are content to ask questions knowing there might not be an answer. This is not an easy process for the masses.

Do not believe in anything simply because you have heard it. Do not believe in anything simply because it is spoken and rumored by many. Do not believe in anything simply because it is found written in your religious books. Do not believe in anything merely on the authority of your teachers and elders. Do not believe in traditions because they have been handed down for many generations. But after observation and analysis, when you find that anything agrees with reason and is conducive to the good and benefit of one and all, then accept it and live up to it.

Buddha

Most go the wrong way every time. The questions become superficial and ill-informed because they have not taken ownership. Instead they ask dead-end questions, “Is this going to be on the test?” Their questions demonstrate a complete lack of desire to think. They might as well be sitting in silence with minds on pause. To think critically, you must want to stimulate your intellect with questions that lead to more questions. You must undo the damage previous traditional rote memorization schooling has done to your curiosity. You need to want to resuscitate your mind.⁸

Probability theory is the underpinning of the modern world. Current research in both physical and social sciences cannot be understood without it. Today’s politics, tomorrow’s weather report, and next week’s satellites depend 
on it.⁹

Linear versus Nonlinear

Chaos theory dictates a nonlinear universe. Our world does not move in a straight line. Spending your time looking for perfect is an exercise in futility. The future is unknown no matter how educated the fundamental forecast. Manus J. Donahue III, author of An Introduction to Chaos Theory and Fractal Geometry, paints a picture of our chaotic, nonlinear world:

The world of mathematics has been confined to the linear world for centuries. That is to say, mathematicians and physicists have overlooked dynamical systems as random and unpredictable. The only systems that could be understood in the past were those that were believed to be linear, that is to say, systems that follow predictable patterns and arrangements. Linear equations, linear functions, linear algebra, linear programming, and linear accelerators are all areas that have been understood and mastered by the human race. However, the problem arises that we humans do not live in an even remotely linear world; in fact, our world must indeed be categorized as nonlinear; hence, proportion and linearity is scarce. How may one go about pursuing and understanding a nonlinear system in a world that is confined to the easy, logical linearity of everything? This is the question that scientists and mathematicians became burdened with in the nineteenth century; hence, a new science and mathematics was derived: chaos theory.¹⁰

I’d say the non-normal distribution is what we arbitrage. That is what you make profits from.

Richard Dennis

Everyone’s entitled to their own opinion, but they’re not entitled to their own facts.

Daniel Patrick Moynihan¹¹

Although a nonlinear acceptance is new for many, it is not a new principle inside trend following trading. The big events such as the 2008 market crash, or Brexit 2016, are examples of nonlinear events. Trend following won during these events because it’s built to expect the unexpected. Lack of linearity, or cause and effect, was not unanticipated. How did trend following manage this preparation for events no one could predict? What set it apart is that trend following, deep down, is stati­stical thinking.

Gerd Gigerenzer notes the power of statistical thinking:

At the beginning of the twentieth century, the father of modern science fiction, Herbert George Wells, said in his writings on politics, “If we want to have an educated citizenship in a modern technological society, we need to teach them three things: reading, writing, and statistical thinking.” At the beginning of the twenty-first century, how far have we gotten with this program? In our society, we teach most citizens reading and writing from the time they are children, but not statistical thinking.¹²

I have no special talents. I am only passionately curious.

Albert Einstein

One of my favorite examples of statistical thinking is a case study involving the birth ratio of boys and girls. There are two hospitals. In the first one, 120 babies are born every day; in the other, only 12. On average the ratio of boys to girls born every day in each hospital is 50/50. However, one day in one of those hospitals twice as many girls are born as boys. In which hospital was it more likely to happen? The answer is obvious to numbers thinking, but as research shows it’s not so obvious for the untrained: It is much more likely to happen in the small hospital. The probability of a random deviation of a particular size from the population mean decreases with the increase in the sample size.¹³

Standard deviation measures the uncertainty in a random variable (in this case, investment returns). It measures the degree of variation of returns around the mean (average) return. The higher the volatility of the investment returns, the higher the standard deviation will be.

National Institute of Standards and Technology¹⁴

Statistical puzzles about birth and gender tie directly to trend following. Take two traders who on average win 40 percent of the time with winners being three times as large as losers. One has a history of 1,000 trades and the other has a history of 10 trades. Who has a better chance in the next 10 trades to have only 10 percent of total trades turn out as winners (instead of the typical 40 percent)? The one with the 10-trade history has the better chance. More trades in a history mean a greater probability of adhering to the average. Fewer trades mean a greater probability of deviation from the average.

Consider a friend who receives a tip and makes quick money. He tells everyone about his newfound trading prowess. You are impressed. But you would be less impressed if you were a statistical thinker because you would realize immediately his population of tips was extremely small. He could as easily follow the next great stock tip and blow up. One tip means nothing. The sample is too small.

The difference between these two views is why great trend followers have grown from one-person shops to firms that routinely beat the so-called Wall Street powerhouses. Why did Wall Street sit by and allow trend traders to enter and dominate arenas they could, and perhaps should, have dominated? The answer lies in Wall Street and Mains Street’s fascination with benchmarks. Wall Street is after index-like performance (benchmarks) because their clients think they can avoid risk and control return (fantasies die hard), whereas trend following is focused on absolute performance—monthly calendars be damned.

On the other hand, large, established Wall Street firms grounded in EMT judge success with measures of central tendency. The large banks and brokerages view an average measure (mean) and the variation from average to determine whether they are winning or losing. They are beholden to investors’ irrational desires. The trend following mindset is counter to their entire business model.

They go in wrong directions with their volatility understanding. Volatility around the mean (standard deviation) is the de facto Wall Street risk definition. Typical Wall Street types, long-only types, aim for consistency instead of absolute returns. As a result returns are average by design. They worship the normal distribution:

Normal distributions are the bedrock of finance, including the random walk, capital asset pricing, value-at-risk, and Black-Scholes models. Value-at-risk (VaR) models, for example, attempt to quantify how much loss a portfolio may suffer with a given probability. While there are various forms of VaR models, a basic version relies on standard deviation as a measure of risk. Given a normal distribution, it is relatively straightforward to measure standard deviation, and hence risk. However, if price changes are not normally distributed, standard deviation can be a very misleading proxy for risk.¹⁵

Mathematics and science are two different notions, two different disciplines. By its nature, good mathematics is quite intuitive. Experimental science doesn’t really work that way. Intuition is important. Making guesses is important. Thinking about the right experiments is important. But it’s a little more broad and a little less deep, so the mathematics we use here can be sophisticated. But that’s not really the point. We don’t use very, very deep stuff. Certain of our statistical approaches can be very sophisticated. I’m not suggesting it’s simple. I want a guy who knows enough math so that he can use those tools effectively but has a curiosity about how things work and enough imagination and tenacity to dope it out.

Jim Simons¹⁶

Luck is largely responsible for my reputation for genius. I don’t walk into the office in the morning and say, “Am I smart today?” I walk in and wonder, “Am I lucky today?”

Jim Simons¹⁷

The problem with standard deviation as a risk measurement is seen when two traders have similar standard deviations, but show an entirely different distribution of returns. One might look like the familiar normal distribution, or bell curve. The other might show statistical characteristics known as kurtosis and skewness. In other words, the historical pattern of returns does not resemble a normal distribution.

Trend following never has and never will produce returns that exhibit a normal distribution. It will never produce consistent average returns that hit benchmarks quarter after quarter. When trend followers hit home runs in the zero-sum game and win huge profits from the likes of Barings Bank, Long-Term Capital Management, and the 2008 market crash, they are targeting the edges or those fat tails of a non-normally distributed world.

Jerry Parker, the most successful of the trained Turtles: “The way I describe it is that overlaying trend following on top of markets produce a non-normal distribution of trades. And that’s sort of our edge—in these outlier trades. I don’t know if we have an inherent rate of return, but when you place this trend following on top of markets, it can produce this distribution—the world is non-normal.”¹⁸

Jean-Jacques Chenier, like Parker, knows markets are far less linear and efficient than the typical view. Remember, not everyone across markets plays to win. Some might be hedgers, playing to lose, using the markets as insurance: “The Bank of Japan will intervene to push the yen lower . . . a commercial bank in Japan will repatriate yen assets overseas just to window dress its balance sheets for the end of the fiscal year. These activities create liquidity but it is inefficient liquidity that can be exploited.”¹⁹

One would not expect to see a home-improvement volume with the title The New Reality of Plumbing. But the science of investing, at least as it is propagated by financial writers, undergoes a seeming revolution every couple of thousand points on the Dow.²⁰

The risk-reducing formulas behind portfolio theory rely on a number of demanding and ultimately unfounded premises. First, they suggest that price changes are statistically independent from one another . . . The second assumption is that price changes are distributed in a pattern that conforms to a standard bell curve. Do financial data neatly conform to such assumptions? Of course, they never do.

Benoit B. Mandelbrot²¹

To better understand Parker’s words, it helps to break down the concepts of skew and kurtosis. Skew measures the statistical likelihood of a return in the tail of a distribution being higher or lower than commonly associated with a normal distribution. For example, a return series of –30 percent, 5 percent, 10 percent, and 15 percent has a mean of 0 percent. Only one return is less than 0 percent, whereas three are higher but the one that is negative is much farther from the 
mean (0 percent) than the positive ones. This is called negative 
skewness. Negative skewness occurs when the values to the left of (less than) the mean are fewer, but farther from the mean than the values to the right of the mean. Positive skewness occurs when the values to the right of (more than) the mean are fewer, but farther from the mean than the values to the left of the mean.²²

Trend following exhibits a positive skew return profile. Kurtosis, on the other hand, measures the degree to which exceptional values, much larger or smaller than the average, occur more frequently (high kurtosis) or less frequently (low kurtosis) than in a normal (bell-shaped) distribution. High kurtosis results in exceptional values called fat tails, which indicate a higher percentage of very low and very high returns than would be expected with a normal distribution.²³

Skew may be either positive or negative and affects distribution symmetry. Positive skew means there is a higher probability for a significant positive return than for a negative return the same distance from the mean. Skew will measure the direction of surprises. Outliers, or extremes in performance not normally associated with a distribution, will clearly affect skewness. The crash of 1987 is usually considered an extreme outlier. For example, a positive outlier will stretch the right-hand tail of the distribution. Because this method eliminates losing positions and holds profitable positions, historically there has been a tendency for positive outliers and a higher chance of positive returns. A negative skew results in a higher probability of a significantly negative event for the same distance from the mean.²⁴

Skewness is a measure of symmetry, or more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the center point.

National Institute of Standards and Technology²⁵

These concepts are not as entertaining as listening to the latest money honey paraded out by finance shows to serenade sweet nothings—literally nothings. Few see the use for statistical thinking when they can trust a hot model to think for them. If you forget these moneymaking basics, you will never see the reality great trend following traders see—the reality of a making a fortune when the next black swan arrives.

Kurtosis is a measure of whether the data are peaked or flat relative to a normal distribution. That is, data sets with high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have heavy tails. Data sets with low kurtosis tend to have a flat top near the mean rather than a sharp peak. A uniform distribution would be the extreme case.

National Institute of Standards and Technology²⁶

Compounding

Jim Rogers’s Investment Biker was one of my first Wall Street books. He brought so much passion and common sense to the table. Nearly 14 years later in early 2008, I interviewed him for my first documentary film (Broke) at his home in Singapore. (My Rogers visits never stopped; I saw him in 2014 and 2016, too). Even though I had been up for nearly 48 hours straight (going around the world does take 20 hours in the air) when I did the interview, the classic moneymaking lessons were on 
the table.

Rogers, who is not a technical trend following trader, but who has made a fortune trading trends, put the importance of compounding at the top of his list: “One of the biggest mistakes most investors make is believing they’ve always got to be doing something . . . the trick in investing is not to lose money . . . the losses will kill you. They ruin your compounding rate; and compounding is the magic of investing.”²⁷

For such a long time we thought that most data must have a normal distribution and therefore that the mean is meaningful. Much of the world around us is not normal . . . [and] it is so difficult to see the simplest things as they really are. We become so used to our assumptions that we can no longer see them or evidence against them. Instead of challenging our assumptions, we spend our time studying the details, the colors of the threads that we tear from the tapestry of the world. That is why science is hard.²⁸

You can’t get rich overnight, but with a proper compounding perspective you at least have the chance to make big money over a lifetime. For example, if you manage to make 50 percent a year in your trading you can compound an initial $20,000 account to over $616,000 in seven years. Is 50 percent unrealistic? Perhaps. However, do the math again using 
25 percent. You can be a trend follower, make 25 percent a year, and spend all of your profits each year. Or you can apply trend following and possibly compound your 25 percent a year for 20 or more years and become filthy rich. Look at a hypothetical investment of $20,000 (see Table 8.1):

Say goodbye to a nice, steady, equilibrium perspective. Equilibrium equals death. Things do not rock along smoothly, change in small increments. Change is catastrophic. We must learn to adapt because we cannot predict.²⁹

A trend example further illustrates the point. In October 1997 David Harding launched his Winton Futures Fund, which provided investors with annualized returns of 21 percent per year for his first 10 years. To put that in context, if you had been the buyer of Vincent van Gogh’s “Irises” in 1947, you would have paid $80,000. The next time it changed hands, in 1987, it was bought for $53.9 million. This seems like a huge increase in value, but mathematically it’s a compounded average annual growth rate of 17.7 percent, which is less than the annualized returns in Harding’s fund.

The acceptance of compounding math is not intuitive in a world focused on prediction hocus pocus, instant gratification, and tweets by the bushel. However, if there is evidence trend following thrives and flourishes in a compounded nonlinear world, and there is, it’s worth 
considering the specific people, operations and philosophies religiously at work against wider acceptance.

Summary Food for Thought

• Donald Rumsfeld: “Reports that say that something hasn’t happened are always interesting to me, because as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns—the ones we don’t know we don’t know. And if one looks throughout the history of our country and other free countries, it is the latter category that tends to be the difficult ones.³⁰
• If you can’t think in numbers, don’t play the game.
• The edges of the bell curve are opportunity.
• Probable events are not always certain and extremely improbable events are not always impossible (i.e., Black Swans).
• Bill Bonner: “If you had asked a group of investors, in August 1929, what was likely to happen on Wall Street, you’d have heard a range of views. You might even have found a crank or two who predicted a market crash. But the majority view was nothing like what happened.”³¹