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THE LIES WE’RE TOLD: A FORMAL EXPLORATION OF FINANCIAL FACTS

Dear Readers,

This paper presents only those truths in finance that are absolutely, undeniably certain—facts that cannot ever turn out to be false. They are as unquestionable as the spherical shape of the Earth. Every claim follows directly from arithmetic, standard definitions, and overwhelming, universally accepted empirical confirmations. No uncertain theories or speculative hypotheses are introduced; these points are as firmly established and permanent as the fundamental laws of mathematics and geometry.

OVERVIEW AND MOTIVATION

The financial industry often promotes complex, self-serving narratives that benefit intermediaries at the expense of less-informed participants. By focusing exclusively on stable, irrefutable facts—those grounded in the simplest and most robust arithmetic, logic, and empirical observations—we provide a baseline understanding that no future discovery or reinterpretation will ever overturn. Recognizing these truths ensures rational decision-making, free from misleading claims or unwarranted speculation.

FACT 1: ACTIVE VS. PASSIVE MANAGEMENT (SHARPE, 1991)

William F. Sharpe’s “The Arithmetic of Active Management” establishes an arithmetic truth that nothing can refute:

1. The Market as a Whole:

All investors together hold the entire market. Passive investors hold the whole market portfolio (M). Active investors deviate from M, but collectively, all active plus all passive holdings sum exactly to M.

2. Equal Returns Before Costs:

Before accounting for any expenses, the return on all actively managed dollars, taken together, must equal the return on the entire market, which is also the return on each passive dollar. This is a matter of simple arithmetic—no exceptions, no conditions.

3. Guaranteed Underperformance After Costs:

Active management incurs strictly higher costs (research, trading fees) than passive management. Since pre-cost returns are equal, these extra costs ensure that, net of expenses, the average actively managed dollar underperforms the passive dollar by precisely that cost difference. Nothing can ever change this fundamental arithmetic fact.

This truth is as timeless and immovable as 2+2=4. It cannot be disproven.

FACT 2: ASYMMETRIC INFORMATION AND INEVITABLE DISADVANTAGE (AKERLOF, 1970)

George Akerlof’s “The Market for Lemons” proves that when one party is better informed than the other, the less-informed party always ends up worse off. This universal principle, demonstrated repeatedly across countless markets, applies directly to stock trading:

If you, as a less-informed trader, continually face a vastly better-informed, rational professional (like Warren Buffett), you cannot outsmart or outprofit them. Attempting to beat such a well-informed counterparty is as hopeless as challenging John McEnroe at the peak of his tennis career—no matter what you do, you will not emerge with a net gain. This fact is absolute and can never be proven wrong.

FACT 3: ZERO-SUM BEFORE COSTS, NEGATIVE-SUM AFTER COSTS

In a closed market system, all gains and losses among participants net to zero before costs. With the introduction of fees and commissions, total wealth diminishes, making the competition negative-sum after costs. This is a straightforward arithmetic truth—unassailable and permanent.

FACT 4: ALPHA (EXCESS RETURNS) AS A ZERO-SUM AND THEN NEGATIVE-SUM GAME

While the overall market may rise over time, allowing everyone holding the entire market to share in absolute gains, attempts to surpass the market’s return (to earn “alpha”) remain a zero-sum competition before costs. If some investors achieve positive alpha, others must have negative alpha. Once costs are included, the search for alpha becomes negative-sum—ensuring, on average, that participants lose value in their collective pursuit of beating the market. This balance cannot be overturned; it follows directly from arithmetic and the structure of markets.

EMPIRICAL CONFIRMATION: THE TRIUMPH OF PASSIVE INVESTING

These truths have guided real-world behavior. As John Bogle of Vanguard famously advocated based on these irrefutable facts, investors have shifted en masse from active to passive strategies. Today, the majority of investment dollars are managed passively, reflecting the incontrovertible logic we’ve described.

This outcome is as definitively established as the Earth’s spherical shape—so thoroughly and repeatedly confirmed that doubting it would be irrational. There is no conceivable future event that could rewrite the arithmetic of market composition or negate the persistent empirical confirmations supporting these truths.

WHY THIS MATTERS FOR RETAIL INVESTORS

Retail investors, less informed and facing a negative-sum environment after costs, cannot collectively beat the market or consistently best their better-informed counterparts. Recognizing these absolute facts prevents delusional attempts to outsmart professionals with superior information. The rational, fact-aligned choice is to embrace passive, low-cost investing. This approach is as secure and undeniably sound as acknowledging that the Earth is not flat.

CONCLUSION

The facts presented are final, unconditional, and invulnerable to refutation. They stem from basic arithmetic, standard market definitions, and universal empirical validation—just like fundamental truths in mathematics or well-established scientific observations. By understanding these permanent truths, investors can navigate the financial landscape with clarity and confidence, immune to the misleading narratives and sales pitches that arise from ignorance or self-interest.

No new evidence will ever emerge to contradict these statements, as they are grounded in absolute arithmetic certainties and exhaustive empirical confirmations. Embrace these truths, and choose a strategy aligned with them—just as you accept Earth’s shape without doubt.

Additional Incontrovertible Facts:

Fact 1: The Universal Application of Bounded Rational Utility Maximization in Arms-Length Commercial Transactions

In everyday, market-based exchanges between unrelated, self-interested parties—so-called “arms-length commercial transactions”—the principle that individuals strive to maximize their utility, within the limits of their knowledge and cognitive capabilities, is never violated. This is not a speculative assumption; it is a stable, empirically validated fact of human economic behavior.

Outside these commercial contexts, people often act against their narrow economic interests. For example, volunteering for the army, donating to charity, or providing gifts to family members may prioritize moral values, patriotism, or emotional bonds over immediate economic gain. These are non-market, non-commercial settings where decisions reflect complex motives beyond utility maximization.

However, within arms-length commercial transactions, where each participant can easily choose a better deal or walk away if a trade does not serve their interests, individuals consistently aim to improve their own welfare. They do so to the best of their abilities—this is what is meant by “bounded rationality.” People are not infinitely wise or perfectly calculating, as evidenced by cognitive biases and imperfect information, but they do not intentionally choose worse deals when clearly better ones are available. Over time, only behavior that aligns with bounded rational utility maximization remains stable in these market environments.

This claim is thoroughly consistent with the observations of Jensen and Meckling in their seminal 1994 paper on the nature of man and utility maximization in economics. To date, no credible evidence contradicts this fact of human behavior in the context of arms-length commercial transactions. It stands as an empirically confirmed truth that cannot logically or empirically turn out to be false under these conditions.

Fact 2: The Universal Application of Rent-Seeking in Arms-Length Commercial Transactions (The Rent-Seeking Lemma)

The Rent-Seeking Lemma holds that rational, utility-maximizing agents—when given the opportunity to profit at low relative cost—will extract value from others without contributing additional productivity. This behavior, known as rent-seeking, leads to market inefficiencies and underscores the need for robust property rights and well-functioning markets to limit such exploitation.

This phenomenon is well-rooted in Agency Theory, notably from Jensen and Meckling’s seminal 1976 paper, Theory of the Firm, which introduced the principal-agent problem. In arms-length commercial transactions—where each participant seeks to maximize personal welfare—agents (e.g., managers) may favor their self-interest over that of principals (e.g., owners). In their later work, The Nature of Man (1994), Jensen and Meckling further formalized economic systems assuming rational, utility-maximizing individuals operating under bounded rationality. This framework aligns with the Rent-Seeking Lemma: rational agents, facing exploitable opportunities, will secure unearned gains at others’ expense, diminishing overall market efficiency.

Akerlof’s 1970 paper, The Market for Lemons, provides empirical confirmation. It shows that information asymmetries allow better-informed participants to consistently gain at the expense of less-informed counterparts. In this context, agents engage in rent-seeking by redistributing wealth without producing new value. Both Agency Theory and public choice theory (pioneered by Gordon Tullock and James Buchanan, the latter a 1986 Nobel Laureate) acknowledge these distortions. Such rent-seekers—akin to what Lenin termed “economic parasites”—acquire wealth without enhancing GDP, a point recognized by both Marxist and free-market critics of unproductive extraction.

However, Marx erred in assuming that bourgeois principals could exploit better-informed workers. Agency Theory and observed market behaviors indicate the opposite: informational advantages inherently benefit agents at the expense of principals. Workers, by definition, know the quality of their own labor better than their employers do, and both parties are equally informed about wages. In such a setting, principals cannot systematically extract “surplus value” from more knowledgeable workers. Rather, rent-seeking advantages flow from better-informed agents to less-informed principals—reversing the direction Marx imagined.

The tragic consequences of embracing unsound theories are exemplified by historical events like the Holodomor in Ukraine, where flawed collectivist policies resulted in catastrophic famine and even instances of cannibalism. Such outcomes highlight the vital importance of basing economic and political structures on accurate, empirically validated principles rather than on ideologically driven, empirically unsupported premises.

In summary, the Rent-Seeking Lemma, supported by Agency Theory and empirical research, provides a truthful lens to understand rational agent behavior in arms-length commercial transactions. By recognizing these stable, empirically confirmed facts, we can design policies and institutions that are grounded in factual reality, thereby avoiding the catastrophic errors spawned by unverified theories.

Moreover, it is empirically impossible for capitalist principles, operating under arms-length, well-informed labor transactions, to extract unearned wealth in the form of “surplus value” from workers who hold better information about their own labor quality and are on equal informational footing regarding wages. Under such conditions, the notion of systematic exploitation of workers by principals does not align with the evidence or established economic principles, reinforcing the importance of factual accuracy in our understanding of economic interactions.

Below is a version of the formalization expressed in plain text without LaTeX, maintaining the logical structure and clarity:

Formalization of the First Welfare Corollary (No Externalities, Symmetric Information, Voluntary Exchange)

Definitions and Assumptions:

1. Set of Agents:

Consider a finite set of agents N = {1,2,…,n}.

2. Endowments and Goods:

Each agent i in N initially holds a bundle of goods, denoted by ω_i. The vector ω = (ω_1, ω_2, …, ω_n) describes the initial allocation of goods among all agents.

3. Preferences and Utility Functions:

Each agent i has a utility function u_i that assigns a real-valued utility to any bundle of goods. The utility functions are continuous, monotone, and strictly quasi-concave, standard assumptions in economic theory. These properties ensure well-behaved preferences over goods.

4. Voluntary (Unfettered) Exchange:

An exchange or reallocation from ω to x = (x_1, …, x_n) is voluntary if and only if each agent i strictly or weakly prefers x_i to ω_i. Formally:

For all i in N, u_i(x_i) ≥ u_i(ω_i).

Additionally, at least one agent must be strictly better off:

There exists some j in N such that u_j(x_j) > u_j(ω_j).

5. Symmetrically Informed Exchange:

The exchange is symmetrically informed if all relevant information about the goods and the terms of trade is equally accessible and verifiable by all agents involved. No agent holds a private informational advantage that could lead to exploitation.

6. No Externalities:

There are no externalities. Each agent i’s utility u_i depends only on the bundle of goods x_i that i holds after the exchange, and not directly on what others hold, except through the terms of the voluntary trade itself. No outside party is harmed or benefitted by the transaction in a way not accounted for in the preferences of the participating agents.

Given Conditions (Two Facts from Context):

• Fact A: In a setting of symmetrical information and no externalities, a voluntary exchange cannot make any participant worse off. If an agent would be worse off, they would not voluntarily agree to the transaction.

• Fact B: Agents are at least weakly rational utility maximizers, even if boundedly so. In arms-length commercial transactions, each agent consents only if they expect no decrease in their own utility. Thus, each agent checks their situation carefully before agreeing, ensuring no rational agent accepts a detrimental deal.

Statement of the First Welfare Corollary:

“First Welfare Corollary”: If there are no externalities and the exchange is symmetrically informed and voluntarily agreed upon by rational, utility-maximizing agents, then the resulting exchange is guaranteed to be Pareto-improving.

Pareto-improving means the new allocation x is at least as good for all agents as their initial allocation ω, and strictly better for at least one agent.

Proof Sketch:

1. Start with initial allocation ω.

2. Agents consider a new allocation x. The exchange is voluntary, so no agent i accepts x_i unless u_i(x_i) ≥ u_i(ω_i). Because at least one agent j strictly prefers x_j over ω_j, we have:

u_i(x_i) ≥ u_i(ω_i) for all i in N,

and u_j(x_j) > u_j(ω_j) for at least one j in N.

3. Since all agents are at least as well off, and no agent is worse off, and at least one agent is strictly better off, this by definition is a Pareto improvement.

4. Symmetric information ensures no hidden exploitation. With equal information, no agent agrees to a deal that would lower their utility, because they can accurately assess the terms.

5. With no externalities, no outside party is harmed. Thus, considering only the participating agents, the transaction leaves no one worse off, improves at least one individual’s situation, and thus increases overall Pareto efficiency.

Conclusion:

Under the stated assumptions—no externalities, symmetric information, rational (bounded rational) utility-maximizing agents, and voluntary agreement—the resulting reallocation must be Pareto-improving. This corollary follows logically and cannot be overturned by future discoveries, as it depends solely on the defined conditions and classical principles of rational choice and voluntary trade.

Thus, the first welfare corollary stands as a stable, unassailable logical consequence of these economic fundamentals.