In finance, arbitrage is an essential framework to understand asset pricing. However, the study of anomalies also called as premiums, which are not arbitrageable has led to a debate regarding whether markets are efficient in correcting price imbalances or is inefficiency a reality. This is why the Economics Nobel prize 2013 was awarded to both the behavioral and fundamental school. This paper explains the circular argument between the three schools of thought. The Fama school which uses factors to explain asset performance, the behavioral school which is focused on psychological biases and the old Beta school which consider the arguments of value vs. growth are all fleeting.

Arbitrage; opportunity or challenge

Arbitrage is an opportunity to buy low and sell high in two markets, lock into a price imbalance for profit. An ideal trade is buying low and sell high. Arbitrageurs do both legs at same time. Myron Scholes stated the objective of LTCM, “It would function like a giant vacuum cleaner sucking up nickels that everyone else had overlooked.” Clearly, there is a limitation in societal understanding of what is arbitrageable and what is not.

Non-Arbitrageable Anomalies

Sometimes these non-arbitrageable opportunities are referred to as anomalies. The ‘Size Premium’, ‘Value Premium’, ‘Equity Premium’ etc. The equity premium puzzle refers to the phenomenon that observed returns on stocks over the past century are much higher than returns on government bonds. Equity Premium is a puzzle because the premium is not arbitraged away. The frequently recurring anomalies brought behavioral finance into existence. Starting Herbert Simon who suggested that the definition of the rational man needed rethinking. Anomalies violate modern financial and economic thought, which assume rationality.

The size premium is the historical tendency for the stocks of firms with smaller market capitalizations to outperform the stocks of firms with larger market capitalizations. Value premium refers to the greater risk-adjusted return of value over growth (stocks). Size premium is also considered a non-arbitrageable opportunity. In 1964, economists Eugene Fama and Kenneth French analyzed decades of stock prices and found consistent and significant return premiums related to both small-cap and value stocks. These premiums are often present. The F&F TFM is both a historical milestone and modern mystery in the study of finance. There is still no widely accepted explanation for these premiums, but they exist. Economic theory suggests that the outperformance of these two types of stocks should either never happen, or should be arbitraged away immediately upon identification. The existence and persistence of these premiums remain a puzzle.

Anomalies come and go

John C. Bogle, have argued that no value premium exists, claiming that Fama and French’s research is period dependent. Bogle is the challenges the value and size premium school.

“While gross performance reverts to the mean self-evident pattern of mean reversion. Yet as we observe these extended cycles of mean reversion, it must occur to you that investors ought to be able to capitalize on them, riding one horse until it tires, then leaping to the other.”

End of behavioral Finance

The case for what causes inefficiency, what explains it has been simplified by the behavioral economists, using behavioral reasons for anomalies (cases of inefficiency). Unfortunately, this has made the subject a subjective discourse rather than something objective. Ideas like anomalies are here to stay, markets can’t be predicted, but some forms of extreme anomalies can be profited from lead to the idea of behavioral funds. Adjusted for risk, behavioral funds were tantamount to value investing. Behavioral finance fund performance proved that anomalies can’t be identified and exploited on a persistent basis. The behavioral model accepts it’s temporal limitations.

The five aspects Thaler points out in his paper ‘End of behavioral finance’ (a term he confidently used to suggest that behavioral finance will be the only form of finance left) are 1) The equity premium puzzle, 2) Predictability, 3) Dividends, 4) Volatility and 5) Volume myth. All of these five aspects can be explained as mean reversion failures.

First; the equity premium puzzle is that the undue premium equities get over treasuries are more than justified by the inherent risk in equities. So, the question behavioral finance is asking here is why equity premium (above the risk premium) does not revert to the mean (vanish), or why don’t equities erase the respective premium vs. treasuries over a certain period.

Second; behavioral finance suggests that predictability in markets is a factor of mispricing. When value gets mispriced versus glamor, it invariably corrects and delivers abnormal returns. Here behavioral finance suggests that because a mispriced asset reverts to mean it delivers returns. This again is a case of a mean reversion failure followed by a regular mean reversion.

Third; dividends, i.e. why do most large companies pay cash dividends? And why do stock prices rise when dividends are initiated or increased when companies can make their taxpaying shareholders better off by repurchasing shares rather than paying dividends? Here behavioral finance seems to be questioning why dividend stocks earn a premium when they shouldn’t. Or, in other words why dividend premium should not revert to a mean value (vanish)? Fourth and fifth; volatility and volume are other cases of mean reversion failure. Both volatility and volume are unexplained, exhibit extreme behavior and don’t adhere to any standard models.

Circular Argument

Fama said that CAPM is incomplete and factors are important (A). Behavioral finance is more keen to explore behavioral flaws and psychological drivers of anomalies (B). The Bogle argument is that Beta is king and premiums come and go, value and growth move in and out of favor. Both factors are period dependent and Mean Reversion is a reality that drives markets (C). And finally, though behavioral finance accepts the reversion to mean (DeBondt and Thaler, 1985) it still sticks to behavioral explanations for ideas that are intrinsically connected to mean reversion failure. Behavioral finance also fails to develop the idea of intertemporal choices and it’s importance in human decision making, which suffers from hyperbolic discounting.

Circular Argument

Circular Argument


Arbitraging the Anomalies

Mean reversion failure is a bigger problem to understand than psychological reasons why anomalies happen. The idea of reversion is common to both fundamental and behavioral thinking. Both fundamentalists and behavioral economists underplay the idea of reversion. While Beta proponents overplay it. The industry is arguing over whether mean reversion works or fails. If it fails, it creates anomalies (premiums), which can’t be arbitraged away. While if it works, value outperforms growth and vice versa. Let’s for a change assume there was a factor, which could explain Mean Reversion failure and successes. This means it could explain all existing factors, their successes, and shortcomings, explain fundamental and behavioral models and explain anomalies.

If premiums come and go and Beta has been considered dead, we can’t ignore the problem anymore. The academic debate has a circular argument. The sooner we accept it, the faster we can move on to understanding why anomalies happen and how they can be arbitraged away.


Mean Reversion Indicator, Pal, 2012
Mean Reversion Framework, Pal, 2015
Momentum and Reversion, Pal 2015
Regression towards mediocrity in Hereditary Stature, Galton, 1886
Power laws, Pareto distributions and Zipf’s law, M. E. J. Newman, 2006
CAPM is CRAP (or, the Dead Parrot Lives!), Montier, 2013
Why CAPM is not CRAP, Pal, 2014
DeBondt and Thaler, 1985
The Stock Market Universe—Stars, Comets, and the Sun, John Bogle, 2001
The End of Behavioural Finance, Pal, 2014