We are BACK!
Dear Reader,
Welcome to the premier issue of the Haykov Foundation's Mathecon Investment Letter. This edition marks the beginning of our journey through the complex world of mathematical economics, intertwined seamlessly with practical investment strategies. At the heart of our exploration is a principle that is both elemental and profound: every economic action is purpose-driven. Through the lens of praxeology—the study of purposeful behavior—we investigate the quest for utility maximization, whether in the pursuit of wealth, satisfaction, or the achievement of the best possible outcomes within certain limitations.
After a deliberate hiatus, spent deeply immersed in the study of mathematical economics, we are thrilled to return, equipped with actionable insights into investment. In this inaugural newsletter, we are excited to introduce Transparent Network Technology, a revolutionary advancement in the field of investment.
Welcome to the Mathecon Investment Letter from the Haykov Foundation, where we embody the ethos of the classic film Wall Street: "We don’t throw darts at a board. We only bet on sure things." In Mathecon, our investments are predicated on the solid ground of empirical facts and logical deduction alone. Echoing the discernment of Arthur Conan Doyle, our approach is methodical: we entertain no assumptions. By discarding the impossible—those notions that stand in opposition to the facts—what remains, no matter how improbable, must align with empirical evidence and logical analysis to represent the truth.
Warmest regards,
Joseph Mark Haykov
The Mathecon Newsletter
Introduction
Mathematical economics, illustrated by the first and second welfare theorems and epitomized by the Arrow-Debreu model, represents a monumental achievement. However, it appears not to have garnered the recognition it truly merits. This achievement is comparable in significance to Andrew Wiles' groundbreaking solution to Fermat's Last Theorem in 1994—a puzzle that eluded mathematicians for over three centuries. Just as Wiles' work resolved a longstanding mathematical enigma, the Arrow-Debreu model provides a theoretical framework that supports core principles proposed by Adam Smith in 'The Wealth of Nations' (1776). Smith posited that labor specialization, fueled by efficient trade, enhances collective consumption and reduces the workload by increasing labor productivity. Despite widespread acceptance, akin to the Riemann Hypothesis, Smith's principles lacked formal underpinning until 1954, when Arrow and Debreu offered definitive evidence, affirming the efficacy of market mechanisms nearly 200 years later. This timeline is notably swift, especially in the realm of logical deduction and mathematical reasoning, considering it took over 350 years to prove Fermat's Last Theorem.
In practice, the validity of Smith's conjecture on labor specialization and its impact on productivity is evident, even in the absence of mathematical proof. For instance, historical specialization in sectors like farming versus fishing significantly enhanced productivity. Following Smith’s era, the reorganization of production methods, particularly through the assembly line, facilitated further subdivision of labor into specialized tasks, leading to a dramatic increase in efficiency. Yet, it is the specialization in developing advanced means of production—such as automobiles, airplanes, genetically modified organisms, MRI machines, computers, robotics, drones, artificial intelligence, and automation technologies—that has profoundly boosted productivity. These innovations have not only markedly improved productivity to date but are also poised to drive unprecedented improvements in overall productivity in the near future.
The essence of the Arrow-Debreu model lies in its foundational axiom, which it shares with mathematical game theory and is deeply rooted in praxeological science—the study of human action. This axiom posits that individuals act as rational utility maximizers, always striving to maximize their benefits. This pursuit, known as maximizing subjective utility, unfolds within an environment characterized by ideal trade conditions and perfect information, leading to outcomes of Pareto efficiency—where no individual can be made better off without making someone else worse off. Such a framework bestows upon the model both theoretical sophistication and empirical relevance. Observations have shown that when real-world conditions approximate the Arrow-Debreu assumptions—marked by free, unrestricted, and symmetrically informed trade—there tends to be a notable optimization of per capita GDP levels and overall improvements in living standards. However, it's important to note that these ideal conditions are seldom fully met in reality, highlighting the model's aspirational value in guiding economic policies towards more efficient market outcomes.
The Arrow-Debreu model serves as a crucial analytical tool for pinpointing market inefficiencies by highlighting deviations from its idealized principles. George Akerlof’s seminal work, 'The Market for Lemons,' for instance, delves into the consequences of information asymmetry, thereby underscoring the model’s significance in illuminating and tackling market imperfections. A prime example of the model's theoretical principles being tested in reality is seen in the used car market. Historically, the issue of asymmetric information—where sellers have more information about the product than buyers—allowed unscrupulous dealers to exploit consumers. This challenge was significantly mitigated by the advent of CarFax and similar services, which democratized access to vehicle histories, thus beginning to address the informational imbalance.
Additionally, the economic disparity between Haiti and the Dominican Republic starkly illustrates the consequences of straying from the Arrow-Debreu model's assumption of unfettered trade. The significant differences in their GDPs highlight the economic costs associated with barriers to trade and the lack of law enforcement that results in involuntary exchanges. This scenario underscores Akerlof’s point about the adverse effects of departing from the Arrow-Debreu model’s assumptions—specifically, the implications for symmetric information in transactions and the principle of voluntary exchange. Such real-world examples illuminate the practical value of the model in understanding and addressing economic inefficiencies.
These examples highlight the significant impact of information asymmetry and involuntary trade on economic efficiency, as objectively measured by real GDP per capita, demonstrating the efficiency losses that occur when the principles of free and informed trade are not upheld in real-world scenarios. For a deeper insight into the importance of incorporating information asymmetry into economic models, one can turn to 'The Theory of the Firm' by Michael C. Jensen and William H. Meckling. This seminal work in corporate finance introduces the concept of agency costs, which arise from the asymmetric information between firm owners (shareholders) and their managers. Agency costs represent a form of market inefficiency that occurs when managers, who are tasked with operating the business on behalf of the shareholders, pursue their own interests at the expense of the owners.
Jensen and Meckling argue that reducing these costs necessitates a commitment to enhancing transparency and ensuring the symmetric distribution of information among all shareholders. By aligning the interests of the management with those of the shareholders, a significant challenge in corporate governance and finance is addressed. This alignment not only mitigates the inefficiencies caused by information asymmetry but also promotes a more equitable and efficient market environment. Thus, their work underscores the critical need for economic models to account for information asymmetry, highlighting its pervasive influence on market dynamics and the importance of strategies to counteract its effects.
While the Arrow-Debreu model's theoretical underpinnings are robust, translating these principles into actionable economic policy and investment strategies presents considerable challenges. Central banks, including the US Federal Reserve, often utilize "General Equilibrium" models inspired by the Arrow-Debreu framework to inform monetary policy decisions. These models presuppose conditions of unrestricted exchange and symmetric information to forecast market equilibria. Yet, such assumptions starkly contrast with the realities of market dynamics, characterized by prevalent information asymmetry and various trade barriers. This gap between theoretical idealism and practical reality underlines why seasoned investors, including Warren Buffett, approach these models with caution. Their skepticism is not unfounded but is based on the models’ historical struggles to accurately predict economic indicators like recessions, interest rates, and inflation.
Despite these practical shortcomings, the Arrow-Debreu model, when applied with discernment, yields invaluable insights into the nature of economic equilibria and delineates the conditions under which welfare and efficiency, as defined within the model, can be maximized. This situation is akin to how the Pythagorean theorem operates with absolute reliability within the constraints of Euclidean geometry; similarly, the Arrow-Debreu model guarantees optimal outcomes, provided its assumptions remain unbreached in real-world applications. However, leveraging this model effectively in economics demands a nuanced integration of its theoretical axioms with the tangible complexities of the global economic environment.
Drawing a parallel to the realm of geometry, just as the assumptions of Euclidean geometry do not always align with real-world phenomena—thus necessitating the use of Riemannian geometry for accurate GPS triangulation on Earth, which accounts for the curvature of space and time dilation effects between satellite and Earth-based clocks—similarly, the foundational assumptions of the Arrow-Debreu model seldom fully correspond with the complexities of real-world markets. This incongruity between theory and practice necessitates the exploration of alternative economic theories and mathematical methods that can more accurately capture the nuances of market dynamics, akin to how Riemannian geometry provides the mathematical framework necessary for certain applications in physics.
Despite these challenges, the Arrow-Debreu model remains a cornerstone of economic theory and analysis. Its strength lies in its rigorous and formal axiomatic foundation, rendering it an indispensable tool for examining economic dynamics and informing policy decisions. The true value of the model lies in its ability to delineate precisely the conditions necessary for market efficiency, thereby highlighting the specific factors whose absence leads to inefficiencies in real-world economies. Understanding these conditions enables economists to better navigate the complexities of economic systems and to develop strategies that can enhance welfare and efficiency, even when the idealized assumptions of the model are not fully met.
Asymmetric Information in Economics: A Mathecon Perspective
Behavioral Mathematical Game Theory, commonly known as Mathecon, examines the intricate intersection of mathematical economics and game theory, rooted in the praxeological principle of rational utility maximization. In this conceptual framework, individuals—referred to as "players" within game theory—perform dual roles as both consumers and producers. Their goal is to maximize their economic "payoff," which involves not only maximizing the subjective utility derived from consuming goods and services but also minimizing the costs associated with obtaining these benefits: the time and effort required to earn the money necessary for their purchase.
In the realm of mathematical economics, the quest for personal benefit is deeply intertwined with the subjective utility gained from employing earned wages to procure goods and services. Hence, money extends beyond its elementary role of merely denominating wages. It assumes a pivotal role as a measure of purchasing power, acting as a store of value that includes both our savings and the wages we earn in the tangible economy. Analogous to how degrees Celsius quantify temperature, the dollar quantifies purchasing power, reflecting the capacity of bank funds to enable transactions. This multifunctional nature of money—serving both as a unit of account and as a measure of purchasing power—forms a fundamental aspect of the Arrow-Debreau framework. In this model, prices are expressed, and transactions are valued, using money as the unit of account, highlighting its critical mathematical function in economic theory.
Furthermore, the cycle of wage expenditure illustrates money's pivotal roles beyond a mere unit of account, acting also as a crucial medium of exchange. This dual functionality, as hypothesized by the Jevons-Menger-Walras theory, addresses the inherent limitations of barter systems, specifically the double coincidence of wants dilemma, by facilitating a more sophisticated network of economic interdependence. This modern system effectively mirrors the age-old practice of exchanging labor for the products of others' labor.
In the Arrow-Debreu model, such economic interactions are framed as inherently mutually beneficial. Individuals exchange their labor for wages, which in turn are used to purchase goods and services produced by others. This symbiotic relationship fosters both consumer and producer surplus, guiding the economy towards a state of Pareto optimality. Essentially, this model exemplifies the optimization of a collective welfare function, where each transaction serves to enhance subjective utility incrementally.
As previously discussed, for an exchange to be truly mutually beneficial and have the potential to contribute to Pareto improvements, it must occur within a framework of unfettered and symmetrically informed transactions. However, the reality often deviates from this ideal. Despite the inherent risk of fraud facilitated by asymmetric information—where sellers have more knowledge about product quality than buyers—natural market mechanisms serve to discourage such deceptive behavior effectively.
The challenge of concealing the quality of perishable items, such as fish, starkly contrasts with products like eggs, whose quality becomes apparent only after purchase. Asymmetric information predominantly enables fraud when there's a notable gap between the anticipated and actual benefits of a transaction. This risk is often mitigated by the transparency of information about the products involved, as seen with perishable goods such as fish, but not always possible with others, like eggs.
In practice, the most robust defense against the sale of substandard goods is the prospect of repeat business. Merchants who compromise on quality not only face the risk of losing customers but also, potentially, their entire operation. Thus, the effort to counteract fraud driven by asymmetric information hinges less on inherent honesty and more on the practical realization that deceptive practices alienate repeat customers, threatening the longevity of a business.
However, in environments lacking robust fraud-prevention mechanisms—common in much of internet commerce—the frequency of fraud significantly increases, leading to substantial financial losses. This underscores the complexity of ensuring transactional integrity in digital marketplaces, where traditional mechanisms of fraud deterrence may not be as effective.
Platforms like Amazon play a pivotal role in reinforcing transactional integrity by addressing the challenges of asymmetric information in commerce. By ensuring that the quality of goods and services matches their descriptions and securing financial transactions, these platforms significantly lower the risk of fraudulent activity. Amazon stands out in its efforts to combat fraud, thereby improving market efficiency. It achieves this by diminishing information asymmetry and bolstering trust among parties involved in transactions. This approach not only enhances the online shopping experience but also sets a benchmark for how digital marketplaces can create a more transparent and trustworthy environment.
The effectiveness of platforms such as Amazon in countering the adverse effects of asymmetric information not only demonstrates online retail's capacity to enhance market efficiency but also highlights a fundamental economic principle: the achievement of optimal efficiency and mutual benefit in transactions is contingent upon reducing the exploitation of asymmetric information. While this analysis refrains from making moral judgments about these dynamics, it unmistakably points out a marked departure within the stock market from the ideal of symmetrically informed trading. This divergence draws attention to the intricate nature of information dissemination in financial markets and its significant impact on both market efficiency and fairness.
In the stock market, the presence of asymmetric information grants individuals with superior knowledge the ability to significantly increase their wealth, often at the expense of less informed participants. This scenario is akin to a tennis tournament where a few top players claim the majority of the rewards. Such a situation vividly demonstrates the critical influence of information asymmetry on the economic landscape, creating a chasm between the theoretical ideals of equitable trade and the realities of the market.
Beyond Efficiency: Unraveling the Realities of Information Asymmetry in Financial Markets
This paper examines the core assumptions underlying derivative pricing, with a particular focus on the Black-Scholes model. Our analysis identifies that the model's dependence on the principle of market efficiency not only eclipses simpler and more intuitive approaches but also significantly diverges from the perspectives offered by the Arrow-Debreu theorem. According to the theorem, market inefficiency is an inherent outcome in scenarios marked by asymmetric information, a condition that arbitrage mechanisms can only address to a limited extent. In contrast, the Black-Scholes model, which is based on the assumption of a perfectly efficient market, fails to account for the widespread presence of information asymmetry. This oversight neglects the reality that enables astute investors, such as Jim Simons and Warren Buffett, to consistently achieve superior performance in the market.
William F. Sharpe's pivotal 1991 paper, "The Arithmetic of Active Management," sheds light on the fundamental contradictions within financial models based on market efficiency. Sharpe demonstrates that the remarkable gains achieved by some active investors are counterbalanced by the losses incurred by others in the active trading arena. This dynamic is attributed to the fact that the total profits of all active traders are, by necessity, limited to the overall return of the market—an accounting principle. Such insights not only highlight the zero-sum nature of active investment strategies but also call into question the underlying assumptions of models that rely on market efficiency. Sharpe's analysis prompts a critical reevaluation of existing financial theories, drawing attention to the role of cognitive biases and overlooked premises in shaping market behavior.
This paper scrutinizes the core axioms underpinning the notion of market efficiency, setting the stage for the development of more sophisticated and realistic financial frameworks. Such advancements are pivotal for deepening our theoretical comprehension of financial markets and enhancing the efficacy of decision-making strategies in practice. We argue for a departure from conventional models in favor of methodologies that more faithfully represent the intricacies of real-world market dynamics. It is our expectation that this paradigm shift will not only open new avenues for research but also yield tangible improvements in the application of financial theory.
The Arrow-Debreu framework's depiction of market inefficiencies is vividly underscored by the strategies of investors who leverage informational advantages to outperform the market. A prime example is Ken Griffin's Citadel, which strategically acquires order flows from platforms like Robinhood. This practice, aimed at capitalizing on information asymmetries, peels back the curtain on the mechanisms of 'free' stock trading services offered to retail investors, revealing the strategic depth 'smart money' investors employ to secure retail order flow for advantageous trading. This dynamic, where 'smart money' seeks 'dumb money' counterparts to outperform the market, brings to light a fundamental market truth: the total profits of active trading are bound by the overall market return—an accounting principle.
These narratives emphasize a core market reality: the outperformance of one investor necessitates the underperformance of a less informed party. This zero-sum nature of market transactions, spotlighted by William F. Sharpe, directly correlates the successes of active traders to the detriments of their less savvy counterparts. This reality challenges the ideals of mutual benefit, market efficiency, or information symmetry in financial exchanges, instead painting a picture of a highly competitive arena where only the most strategically astute thrive.
The pivot towards passive investment strategies has been profoundly influenced by John Bogle's pioneering advocacy. His dedicated efforts illuminated the daunting challenges posed by informational asymmetries in markets dominated by well-informed and strategically superior investors. A fundamental insight into the nature of money as a mere unit of account for wealth measurement reveals a crucial truth: real wealth is defined by purchasing power, fundamentally linked to the output designated for final consumption—real GDP. A segment of this GDP is consumed by workers, as compensation for their labor, and by owners of production resources, like landowners. Therefore, the tangible wealth accessible to collective market owners, as represented by indices such as the S&P 500 and, more broadly, the Russell 3000, boils down to the profits produced by the companies within these indices.
The significant role of S&P 500 companies in contributing to nominal GDP underscores an essential investment principle: owning shares in these entities is akin to holding a stake in the nominal GDP's production mechanism. This ownership serves as a defense against the erosion of purchasing power, making it a more resilient investment compared to bonds, which are more susceptible to sudden purchasing power shifts. Consequently, investing in the S&P 500 index, by its considerable contribution to nominal GDP, inherently diminishes the risk of purchasing power loss, closely tied to the nominal GDP it underpins. Thus, the S&P 500 index is not a zero-risk investment but a strategic option that effectively minimizes 'true risk'—the risk of losing purchasing power—making it a lower-risk alternative to traditional bond investments because of its direct correlation with and impact on the key economic metric it relies upon.
In essence, the S&P 500 index represents the most cost-effective way to maintain the lowest 'true-risk' portfolio, where risk is quantified by the potential loss of purchasing power. This realization has led to more than half of all investment capital flowing into index funds, with the trend of moving from actively managed to passively managed funds showing no sign of abating. This shift significantly addresses the issue of asymmetric information in financial trading, a change attributed in large part to John Bogle's contributions.
In wrapping up, it becomes clear that 'fair value' in financial markets is a complex and elusive notion. The pricing of derivative contracts, heavily influenced by the potential for arbitrage opportunities, often diverges from any universally recognized fair value, particularly when arbitrage is not feasible. This discrepancy is starkly illustrated by instruments such as VIX futures, where derivative pricing is largely dictated by the collective market expectations, leading to phenomena like constant contango and backwardation. These conditions arise because arbitrage cannot effectively regulate derivative prices when the underlying assets are untradeable. As a result, it is the strategic exploitation of market opportunities, rather than an abstract principle of fairness, that ultimately shapes the real-world prices of derivative contracts. This reality poses significant challenges to conventional views on market efficiency and the applicability of established financial models.
In future editions of this newsletter, we will delve into more sophisticated strategies for investing in options. For now, we turn our attention to how Transparent Network Technology can play a crucial role in mitigating asymmetric information within banking transactions.
TNT: Independently Verifiable Proof of Fractional Asset Ownership
In our quest to not only illuminate errors in derivatives pricing but also enrich our newsletter readers with valuable insights, we spotlight Transparent Network Technology (TNT). This avant-garde solution effectively addresses transactional asymmetric information, enabling owners to substantiate their fractional asset ownership. The mechanism mirrors the legal establishment of fractional ownership seen in condominium units, achieved through successive title transfers. These transfers are irrevocably initiated by the seller, who unmistakably cedes ownership, and concurrently by the buyer, who undertakes future ownership obligations such as taxes and association fees.
It's imperative to acknowledge that the legal acknowledgment of ownership transfer necessitates the active participation of both buyer and seller. This dual-execution requirement forms the backbone of TNT's promise to deliver a transparent and secure method for validating fractional asset ownership. Through pioneering, patent-pending methodologies like batch processing and dual digital signatures, TNT addresses the prevalent issue of information asymmetry in trading contexts.
Operational Mechanics of TNT:
Digital Signatures: At the heart of TNT's infrastructure, transactions are dual-signed digitally—by the seller, through the act of "spending" their "TNT-coin," and by the buyer, who must endorse the incoming credit. This requirement is foundational to the transaction's legitimacy.
Batch Processing: TNT's innovative batch processing system collects digital signatures for transactions, delineating a clear temporal process. Payment requests, or debits, are initiated during odd minutes, analogous to a daytime check deposit at banks. These are then authorized and processed during even minutes—reminiscent of nighttime check processing—allowing for a consensus on pending payments, previous wallet balances, and fund sufficiency. This method ensures that requests issued in the preceding odd minute are validated, signed by all participating entities, and indelibly recorded in the following even minute.
Blockchain Registration: Following the acquisition of necessary digital signatures from both transaction parties, the deal is permanently etched into the blockchain. This step not only secures the transaction as legally binding, having received explicit consent from both parties but also solidifies the transfer's non-repudiability.
By enabling transactions that are transparently recognized and mutually validated by all involved parties, TNT empowers its clients with the means to furnish independently verifiable proof of fractional asset ownership. This capability, deemed sufficiently robust for legal scrutiny, significantly diminishes the risks and ambiguities brought about by information asymmetry in asset trading.