Public Service Announcement


A Perpetual Free Lunch?


One famous free meal in history was the twice-daily manna for the community. Another famous free meal was the loaves and fishes for the multitudes. The Three-Factor Model for stock pricing is alleged to be in effect a perpetual free lunch for investors worldwide. Instead of bread- and flesh-flavored manna or loaves and fishes, the two miraculous ingredients of the model are the size and value factors. Size (market capitalization) and value (book-to-market equity ratio) inspired the founding of many stock mutual funds.


In simple form, the Three-Factor Model is R = M + S + V. In words, expected return is determined by market, size and value. Based on empirical samples, it alleges that to increase return, one should buy small-cap high-value (value-style) stocks and sell large-cap low-value (growth-style) stocks.


Yet this increasingly adopted modern-day miracle is a fatal fallacy. The model commits the fallacy of circular reasoning, a/k/a begging the question, in which a premise is taken to be the same as the conclusion to a logical argument. Technically speaking, it is a logically circular type of single-equation simultaneity, which occurs when the same identical variable, such as price or shares, appears on both sides of the model equation. The size and value fallacies are concealed. They are fatal because they are irremediable. They are terminal because they end an argument and cause a model to be rejected.


The Three-Factor Model is a hoax created by prominent academicians who have reason to know it is not scientific. The fatally fallacious size and value stock-pricing factors are a contagion spreading to bourses worldwide. Because of the fatal fallacy, the Three-Factor Model is meaningless, non-interpretable, indeterminate and pseudo-scientific.


If you believe the Three-Factor Model earns consistent long-term average risk-adjusted expected returns higher than general stock market indexes, then you will believe the analogous Two-Factor Model does so. In math, R = C + D. In words, expected return is determined by capital gains and dividends. This is a definition of total return, and definitions are a form of circular reasoning.


If you believe in the Three-Factor Model and in the Two-Factor Model, then you will believe in the analogous One-Factor Model. In math, R = R. In words, expected return is determined by return. This is an identity and a tautology, which are forms of circular reasoning.


If you believe in these three logically equivalent models, then you implicitly believe in a perpetual free lunch. The investors who so believe pay excessive asset management fees on size-related and value-related index mutual funds for the false promise of higher expected returns. The typical retirement-savings plan investor loses $20,000 due to these excess fees. Excess fees are estimated to exceed one billion U.S. dollars total in a year.

If you so believe, maybe it is time to refresh your skills in critical thinking and to review your stock investments to identify implicit free lunches.



Press Release   |   Scientific Research*


*Documents to View or Download:

Evolution of Stock Pricing

Investment Style Box and the Three-Factor Model

What Is Circular Reasoning?

Visual Detection of Circular Reasoning: Three-Factor Model

Fatal Fallacy: Summary

and more