In the world of investment management, there's a widespread problem of mediocre results. This isn't because passive investment strategies are brilliant, but rather because the academic understanding of a statistical concept called "mean reversion" has been misunderstood. Many psychologists and economists who have won Nobel prizes have not addressed the statistical concept in their theories, which has led to a mistaken belief that active investment managers are generally incompetent.

The way passive asset managers operate, particularly through methods like market capitalization, gives them an unfair advantage. Passive investors can simply bet on the companies that are already doing well, while active managers are tasked with predicting the future performance of investments, which is extremely difficult. Even if active managers succeed in outperforming the market for a short period, it's very challenging to do so consistently over the long term because they are essentially competing against a herding market, which should never be considered as a benchmark for several reasons. Such markets lack stability and can be disconnected from asset fundamentals, leading to extreme volatility and short-term focus. Relying on herding markets as benchmarks may risk portfolio losses, discourage diversification, and fail to align with long-term financial goals. Additionally, these markets may lack efficiency, foster unrealistic expectations, and discourage individuality in investment strategies. Furthermore, herding markets can be susceptible to manipulation and offer little accountability for investment managers.

The "wisdom of crowds" suggests that diverse groups can make more accurate decisions than individuals. While often effective, it has limitations. Biased or manipulated information can skew outcomes, and groupthink may stifle independent views. Inexperienced participants or a lack of expertise can diminish the crowd's effectiveness. Noise and errors in judgments can also impede accuracy. Information cascades may lead to blindly following others, and the size and diversity of the crowd matter. Additionally, in time-sensitive situations, this approach may not be practical. So, while the wisdom of crowds has merit, it's vital to consider its potential pitfalls and suitability for specific contexts.

The paradox of unbeatable mediocrity in the context of investment management emerges when the "wisdom of crowds," often deemed mediocre at best, is regarded as the benchmark for decision-making. While the wisdom of crowds can provide reasonably accurate consensus views, it represents a collective average rather than exceptional insights. Passive investment strategies, relying on market indexes shaped by this consensus, essentially follow the crowd's sentiment. In contrast, active investment managers aim to outperform this benchmark, but the challenge lies in consistently surpassing a mediocre standard. This challenge is exacerbated by information asymmetry, favoring passive strategies with readily available, consensus-driven information. As a result, active managers often struggle to consistently outperform the crowd's mediocrity, leading to the paradox where the seemingly average approach (passive investing) outpaces those striving to beat it (active managers).

AI faces challenges in resolving the paradox between passive investing and its well-defined, unchanging rules versus AI's dynamic and often opaque nature. For AI to make meaningful contributions, it must grasp the mathematical foundations of market capitalization (MCAP), recognize biases, and propose controls that don't compromise risk-weighted performance. Achieving this delicate balance necessitates a blend of common sense, intelligence, and historical knowledge of statistical methods, a domain where AI holds potential for excellence. To embark on this journey, it's crucial to understand how the concepts of equilibrium and disequilibrium have led to a divergence between Economics and Science. While Science has advanced in deciphering complexity in the natural world, Economics has centered around seminal statistical laws like 'mean reversion.' Unfortunately, Economics has oversimplified these laws with causal explanations, resulting in the unremarkable indexing concept developed in 1871, which has become a dominant force in modern investing.

Mediocrity

Mediocrity is a state characterized by being average or ordinary in terms of quality, skill, ability, or performance. It signifies a lack of excellence or outstanding qualities in a particular area. Often, mediocrity is associated with conformity, where individuals adhere to established norms and standards without pushing themselves to achieve greater heights. This conformity can result from a preference for comfort and a resistance to change or risk-taking that might lead to exceptional outcomes.

One significant aspect of mediocrity is its relative nature. People often perceive themselves as mediocre when they compare their achievements to those of others who excel in a particular field. However, it's essential to recognize that mediocrity is not an absolute standard; it varies from one context to another and is subjectively assessed.

Mediocrity can significantly impact personal and professional growth. Those who settle for mediocre performance may miss opportunities for learning, improvement, and development. Their reluctance to step out of their comfort zone and challenge themselves can limit their potential and restrict the opportunities available to them.

Paradox

A paradox is a statement, proposition, or situation that seems to be self-contradictory or logically absurd, but upon closer examination, may reveal a deeper truth or make sense in a specific context. Paradoxes often challenge our understanding of reality and logic, prompting us to think critically and reconsider our assumptions.Paradoxes are important in philosophy, mathematics, and science as they often highlight areas where our understanding of the world may be incomplete or where our intuitions about reality can lead to seemingly contradictory conclusions. Scientists and philosophers use paradoxes as tools for deepening their exploration and understanding of complex concepts. Science is full of paradoxes.

Scientific Equilibrium

Throughout history, the concept of equilibrium has been a cornerstone of scientific thought, spanning fields such as physics, chemistry, and biology. Equilibrium represents a state of balance or stability where opposing forces or factors achieve near-perfect equilibrium. In physics, it signifies the absence of a net force on an object, while in chemistry, it arises when the rates of forward and reverse reactions are equal. In ecology, it describes a balanced state within an ecosystem. Equilibrium is vital for comprehending how systems respond to changes and disturbances and for identifying conditions of stability.

The roots of the equilibrium concept trace back to ancient Greece, where philosophers like Aristotle contemplated balance and rest in their studies of motion and the natural world. Aristotle's discussions on "natural places" and "natural motion" laid the early philosophical foundations for understanding how objects naturally seek states of balance. However, it was the brilliant minds of thinkers like Archimedes in the 3rd century BCE that solidified the concept of equilibrium. Archimedes' formulation of Archimedes' Principle, describing how objects submerged in fluids experience an upward force equal to the weight of the displaced fluid, marked a significant leap in understanding equilibrium within fluid systems.

The 17th century ushered in groundbreaking insights into equilibrium and motion, courtesy of Galileo Galilei and Sir Isaac Newton. Galileo's explorations into mechanics and his development of the principle of inertia laid the groundwork for our contemporary understanding of objects at rest or in uniform motion. Newton's laws of motion, notably the First Law of Motion (law of inertia), provided a comprehensive framework for comprehending how objects behave in states of equilibrium or non-equilibrium. This law asserts that an object at rest will remain stationary, and an object in motion will persist at a constant velocity unless acted upon by an external force. As the 18th and 19th centuries unfolded, the study of equilibrium expanded into thermodynamics and chemistry. Renowned scientists such as Antoine Lavoisier and Joseph Louis Gay-Lussac made significant contributions to our understanding of chemical reactions and the concept of chemical equilibrium, which pertains to the balance of reactants and products in a chemical system.

Economic Equilibrium

Economic equilibrium, akin to its scientific counterparts, involves the balance of supply and demand, resulting in stable prices. Unlike in science, economics employs equilibrium to describe market conditions, where it signifies the point at which the quantity of a product supplied equals the quantity demanded at a specific price. This equilibrium leads to market-clearing prices and quantities, with no inherent tendency for change. Economic equilibrium considers factors like consumer preferences, production costs, and government policies, making it a dynamic process where markets adapt to changing conditions, primarily focusing on prices and quantities.

Economic equilibrium has a rich history, with early contributions attributed to French economist Léon Walras, who laid the groundwork for general equilibrium theory in his 1874 work "Elements of Pure Economics." This theory explores competitive market equilibrium where supply equals demand for all goods and services, forming the foundation for modern economic analysis. Another economist, Alfred Marshall, expanded on equilibrium in his 1890 book "Principles of Economics," introducing the concept of partial equilibrium, emphasizing how individual markets reach balance between supply and demand, even if the broader economy lacks full general equilibrium. These early contributions paved the way for later advancements by economists like Paul Samuelson, Kenneth Arrow, and Gerard Debreu, who formalized general equilibrium theory.

The concept of comparative advantage, introduced by David Ricardo in the 19th century, plays a pivotal role in economics, especially in international trade. It aligns with equilibrium by guiding resource allocation and trade patterns, tending to lead to market equilibrium. Comparative advantage underscores the benefits of specialization and trade in enhancing economic welfare and efficiency, representing a cornerstone in the study of international economics and trade theory.

Scientific Disequilibrium

Scientific disequilibrium has played a pivotal role in reshaping our understanding of fundamental principles in physics and cosmology. Notable examples include the double-slit experiment, which challenged classical physics by revealing the dual nature of particles and waves, and Galileo Galilei's experiments overturning Aristotelian beliefs about falling objects, laying the foundation for modern physics. Edwin Hubble's observations of redshifts in galaxies challenged the static model, supporting the Big Bang theory. Maxwell's demon, a thought experiment by James Clerk Maxwell, illustrated thermodynamic disequilibrium by challenging the second law of thermodynamics. Schrödinger's cat, proposed by Erwin Schrödinger, showcased quantum mechanical disequilibrium by highlighting the paradox of a cat being both alive and dead until observed.

These instances of disequilibrium arose when experimental results contradicted existing theories, prompting scientists to reevaluate fundamental principles and develop new frameworks, thus advancing science. Scientific disequilibrium is a catalyst for progress, fostering critical inquiry and pushing the boundaries of knowledge, highlighting the dynamic and evolving nature of science.

Erwin Schrödinger's essay "What Is Life?" contributed significantly to the understanding of life at the molecular level during a time of scientific disequilibrium. Schrödinger proposed that life's orderliness could be explained by the presence of "aperiodic" crystals, akin to a genetic code stored in DNA. His work influenced research in molecular biology and genetics, contributing to the modern understanding of life at the molecular and genetic levels.

Economics Disequilibrium

Disequilibrium in economics refers to a state where the quantity of a product supplied does not match the quantity demanded at the prevailing market price, resulting in surpluses or shortages. A surplus occurs when supply exceeds demand, suggesting high prices, while a shortage arises when demand exceeds supply, indicating low prices. Economists view markets as dynamic and self-adjusting. In disequilibrium, market forces come into play, with prices acting as signals. Surpluses lead to price reductions to boost purchases, while shortages prompt price increases to maximize profits.

Various factors like changing consumer preferences, production costs, government interventions, external shocks, and market imperfections can cause disequilibrium. Economics deals with disequilibrium differently than science. In economics, disequilibrium is seen as a temporary and correctable state, with markets gradually returning to equilibrium. The price mechanism is central to addressing disequilibrium, as rising prices reduce shortages, and falling prices alleviate surpluses. Disequilibrium is considered a natural part of market dynamics, where competition, consumer choices, production capabilities, and policies adjust supply and demand. Government intervention, like price controls or subsidies, may occur during severe disequilibrium but can be contentious.

Despite recognizing disequilibrium, economic analysis often focuses on equilibrium models for predicting market behavior. These models assume markets tend to move toward equilibrium in the long term. Unlike science, which uses disequilibrium for deeper exploration and paradigm shifts, economics prioritizes equilibrium analysis for understanding and predicting market dynamics.

Divergent Approaches

The divergence between economics and science in their treatment of disequilibrium arises from fundamental differences in their objectives, methodologies, and approaches. Economics primarily seeks to comprehend and forecast resource allocation and decision-making in dynamic environments, utilizing equilibrium models to elucidate market behavior. It regards disequilibrium as a temporary condition that markets naturally rectify over time through price adjustments and the interplay of supply and demand. On the other hand, science's primary mission is to unearth the fundamental principles governing the natural world. It welcomes disequilibrium as an opportunity for exploration and deeper comprehension, challenging established theories and fostering the creation of new ones.

While economics strives for predictions within an equilibrium framework, science thrives on embracing disequilibrium, promoting experimentation, innovation, and critical thinking to expand knowledge and instigate paradigm shifts. This distinction underscores society's struggle to utilize science in addressing the issues plaguing modern finance, which fails to explain the inadequacies of our financial theories and the functioning of markets.

Discovery of Mean Reversion 

It might not seem very obvious but mean reversion as a concept is pretty new compared to the idea of equilibrium. Mean reversion is a concept that gained more attention in economics and finance in the 20th century, although its roots can be traced back to earlier discussions of trends and fluctuations in financial markets. The term "mean reversion" itself became more commonly used in the context of asset prices and stock market analysis during the 20th century. While equilibrium has deep historical roots in economic thought, mean reversion emerged as a more specialized concept, particularly in the context of financial markets, in the modern era. Both concepts are important in understanding economic and financial phenomena, but equilibrium has a longer history in economic theory.

The concept of mean reversion in economics can be traced back to the work of several early economists, and it has been discussed in various forms for centuries. While it may be challenging to pinpoint the very first economist to talk about mean reversion, the idea has historical roots in economic thought.

One early reference to mean reversion can be found in the work of Sir Francis Galton, a 19th-century British scientist who explored the concept of "regression toward the mean" in the context of human traits and characteristics. His work laid some of the foundation for later discussions of mean reversion in economics.

In the field of finance and stock market analysis, the concept of mean reversion has also been discussed for a long time. Benjamin Graham, often considered the "father of value investing," wrote about mean reversion in the context of stock prices and the idea that stock prices would tend to revert to their intrinsic values over time.

Moreover, early discussions of mean reversion in stock prices and financial markets were influenced by the work of economists like Louis Bachelier, who introduced the concept of random walk theory in his 1900 doctoral thesis. Random walk theory suggests that price changes in financial markets follow a random and unpredictable pattern, but it also laid the foundation for later discussions of mean reversion.

Overall, mean reversion is a concept that has evolved over time, with contributions from various economists and researchers throughout history. It has been applied in different contexts, from economics to finance, and has played a role in shaping our understanding of how variables tend to revert to their historical averages or norms over time.

Mean reversion and prediction

Mean reversion is a key concept used in economics, particularly in finance and economics dealing with time series data. It refers to the tendency of a variable, such as an asset price or an economic indicator, to revert to its historical average or mean value over time. Mean reversion can be a valuable source of prediction in economics for both short-term and long-term forecasting, although its applicability and effectiveness may vary depending on the specific context.

In the short term, mean reversion suggests that when a variable deviates significantly from its historical average or mean, it is likely to move back toward that mean in the near future. This concept is often used in financial markets. For example, if a stock price experiences a rapid increase, it may be expected to experience a correction as it reverts toward its historical price average. Short-term traders and investors use mean reversion to identify trading opportunities based on the expectation that extreme deviations from the mean are likely to be temporary.

In the long term, mean reversion implies that over extended periods, economic indicators or asset prices are likely to oscillate around their historical averages. This notion is used in various economic forecasts. For instance, when projecting long-term economic growth, economists might assume that an economy will, over time, revert to its historical growth rate. Similarly, in real estate, long-term forecasts often consider mean reversion, suggesting that property values will tend to move toward their long-term average levels.

However, it's crucial to recognize that mean reversion is a simplifying assumption, and its applicability can vary based on the specific economic or financial context. It assumes that historical patterns will persist into the future, which may not always hold true, especially when faced with structural changes, shifts in economic policy, or unexpected events. This unexplained aspect of Mean Reversion, referred to as randomness, falls in the realm of Science outside the boundaries of Economics.

Human Psychology vs. Mean Reversion

In the world of science, disequilibrium is frequently associated with complex, dynamic systems that exhibit inherent unpredictability. Many scientific phenomena, especially those in the natural sciences, are subject to intricate relationships and feedback loops, making them highly sensitive to initial conditions. This sensitivity often results in unpredictability, where small changes in starting conditions can lead to vastly different outcomes, a phenomenon famously illustrated by the butterfly effect. Moreover, at the subatomic level, as observed in quantum mechanics, inherent uncertainty prevails, with particle behavior described by probability distributions rather than deterministic equations. This underscores the fundamental unpredictability of certain natural phenomena. In scientific contexts, disequilibrium is, by design, considered unpredictable due to the complexity, uncertainty, and nonlinear dynamics characterizing these systems.

Conversely, economics, particularly in the realm of finance, approaches disequilibrium differently. It often deals with systems influenced by human behavior, which introduces elements of predictability, particularly in the short to medium term. The concept of mean reversion is a notable example used in economics to make predictions. Mean reversion suggests that asset prices or economic indicators tend to revert to their historical averages over time. Economists and financial analysts employ this concept, along with quantitative models and statistical techniques, to analyze historical data, identify trends, and make short-term predictions. These methods provide a framework for informed decision-making based on empirical observations. Additionally, economic models frequently incorporate assumptions about rational behavior, which further contributes to the potential for predictability. While mean reversion offers valuable insights for short-term predictions, it's important to recognize that long-term forecasts in economics are subject to greater uncertainty, influenced by factors such as structural changes, policy shifts, and unexpected external events.

Shiller's Mean Reversion: A Dynamic Perspective on Asset Prices

Robert J. Shiller, a distinguished economist and Nobel laureate, has significantly shaped our comprehension of asset prices and their intricate behaviors. His body of work presents a compelling dualism, where he utilizes mean reversion as a guiding principle for modeling and prediction in some instances, while in others, he highlights the limitations of mean reversion, portraying it as mere unexplained fluctuations. In this article, we explore Shiller's influential research, revealing the complex interplay between these contrasting perspectives on mean reversion.

One of Shiller's notable contributions is his application of the cyclically adjusted price-to-earnings ratio (CAPE), often referred to as the Shiller PE ratio. This metric captures the long-term cyclicality in stock market valuations by evaluating the price of a stock index in relation to the average of ten years of earnings, adjusted for inflation.

In Shiller's work with CAPE, mean reversion serves as a foundational concept. This approach inherently acknowledges the cyclical nature of corporate earnings, which naturally fluctuate over time. By incorporating the ten-year average earnings in CAPE, Shiller captures the inclination of earnings to revert to a historical average over the long haul.

Shiller's use of CAPE for modeling and prediction hinges on the notion that mean reversion can provide valuable insights into stock market valuations. Significant deviations of CAPE from its historical average suggest that stock prices may have deviated from their equilibrium values. High CAPE values, for instance, may indicate potential overvaluation, often followed by subsequent lower returns, and vice versa.

However, Shiller's comprehensive perspective on mean reversion is not limited to its applications. He also presents a contrasting viewpoint on the limitations of mean reversion. Shiller emphasizes that financial markets seldom exist in a state of consistent equilibrium. Instead, they persist in a state of perpetual disequilibrium, influenced by a multitude of factors, including investor sentiment, macroeconomic conditions, and unforeseen events.

In certain aspects of his work, Shiller challenges the conventional wisdom that financial markets invariably revert to historical averages. He illustrates that mean reversion is not a universal law but a complex phenomenon influenced by various unpredictable factors. In this view, mean reversion is portrayed as nothing more than fluctuations that cannot be entirely explained or predicted.

Robert J. Shiller's research offers a dynamic perspective on mean reversion in asset pricing. His use of CAPE showcases mean reversion as a valuable thesis for modeling and prediction, offering insights into stock market cyclicality and deviations from equilibrium. However, Shiller's broader body of work underscores the inherent complexity of financial markets, where mean reversion often remains elusive and unexplained.

Thaler's Dual Perspective on Mean Reversion in Financial Markets

Richard H. Thaler, another Nobel laureate economist renowned for his work in behavioral economics, offers a dual perspective on the concept of mean reversion in financial markets. His research demonstrates how mean reversion can both explain certain market behaviors and pose limitations when confronted with anomalies driven by human behavior.

In his influential article "Can the Market Add and Subtract" (Thaler, 1987), Thaler explores the role of mean reversion as a thesis for modeling and prediction. He investigates portfolios composed of 3-year worst losers versus 3-year best winners. Thaler's findings reveal that mean reversion is indeed a factor at play. Portfolios comprising 3-year worst losers tend to outperform portfolios of 3-year best winners in subsequent years. This observation underscores the idea that extreme performance, whether exceptionally good or bad, often reverts to a more moderate mean.

Thaler's work with these portfolios highlights mean reversion as a valuable explanatory concept, suggesting that investors' reactions to extreme performance tend to be excessive, leading to subsequent corrections.

In his paper titled "The End of Behavioral Finance" (Thaler, 2005), Thaler indirectly challenges the effectiveness of mean reversion in explaining market anomalies. He examines anomalies that defy traditional mean reversion explanations, emphasizing that they persist due to the influence of human behavior on market outcomes. These anomalies represent instances where asset prices deviate from what historical data would predict.

Implicit in Thaler's challenge to mean reversion is the recognition of behavioral biases exhibited by investors, leading to deviations from rational pricing. These deviations challenge the straightforward application of mean reversion, highlighting the complexities inherent in behavioral finance.

Richard H. Thaler's research provides a dual perspective on mean reversion in financial markets. On one hand, he utilizes mean reversion as a thesis for modeling and prediction, exemplified by his work with portfolios of 3-year worst losers versus 3-year best winners. This demonstrates the tendency for extreme performance to revert to a more moderate mean.

On the other hand, Thaler indirectly challenges the efficacy of mean reversion in explaining anomalies in financial markets. His research underscores the limitations of this concept when confronted with the complexities of human behavior. Thaler's work in behavioral finance suggests that anomalies persist because market participants do not always act rationally, and their behavioral biases can lead to deviations from mean reversion patterns.

Siegel's Perspective on Mean Reversion in Stock Markets

Jeremy Siegel, a renowned economist and finance professor, offers a nuanced perspective on mean reversion in stock markets. His work, particularly highlighted in his influential book "Stocks for the Long Run," focuses on the long-term performance of stocks and the factors that influence it.

In "Stocks for the Long Run," Siegel argues that over extended periods, stocks tend to provide positive real returns that outperform other asset classes. He acknowledges the presence of short-term market fluctuations and volatility but suggests that, in the long run, the stock market follows an upward trajectory. This long-term optimism is rooted in factors such as economic growth and technological progress, which he believes contribute to the positive performance of stocks over time.

Siegel's research also delves into the "equity premium puzzle," which seeks to understand why stocks historically yield higher returns than less risky assets like bonds. In this context, Siegel suggests that the equity premium may be influenced by long-term trends rather than solely by mean reversion. This perspective implies that there are fundamental factors at play that drive the sustained outperformance of stocks over extended periods.

Siegel's viewpoint extends to the relationship between dividend yields and subsequent earnings growth. He argues that this relationship implies a positive expectation for long-term stock returns. While he acknowledges that stock prices can fluctuate and deviate from mean levels in the short term, he believes that over extended periods, the market tends to revert to its long-term trend.

Jeremy Siegel's dual perspective on mean reversion arises from this ineffability of mean reversion, which works and fails, leaving him with an incomplete picture. He recognizes the existence of short-term market fluctuations and deviations from mean levels, his focus is on the long-term upward trend of stock markets. He attributes this trend to fundamental factors like economic growth, technological progress, and the relationship between dividend yields and earnings growth.

Fama’s dualism on Mean Reversion in Stock Markets

The discussion of Eugene Fama's work on the Efficient Market Hypothesis (EMH) sheds light on the dualism surrounding the concept of mean reversion in financial markets. Fama, a renowned figure in finance and a Nobel laureate, is prominently associated with EMH, which has significant implications for our understanding of mean reversion in the context of financial markets.

Fama's EMH asserts that financial markets are efficient, implying that asset prices fully reflect all available information. In an efficient market, the notion of mean reversion faces a formidable challenge because prices are expected to follow a random walk, where past price movements should not hold predictive power over future price movements. This assertion contradicts the conventional idea of mean reversion, which relies on the belief that asset prices tend to revert to historical means over time.

EMH comes in three forms: weak, semi-strong, and strong. The weak form suggests that past prices and trading volumes are already factored into current prices, rendering technical analysis (a method often reliant on mean reversion) ineffective. The semi-strong form extends this concept by proposing that all publicly available information is already incorporated into prices, making fundamental analysis (which can also hinge on mean reversion) futile. The strong form suggests that even insider information is already reflected in prices, leaving no room for profitable mean reversion strategies.

Fama's work on market efficiency aligns with the belief that widespread and exploitable mean reversion in asset prices is unlikely in efficient markets. In this view, any information indicating that an asset's price should revert to a historical mean would already be accounted for in the current price. However, it's important to acknowledge that Fama's perspective, while influential, is not without its critics. Some argue that markets may not be perfectly efficient, and there could be pockets of inefficiency where mean reversion can play a role. Others suggest that market efficiency can vary across different asset classes and time periods.

In summary, Eugene Fama's contributions to the Efficient Market Hypothesis underscore the dualistic nature of mean reversion in finance. While he generally contends that mean reversion may not be a dominant or exploitable phenomenon in efficient markets, the debate over market efficiency and the role of mean reversion remains a topic of ongoing discussion and scrutiny within the field of finance.

Kahneman's Complex Relationship with Mean Reversion

Daniel Kahneman, a Nobel laureate and influential figure in behavioral economics, presents a nuanced perspective on mean reversion in financial and economic contexts. His work explores the interplay between cognitive biases and rational economic principles, shedding light on the complexities of human decision-making.

Kahneman's Prospect Theory, co-developed with Amos Tversky, delves into decision-making under risk and uncertainty. It introduces the concept of loss aversion, emphasizing that individuals often fear losses more than they desire equivalent gains. This cognitive bias can lead to decisions that deviate from mean reversion principles.

For instance, when faced with a portfolio that has incurred losses, individuals might resist mean reversion and hold onto declining assets longer than rational economic principles would suggest, driven by their aversion to realizing losses. This deviation from mean reversion principles is influenced by the psychological bias inherent in Prospect Theory.

Kahneman and Tversky's Endowment Theory explores the psychology of ownership, highlighting the Endowment Effect, where people overvalue items they own compared to their objective market value. This effect suggests that individuals may resist selling assets, even when rational analysis suggests it, due to their attachment and overvaluation of those assets.

In the context of mean reversion, the Endowment Effect challenges the assumption that assets will naturally revert to their historical mean values. Instead, individuals may hold onto assets, resisting mean reversion, and contributing to deviations from equilibrium prices.

Kahneman's work also intersects with mean reversion in a confirming manner through his example involving flight instructors. In this scenario, he observes that instructors who receive praise for exceptional performance tend to see their subsequent performance regress toward the mean, while those who receive criticism for poor performance tend to improve over time, also moving toward the mean.

This phenomenon aligns with the concept of mean reversion, as it suggests that extreme performance tends to revert to a more moderate mean. Kahneman's example illustrates that, in certain contexts, mean reversion can offer valuable insights into human behavior.

Daniel Kahneman's work in behavioral economics provides a confused  view of mean reversion in financial and economic contexts. While his Prospect Theory and Endowment Theory highlight the potential for deviations from mean reversion due to cognitive biases like loss aversion and ownership overvaluation, his example of flight instructors confirms the presence of mean reversion in specific situations.

This complex relationship underscores the need to consider the interplay between cognitive biases and rational economic principles when assessing mean reversion. It highlights that while mean reversion can offer valuable insights, it must be viewed alongside the intricate psychology of human decision-making, where deviations from the mean can occur due to various cognitive biases.

Granger’s Challenge

Clive Granger's work in econometrics and time-series analysis provides valuable insights into the conflicted perspective surrounding mean reversion in financial markets. Granger, a Nobel laureate in economics, developed innovative techniques such as cointegration and the Engle-Granger two-step method, which are foundational in the field of econometrics and have implications for understanding mean reversion.

Granger's approach revolves around the analysis of time-series data, and his work acknowledges that mean reversion may not always be straightforward to detect, especially when individual time series exhibit trends. Cointegration, a concept introduced by Granger and Robert Engle, describes how two or more time series, despite having individual trends, can be linked by a stable long-term relationship. This concept is essential for understanding mean reversion, as it suggests that what may appear as mean reversion over shorter time horizons could actually be the result of underlying long-term relationships among variables.

The Engle-Granger two-step method, developed by Granger, offers a practical approach to testing for cointegration between two time series. It involves first estimating the individual trends in the series and then examining the residuals for stationarity. If the residuals are stationary, it implies the presence of a cointegrating relationship, which can be seen as a form of mean reversion. This method underscores Granger's commitment to rigorous statistical analysis when assessing mean reversion and highlights that it may not always be apparent due to the presence of individual trends.

However, it's important to note that Granger's overall perspective is not necessarily one of advocating for a dual view on mean reversion. Instead, his work is often associated with the belief that markets are generally efficient, aligning with the principles of the Efficient Market Hypothesis (EMH). Granger's approach emphasizes the challenges involved in rejecting EMH and stresses the need for robust empirical evidence to support claims of consistently profitable trading methods. While his methods provide valuable tools for understanding the complexities of financial data, they do not necessarily suggest that mean reversion opportunities are widespread or easily exploitable.

Bogle’s Reversion

In John C. Bogle's work, there is a clear alignment with the concept of mean reversion, but it doesn't necessarily present a dualistic perspective. Instead, Bogle's viewpoint on mean reversion complements his overall investment philosophy, emphasizing the significance of this phenomenon in the context of investments.

Bogle's emphasis on mean reversion corresponds to his philosophy of passive investing and the use of index funds. He underscores that asset prices tend to revert to their long-term averages over time, which is a fundamental aspect of his approach to comprehending financial markets. This perspective implies that active stock picking and market timing can be challenging and often unnecessary, as market prices eventually gravitate back toward their mean.

Moreover, Bogle's advocacy for passive investing, exemplified by the use of diversified portfolios and index funds, aligns with his belief in mean reversion. Passive investing is based on the idea that investors can capture long-term market returns without attempting to predict short-term market fluctuations or chase individual stocks. This approach harmonizes with the expectation that asset prices will, over time, return to their historical averages.

Bogle's focus on mean reversion suggests a disciplined, risk-aware approach to investing. When an asset's price significantly deviates from its historical mean, it may indicate increased risk or the presence of asset bubbles. Bogle's guidance encourages investors to exercise caution in such situations and avoid impulsive decisions based solely on short-term market fluctuations.

While mean reversion is a valuable concept, it is important to note that Bogle's perspective doesn't necessarily present a dualistic view. Instead, it reinforces the idea that investors should maintain a prudent, long-term perspective in their investment strategies, aligning with the principles of rational, low-cost, and patient investing that Bogle advocated throughout his career. Bogle's work underscores the importance of understanding mean reversion as part of a broader investment philosophy rather than as a conflicting perspective.

Pros and Cons of Mean Reversion

Mean reversion, the tendency for asset prices or economic variables to revert to historical averages or long-term trends, offers several potential advantages. Firstly, it provides stability and predictability in financial markets and economic trends, aiding investors and policymakers in anticipating future movements. Secondly, it serves as a valuable valuation metric, helping investors gauge whether an asset is overvalued or undervalued in relation to its historical averages. Lastly, mean reversion can act as an early warning system, signaling when asset prices are at extremes and potentially carrying higher risks.

However, there are notable drawbacks to mean reversion. Importantly, it is not a guaranteed predictor of future performance. Deviations from the mean can persist longer than expected, and market dynamics can change, leading to unexpected outcomes. Eugene Fama's efficient market hypothesis (EMH) casts doubt on the systematic profitability of mean reversion strategies in efficient markets, where all available information is reflected in prices. Behavioral biases, highlighted by Richard Thaler and Daniel Kahneman, can disrupt rational decision-making based on mean reversion signals. These biases can cause investors to either overreact or disregard mean reversion patterns.

Furthermore, accurately identifying mean reversion patterns demands robust data and sophisticated statistical analysis. Poor data quality or inadequate analysis can lead to incorrect conclusions. Mean reversion's time horizons can vary widely, making it challenging for investors with different investment horizons to apply consistently. In different market regimes, mean reversion may operate differently, especially during financial crises or extraordinary events. Additionally, in quantitative modeling, there's a risk of overfitting data to find mean reversion patterns that may not hold up in real-world scenarios.

The concept of mean reversion carries both merits and drawbacks within the realms of finance and economics. While it offers stability and valuable guidance for valuation, it is not foolproof and may encounter challenges in specific market conditions. The works of prominent thinkers have illuminated the intricate and limited nature of mean reversion, echoing sentiments expressed by the Father of Statistics back in 1885. When you distill economic and financial theories to their core, what emerges is a landscape characterized by variability, noise, and causal explanations. This absence of a truly scientific foundation might explain why Robert Solow advocated for acknowledging that economics, despite its merits, cannot be considered a full-fledged science with a capital "S."

The Paradox of Mediocrity

We currently find ourselves within a vast $50 trillion USD passive investing market, a product of Nobel prize-winning research, led by asset managers who have revolutionized global investing by democratizing access. However, this seemingly advanced market often provides, at best, a skewed representation of collective wisdom. It is concentrated, misrepresentative, overly focused on weightings, and fraught with various risks. Remarkably, visionaries in this field have come to a shared realization: mean reversion, while valuable, is not a constant; it behaves randomly. This dilemma has spawned what we now term the Paradox of Mediocrity, where rudimentary, antiquated procedures known as MCAP weighted Indexes are steering the world towards a perilous concentration crisis, all the while asserting their invincibility.

To unravel this paradox, we must embrace several fundamental truths. First, the fact that mediocrity prevails does not adorn it with regal splendor. Just because a theory goes unchallenged does not render it inherently true. The absence of innovation since 1871 does not make our flawed indexing methodologies eternally valid. The proclamations of brilliance by passive investing do not automatically make it brilliant. Similarly, the desire of passive investing to see active managers fade away will not make them vanish. True innovation looms on the horizon, and it commences with the recognition that current versions of economics and finance are on the verge of obsolescence. The more we channel our intellectual efforts into scientific solutions for resolving the Paradox of Mediocrity, the further we will advance into the era of intelligence.