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Beta(ful) Market Hypotheses

Davide Accomazzo, MBA
Davide Accomazzo, MBA

In my many years as a derivative trader and hedge fund manager, I forged a solid and long-lasting relationship with risk. Like a beautiful but dangerous woman, risk permeated my professional life—a constant courtship leading me to many attempts at fully understanding its mysterious ways. A never-ending effort!

The theoretical foundations of risk analysis were laid in business school where I diligently learned of Alpha and Beta, Random Walks and Efficient Market Hypotheses (EMH).* These theories were elegant and pure, like a fresh mantle of snow they seemed to perfectly cover all market uncertainties and provided a boost of confidence to a young man ready to leave his mark in Wall Street.

Yet the one reason why I was fascinated by the markets was the mesmerizing and intellectually challenging example of hedge fund manager extraordinaire George Soros. His book,The Alchemy of Finance, seemed to directly contradict EMH and his highly successful track record was damning evidence. Nevertheless, one of my first large successes came from the application of the bell curve to index returns for an option strategy. It worked like a charm in the roaring late nineties.

This initial success aside, every night I could not shake off that feeling of disconnect from theory to practice. Yogi Berra once said: “In theory there is no difference between theory and practice, in practice there is.” Indeed, while the EMH trading model was successful, the distribution of returns seemed way out of line with even a fat tail distribution. Adding to my discomfort was the clear pattern of price dependency upon past changes (the H factor as Mandelbrot defines it) versus the theory of price randomness.

In 1999 and in 2000 we witnessed a ridiculous bubble in internet and technology stocks and a consequent blow up—a dynamic that really should not have happened in the EMH universe. During 1999 I had decided to tweak my model and added heavy behavioral components. I think such changes saved me from terminal disaster in 2001, 2002 and more recently 2008.

In spite of evidence of misleading logic and cracks in the foundation behind the concepts of Beta and EMH, the theories are still wildly popular among academics.

Academic politics and group thinking may be the cause; after all, almost every economist in the country is one way or the other on the Federal Reserve payroll for example. Yet Beta and EMH are now under attack not only by behavioralists but by mathematicians as well. Benoit Mandelbrot, one of the most influential mathematicians of our times, is very vocal—he started his critique 40 years ago and was derided by the mainstream—against these alluring but ultimately deceiving theories. Paul Wilmott, author of several books on quantitative finance, has also been active in his criticism.

The idea that equity returns are random and therefore should be expected to fall in line with Gaussian distribution models is a bizarre conceptual starting point. While many natural events follow such distribution, why would something like investment returns follow a statistical order? Aren’t stocks prices the result of fear and greed? Aren’t financial markets the making of highly emotional beings? Isn’t information asymmetry a major issue in financial markets? If anything, a clean statistical distribution should have been a last resort explanation for price formation rather then a starting point.

The real world does not move neatly—markets are messy and simple mathematical relationships cannot capture reality.

Equity prices can be explained by more logical (yet less statistical) structural and behavioral relationships. The Capital Asset Pricing Model armed with the false fortitude of the bell curve, reduces everything to one variable, Beta, to explain risk. But does one variable for a system as complex as financial markets make sense?

The buy-and-hold theory forced stocks in people’s portfolios even when valuations were clearly off on the assumption of a consistent equity risk premium. This dynamic snowballed into the commercial explosion of beta-driven portfolios and unhooked Wall Street from any effort to produce intelligent analysis. Portfolio management reduced its legal liabilities and turned the large majority of the asset management universe into a huge marketing machine sucking in money flows which perpetuated the fallacy.

Beta is dead—long live Beta! Or perhaps it never existed.

Maybe Beta was just a mirage of an industry looking for order and economies of scale. In the end, however, investment returns were proven to be influenced not by statistical distributions but by real issues.

Financial markets are highly reflexive as George Soros pointed out 25 years ago, and as a result, equity prices are dependent on the past. Momentum is a constant component of price formation. Also, the structural dynamics of the money management business are clearly heavy influencers of stock prices—the heavy hand of relative performance among money managers and the problem of career and business risk are two of the most important influences in the process of pricing investments. Tax issues and the changing regulatory environment are certainly more important drivers of prices than the Gaussian distribution. Not to mention social contagion, feedback loops, and of course changing technology.

The smart money manager must rely on a much more sophisticated framework than just the bell curve. I like to approach my investments following a 4-level framework (ex-hedge fund manager turned media entrepreneur Todd Harrison follows a similar approach):

  • Structural overview: An analysis of the political, regulatory and technological environment.
  • Fundamental overview: Valuation analysis such as Cyclically Adjusted Price/Earnings ratios and others.
  • Technical market make-up: Momentum, mean reversion, support and resistance, volatility.
  • Sentiment overview: A comprehensive behavioral analysis.

Comprehension of financial markets and the risks they inherently breed is a never-ending process. As elegant as Beta and EMH were they were clearly not the answer.

*The following has been provided by the author to aid the reader in grasping the content of this post. It should by no means be considered a comprehensive overview of contemporary financial models.

Modern Finance and Modern Portfolio Theory began with the idea that stock returns are statistically distributed like most natural events, for example human height and weight follow a Gaussian distribution where 68% of samples are within one negative or positive standard deviation from the mean and 95% of samples are within two standard deviations. Such statistical distribution is shaped like a bell, therefore the name “bell curve.” However, equity returns were exhibiting some anomalies and unexpected values; three standard deviations or more from the mean were much more frequent. The term “fat tail,” indicates the thicker tail end of the bell.

This concept is at the heart of modern finance. Inspired by this idea, Princeton professor, Burton G. Malkiel, wrote extensively about the random walk of earnings. He believed that earnings, and therefore stock prices that reflect those values, were completely random and therefore impossible to consistently forecast correctly. Of course, in order to believe in the previous two ideas (randomness of returns and randomness of earnings) one is to believe that all data samples are independent of each other, just like multiple tosses of a coin.

This approach to equity markets also relied on the assumption that markets participants are fully rational and base their decisions on past observations and by holding rational expectations for future outcomes. Rational portfolios are then constructed based on normal statistical distributions.

Nobel Prize winner Harry Markowitz wrote extensively on Modern Portfolio Theory and perfect market portfolios. The concept of Beta was a natural evolution of Markowitz’ thought process and indicates the statistical relationship between a stock (or portfolio) and the general market. Beta is an idea that eventually ties with the Capital Asset Pricing Model, a tool to price assets based on the risk-free rate, the market risk premium, and the beta factor.

The Efficient Market Hypothesis is the box that holds it all together. If we assume that all market participants are rational and if we believe that all data points are independent and normally distributed, it is then reasonable to expect markets to be very efficient and capable of pricing assets at fair value. In this efficient universe, markets clear all available information and price it instantaneously and market prices are never far from fundamental values.


Benoit Mandelbrot, The (Mis)behavior of Markets, Basic Books, New York, 2004.
James Montier, “Insight: Efficient Markets Theory Is Dead,” Financial Times, June 24, 2009.
George Soros, The Alchemy of Finance, Wiley and Sons, 1994.

Related in the GBR

Is Managed Futures an Asset Class? by Davide Accomazzo, MBA, and Michael “Mack” Frankfurter

Examining the Role of Short-Term Correlation in Portfolio Diversification by Jeffry Haber, PhD, and Andrew Braunstein, PhD

The Buffett Approach to Valuing Stocks by Steven R. Ferraro, PhD, CFA

Author of the article
Davide Accomazzo, Adjunct Professor of Finance
Davide Accomazzo, Adjunct Professor of Finance
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