Source: In the Vastness of Transmitting Enlightenment
Author: Yao Bin
The clear inevitability we perceive is often nothing more than an illusion.
Why do some people seem to have extraordinary luck, and why is it said that the essence of making money in the stock market lies in 'probabilistic action'? As an introductory book on probability science, Leonard Mlodinow's 'The Drunkard's Walk' bears some resemblance to Taleb's 'The Black Swan.' However, while Taleb is more fascinated by the uncertainty brought about by skewed distributions and fat-tail events, Mlodinow focuses on various aspects of probability.
Barron's evaluation of this book states, 'Even if you approach with the skeptical attitude of a drunken stagger, by the time you reach the final pages, you will come to understand and accept intuitively improbable concepts—namely, that probability biases the outcomes of uncertainties in life.' This book offers us a fresh perspective on randomness, enabling a deeper understanding of its impact on investment and daily life.
For me, my earliest encounter with complexity science dates back ten years. At that time, I read Leonard Mlodinow’s 'The Drunkard’s Walk.' However, I was unaware of 'complexity science' then. I also had no knowledge of what are now familiar terms like 'randomness' and 'uncertainty.' It wasn’t until three or four years ago that I realized 'The Drunkard’s Walk' is, in fact, a treatise on complexity science.
Life is a series of random events.
The subtitle of 'The Drunkard’s Walk' is 'How Randomness Rules Our Lives,' clearly highlighting the theme of this work. In the first chapter, Mlodinow writes that if Nazi Germany had not initiated the war, his father would not have immigrated to New York, would not have met his mother, also a refugee, and Mlodinow himself would not have been born. The main thread of our lives is constantly steered in new directions by various random events; these events, along with our responses to them, determine our fate, resulting in lives that are difficult to predict and explain.
However, when assessing and making choices under conditions of uncertainty, we often rely on intuition. Intuitive processing undoubtedly offers evolutionary advantages. Yet, the modern world presents a completely different balance of species strengths, and habitual modes of thinking may lead to suboptimal or even inappropriate decisions. There is a close connection between the part of the human brain that evaluates uncertain situations and the part responsible for processing emotions. Human reactions to uncertainty are so complex that at times, different parts of the brain may arrive at conflicting conclusions, engaging in a struggle to determine which conclusion prevails.
The ability to make sound assessments and choices in the face of uncertainty is rare. Like any skill, experience can improve it. The greatest challenge in understanding the role randomness plays in life is that while the fundamental principles of randomness arise from everyday logic, many of their consequences defy intuition. In any sequence of random events, an unusual event is typically followed by a more ordinary one, purely by chance.
Daniel Kahneman discovered that if a flight cadet performs well, praising him may have no effect; but if he performs poorly, improvement often follows punishment. Many great literary works underwent more than ten or even twenty rejections before being published, yet those writers rarely despaired. Success constructs a chasm between randomness and uncertainty. This is why nearly all successful individuals across fields share a common trait—they never give up.
Many events in our lives result from random factors, whose influence is no less significant than our abilities, diligence, or preparedness to seize opportunities. Thus, the reality we perceive is not a direct reflection of people or circumstances but a blurred image randomized by unforeseen or intricately changing external forces. The link between actions and outcomes is not as direct as we might wish to believe. In other words, having certain behaviors does not guarantee specific results. Therefore, understanding the past is difficult, and predicting the future is equally challenging.
Fund managers and coin tossers
We always tend to underestimate the impact of randomness. If a fund outperforms others significantly over five years, many people would admire it without questioning. Random events are often mistakenly interpreted as signs of success or failure.
In the film industry, an unexpected movie might achieve unprecedented success, while a highly anticipated one could end up being ignored. This best illustrates the issue of randomness. For example, if ten Hollywood executives each flipped a coin ten times, despite equal chances of winning or losing, there would still be definitive winners and losers.
In sports competitions, similar random events can occur. An athlete expected by the audience to win might fail, while an unknown athlete could rise to fame overnight. Therefore, Mlodinow cautions us that when observing remarkable achievements in sports or other fields, we should remember that extraordinary outcomes can happen without extraordinary causes. Random events often appear non-random, so care must be taken not to confuse the two when explaining phenomena.
The theory of randomness is a subtle field where renowned experts have made famous errors and professional gamblers have drawn notoriously correct conclusions. Understanding randomness and overcoming misconceptions requires experience and extensive careful thought. After centuries of effort, scientists have finally learned to look beyond apparent order to uncover the randomness underlying nature and daily life — a remarkable advancement.
Academia has invested significant effort into studying patterns of random success in financial markets. For instance, substantial evidence suggests that stock performance is random or close enough to random that, without insider information or additional costs incurred in trading or account management, one cannot profit from random fluctuations. Nevertheless, in the late 1990s, the average annual salary of securities analysts was approximately $3 million. How did they perform?
A 1995 study revealed that Barron’s magazine annually invites 8 to 12 of the highest-paid 'Wall Street superstars' to a roundtable to recommend stocks, but the returns on those stocks merely matched the market’s average. Studies conducted in 1987 and 1997 showed that stocks recommended by prognosticators on the TV program 'Wall Street Week' performed much worse, lagging far behind the market's average profitability.
Based purely on chance, some analysts or funds will inevitably exhibit impressive patterns of success. Numerous studies indicate that past successful instances in these markets do not serve as reliable indicators of future success; much of this success is largely due to luck.
Bill Miller is an investment figure Mlodinow must mention. As the head of Legg Mason Value Trust, he outperformed the S&P 500 index for 15 consecutive years. For this achievement, he was hailed by Money magazine as 'the greatest fund manager of the 1990s.'
Mlodinow points out that knowing a few other statistics would make one less astonished by the fact that Bill Miller’s consistent performance was the product of a random process. For instance, in 2004, his fund’s return was just under 12%, while the average return of S&P stocks was over 15%. That year, the S&P should have beaten Miller, but 2004 was recorded as one of Miller’s 'victories' because the S&P 500 index is not a simple average of stock prices but a weighted average based on companies’ market capitalization.
Bill Miller’s fund underperformed the simple average of S&P stocks but outperformed the weighted average. In fact, during about 30 '12-month periods' within his streak of consecutive successes, his performance fell short of the weighted average. However, these periods did not align exactly with calendar years, and his consecutive successes were calculated based on calendar years from January 1 to December 31. Thus, in a sense, his streak was somewhat artificial from the start, as the definition of success happened to work in his favor.
To explain more concretely, Mlodinow assumes there are 1,000 fund managers—a number that is certainly an underestimate—who start flipping a coin each year from 1991 (the year Bill Miller’s winning streak began). In the first year, about half of them will flip heads; after two years, about one-quarter will have flipped heads twice; after three years, roughly one-eighth will have flipped heads three times, and so on. Those who flip tails gradually exit the game because they have already failed. After 15 years, the probability of any particular coin-flipper consistently flipping heads is 1 in 32,786.
However, the chance that one of these 1,000 individuals, who started flipping coins in 1990, could consistently flip heads is much higher, approximately 3%. Finally, there is no reason to only consider those who started flipping coins in 1991—these managers could have begun in 1990 or 1970 or any year within the modern mutual fund era. Mlodinow calculated that over the past 40 years, the probability of some manager achieving 15 consecutive years of outperforming the market during any 15-year period was close to 3/4.
On this point, another Nobel laureate in economics, Merton Miller, stated it more clearly: “If 10,000 people observe the stock market and attempt to pick the most profitable stocks, then among these 10,000 people, at least one will succeed, but purely by luck. That’s all that has happened. It’s a game, an opportunistic operation. People think they are doing something purposeful, but in reality, they are not.” Therefore, everyone must draw their own conclusions based on their circumstances, but with an understanding of how randomness operates, such conclusions are unlikely to be overly serious.
‘Laplace’s Demon,’ or the wings of a butterfly?
‘Laplace’s Demon’ is a scientific hypothesis proposed by French mathematician Pierre-Simon Laplace. The demon knows all the forces that govern the world as well as the position of every component of the world. For him, nothing is uncertain, and the future unfolds before his eyes just as the past does.
This assumption represents ‘determinism’: the current state of the world precisely determines how the future will unfold. This implies that individual qualities and the nature of any given situation or environment will directly and unambiguously lead to precise consequences. However, such a world must be an orderly one, where everything can be foreseen, calculated, and predicted.
However, in the 1960s, meteorologist Edward Lorenz discovered that long-term, large-scale weather forecasts often result in unpredictable severe consequences due to tiny factors. Small deviations are unavoidable, making long-term weather forecasting inherently unpredictable or inaccurate. When extended to complex systems, this means that for any complex system, under certain ‘threshold conditions,’ its long-term, large-scale future behavior is extremely sensitive to small changes or deviations in initial conditions. A slight alteration in initial values can lead to vastly different future outcomes, which are often unpredictable or carry a degree of randomness. This is the famous ‘butterfly effect,’ which states that ‘a butterfly flapping its wings in Brazil can generate atmospheric effects that amplify over time, potentially triggering a tornado in Texas.’ Thus, deterministic views of the world fail to meet the conditions required for the predictability envisioned by Laplace.
‘The Drunkard’s Walk’ serves as the prototypical model used in the scientific study of randomness. In life, it also provides an apt metaphor because, like Brownian pollen particles suspended in fluid, we are constantly propelled by random events—first in one direction, then another. We cannot escape these unforeseeable or predictable forces, and these random forces, along with our corresponding reactions, shape the specific paths of most people’s lives. Botanist Robert Brown observed that pollen grains moved as if taking the steps of a drunkard, and this motion ‘is neither caused by the flow of liquid nor by gradual evaporation but belongs to the particles themselves.’ Predicting the direction of a pollen grain’s movement before it occurs is nearly impossible.
However, the role of randomness and chance in speculative success is systematically overlooked. We tend to believe, without justification, that past mistakes must be the result of ignorance or incompetence and can be corrected through further learning and improved insight. In the spring of 2007, when Merrill Lynch’s stock price was $95, its CEO was considered a daring genius. By the fall of 2007, following the collapse of the securities market, he was ridiculed as a reckless cowboy and quickly dismissed. The notion that events are unpredictable is often encapsulated in proverbs like ‘Hindsight is always 20/20.’ The blame game of ‘You should have known this would happen’ frequently plays out. Studies on randomness tell us that crystal-clear scenarios of events are possible, but unfortunately, only in hindsight.
Viewing success through the lens of indeterminism
Charles Perrow, a sociologist at Yale University, founded the Normal Accident Theory, which posits that seemingly negligible secondary factors within complex systems should be anticipated to cause significant events due to randomness under certain circumstances. Brian Arthur, the founder of complexity economics, agrees: the simultaneous occurrence of many minor factors can even enable companies without distinct advantages to outperform their competitors. In the real world, if several similarly sized companies enter the market simultaneously, small random events—unexpected orders, chance encounters with buyers, or sudden managerial inspirations—may determine which companies achieve earlier revenue and eventually become dominant forces in the market through accumulation over time. 'Economic activities are determined by individual transactions so small that they cannot be foreseen. However, these minor random events accumulate and, over time, are amplified through positive feedback.'
Traditional economics holds that predicting consumer preferences leads to success. According to this view, managers should most effectively spend their time studying what makes fans of movie stars or sports figures so captivated. They analyze the past, effortlessly identifying the reasons for success, regardless of what success they aim to explain, and hope to replicate those successes. This is the perspective of market determinism.
Under this perspective, success is primarily attributed to the inherent qualities of an individual or product. However, Leonard Mlodinow insists that we should view success differently—through a non-deterministic lens. Success is largely the result of randomness conspiring with various minor factors, involving an element of luck. In many significant events, outcomes might have been vastly different without those chance encounters with people, unexpected job opportunities, and the random convergence of various small factors.
Bill Gates was ranked by Forbes magazine as the world's richest person for 13 consecutive years. Since founding Microsoft, Bill Gates has earned over 100 dollars every second. During every television program interaction, both the host and the audience eagerly await his words. However, his responses are always quite ordinary and no more creative, unique, or insightful than those of other computer experts. This raises the question: Is it because Bill Gates is godlike that he earns 100 dollars per second, or does he appear godlike because he earns 100 dollars per second?
Clearly, equating one's intelligence with their wealth proportionally is likely a mistake. We cannot see someone’s potential but only their results, so we often assume that results necessarily reflect ability, leading to incorrect judgments about that person. The Normal Accident Theory demonstrates that while the connection between action and life is not entirely random, random influences are just as important as our inherent qualities and actions.
As early as 1960, social psychologist Melvin Lerner recognized that 'if people believe there is a random connection between their actions and rewards, few would make long-term efforts.' Therefore, he concluded, 'to maintain their sanity,' people overestimate the abilities inferred from success. That is, we tend to believe famous movie stars are more talented than struggling ones, and the wealthiest individuals must also be the smartest.
In reality, the apparent inevitability we observe is often nothing more than an illusion. Mlodinow laments that we are too easily deceived by how much money someone has made, forgetting the role played by randomness and contingency. This realization was the starting point for his book, The Drunkard's Walk.
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